diff --git a/ArviZ/dev/.documenter-siteinfo.json b/ArviZ/dev/.documenter-siteinfo.json index 423407d1f..2701275a7 100644 --- a/ArviZ/dev/.documenter-siteinfo.json +++ b/ArviZ/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-12-22T04:18:26","documenter_version":"1.2.1"}} \ No newline at end of file +{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-12-23T22:56:59","documenter_version":"1.2.1"}} \ No newline at end of file diff --git a/ArviZ/dev/api/data/index.html b/ArviZ/dev/api/data/index.html index 0f3aa4570..e3b3800fd 100644 --- a/ArviZ/dev/api/data/index.html +++ b/ArviZ/dev/api/data/index.html @@ -10,12 +10,12 @@ predictions, log_likelihood; kwargs... -) -> InferenceData

Convert data in an MCMCChains.Chains format into an InferenceData.

Any keyword argument below without an an explicitly annotated type above is allowed, so long as it can be passed to convert_to_inference_data.

Arguments

Keywords

Returns

source
ArviZ.from_samplechains — Function
from_samplechains(
+) -> InferenceData

Convert data in an MCMCChains.Chains format into an InferenceData.

Any keyword argument below without an an explicitly annotated type above is allowed, so long as it can be passed to convert_to_inference_data.

Arguments

  • posterior::MCMCChains.Chains: Draws from the posterior

Keywords

  • posterior_predictive::Any=nothing: Draws from the posterior predictive distribution or name(s) of predictive variables in posterior
  • predictions: Out-of-sample predictions for the posterior.
  • prior: Draws from the prior
  • prior_predictive: Draws from the prior predictive distribution or name(s) of predictive variables in prior
  • observed_data: Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values.
  • constant_data: Model constants, data included in the model that are not modeled as random variables. Keys are parameter names.
  • predictions_constant_data: Constants relevant to the model predictions (i.e. new x values in a linear regression).
  • log_likelihood: Pointwise log-likelihood for the data. It is recommended to use this argument as a named tuple whose keys are observed variable names and whose values are log likelihood arrays. Alternatively, provide the name of variable in posterior containing log likelihoods.
  • library=MCMCChains: Name of library that generated the chains
  • coords: Map from named dimension to named indices
  • dims: Map from variable name to names of its dimensions
  • eltypes: Map from variable names to eltypes. This is primarily used to assign discrete eltypes to discrete variables that were stored in Chains as floats.

Returns

  • InferenceData: The data with groups corresponding to the provided data
source
ArviZ.from_samplechains — Function
from_samplechains(
     posterior=nothing;
     prior=nothing,
     library=SampleChains,
     kwargs...,
-) -> InferenceData

Convert SampleChains samples to an InferenceData.

Either posterior or prior may be a SampleChains.AbstractChain or SampleChains.MultiChain object.

For descriptions of remaining kwargs, see from_namedtuple.

source

IO / Conversion

InferenceObjects.from_netcdf — Function
from_netcdf(path::AbstractString; kwargs...) -> InferenceData

Load an InferenceData from an unopened NetCDF file.

Remaining kwargs are passed to NCDatasets.NCDataset. This method loads data eagerly. To instead load data lazily, pass an opened NCDataset to from_netcdf.

Note

This method requires that NCDatasets is loaded before it can be used.

Examples

julia> using InferenceObjects, NCDatasets
+) -> InferenceData

Convert SampleChains samples to an InferenceData.

Either posterior or prior may be a SampleChains.AbstractChain or SampleChains.MultiChain object.

For descriptions of remaining kwargs, see from_namedtuple.

source

IO / Conversion

InferenceObjects.from_netcdf — Function
from_netcdf(path::AbstractString; kwargs...) -> InferenceData

Load an InferenceData from an unopened NetCDF file.

Remaining kwargs are passed to NCDatasets.NCDataset. This method loads data eagerly. To instead load data lazily, pass an opened NCDataset to from_netcdf.

Note

This method requires that NCDatasets is loaded before it can be used.

Examples

julia> using InferenceObjects, NCDatasets
 
 julia> idata = from_netcdf("centered_eight.nc")
 InferenceData with groups:
@@ -39,7 +39,7 @@
 
 julia> idata_copy = copy(idata); # disconnect from the loaded dataset
 
-julia> close(ds);
source
InferenceObjects.to_netcdf — Function
to_netcdf(data, dest::AbstractString; group::Symbol=:posterior, kwargs...)
+julia> close(ds);
source
InferenceObjects.to_netcdf — Function
to_netcdf(data, dest::AbstractString; group::Symbol=:posterior, kwargs...)
 to_netcdf(data, dest::NCDatasets.NCDataset; group::Symbol=:posterior)

Write data to a NetCDF file.

data is any type that can be converted to an InferenceData using convert_to_inference_data. If not an InferenceData, then group specifies which group the data represents.

dest specifies either the path to the NetCDF file or an opened NetCDF file. If dest is a path, remaining kwargs are passed to NCDatasets.NCDataset.

Note

This method requires that NCDatasets is loaded before it can be used.

Examples

julia> using InferenceObjects, NCDatasets
 
 julia> idata = from_namedtuple((; x = randn(4, 100, 3), z = randn(4, 100)))
@@ -47,4 +47,4 @@
   > posterior
 
 julia> to_netcdf(idata, "data.nc")
-"data.nc"
source
\ No newline at end of file +"data.nc"source \ No newline at end of file diff --git a/ArviZ/dev/api/dataset/index.html b/ArviZ/dev/api/dataset/index.html index 6e6fb98fa..df42c1c19 100644 --- a/ArviZ/dev/api/dataset/index.html +++ b/ArviZ/dev/api/dataset/index.html @@ -9,4 +9,4 @@ data::NamedTuple, dims::Tuple{Vararg{DimensionalData.Dimension}}; metadata=DimensionalData.NoMetadata(), -)

In most cases, use convert_to_dataset to create a Dataset instead of directly using a constructor.

source

General conversion

InferenceObjects.convert_to_dataset — Function
convert_to_dataset(obj; group = :posterior, kwargs...) -> Dataset

Convert a supported object to a Dataset.

In most cases, this function calls convert_to_inference_data and returns the corresponding group.

source
InferenceObjects.namedtuple_to_dataset — Function
namedtuple_to_dataset(data; kwargs...) -> Dataset

Convert NamedTuple mapping variable names to arrays to a Dataset.

Any non-array values will be converted to a 0-dimensional array.

Keywords

  • attrs::AbstractDict{<:AbstractString}: a collection of metadata to attach to the dataset, in addition to defaults. Values should be JSON serializable.
  • library::Union{String,Module}: library used for performing inference. Will be attached to the attrs metadata.
  • dims: a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are:
    • Symbol: dimension name
    • Type{<:DimensionsionalData.Dimension}: dimension type
    • DimensionsionalData.Dimension: dimension, potentially with indices
    • Nothing: no dimension name provided, dimension name is automatically generated
  • coords: a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated.
source

DimensionalData

As a DimensionalData.AbstractDimStack, Dataset also implements the AbstractDimStack API and can be used like a DimStack. See DimensionalData's documentation for example usage.

Tables inteface

Dataset implements the Tables interface. This allows Datasets to be used as sources for any function that can accept a table. For example, it's straightforward to:

\ No newline at end of file +)

In most cases, use convert_to_dataset to create a Dataset instead of directly using a constructor.

source

General conversion

InferenceObjects.convert_to_dataset — Function
convert_to_dataset(obj; group = :posterior, kwargs...) -> Dataset

Convert a supported object to a Dataset.

In most cases, this function calls convert_to_inference_data and returns the corresponding group.

source
InferenceObjects.namedtuple_to_dataset — Function
namedtuple_to_dataset(data; kwargs...) -> Dataset

Convert NamedTuple mapping variable names to arrays to a Dataset.

Any non-array values will be converted to a 0-dimensional array.

Keywords

  • attrs::AbstractDict{<:AbstractString}: a collection of metadata to attach to the dataset, in addition to defaults. Values should be JSON serializable.
  • library::Union{String,Module}: library used for performing inference. Will be attached to the attrs metadata.
  • dims: a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are:
    • Symbol: dimension name
    • Type{<:DimensionsionalData.Dimension}: dimension type
    • DimensionsionalData.Dimension: dimension, potentially with indices
    • Nothing: no dimension name provided, dimension name is automatically generated
  • coords: a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated.
source

DimensionalData

As a DimensionalData.AbstractDimStack, Dataset also implements the AbstractDimStack API and can be used like a DimStack. See DimensionalData's documentation for example usage.

Tables inteface

Dataset implements the Tables interface. This allows Datasets to be used as sources for any function that can accept a table. For example, it's straightforward to:

\ No newline at end of file diff --git a/ArviZ/dev/api/diagnostics/index.html b/ArviZ/dev/api/diagnostics/index.html index fcc17202b..825a9e271 100644 --- a/ArviZ/dev/api/diagnostics/index.html +++ b/ArviZ/dev/api/diagnostics/index.html @@ -3,8 +3,7 @@ gtag('js', new Date()); gtag('config', 'G-W1G68W77YV', {'page_path': location.pathname + location.search + location.hash});
GitHub

Diagnostics

Bayesian fraction of missing information

MCMCDiagnosticTools.bfmi — Function
bfmi(energy::AbstractVector{<:Real}) -> Real
-bfmi(energy::AbstractMatrix{<:Real}; dims::Int=1) -> AbstractVector{<:Real}

Calculate the estimated Bayesian fraction of missing information (BFMI).

When sampling with Hamiltonian Monte Carlo (HMC), BFMI quantifies how well momentum resampling matches the marginal energy distribution.

The current advice is that values smaller than 0.3 indicate poor sampling. However, this threshold is provisional and may change. A BFMI value below the threshold often indicates poor adaptation of sampling parameters or that the target distribution has heavy tails that were not well explored by the Markov chain.

For more information, see Section 6.1 of [Betancourt2018] or [Betancourt2016] for a complete account.

energy is either a vector of Hamiltonian energies of draws or a matrix of energies of draws for multiple chains. dims indicates the dimension in energy that contains the draws. The default dims=1 assumes energy has the shape draws or (draws, chains). If a different shape is provided, dims must be set accordingly.

If energy is a vector, a single BFMI value is returned. Otherwise, a vector of BFMI values for each chain is returned.

source

Effective sample size and $\widehat{R}$ diagnostic

MCMCDiagnosticTools.ess — Function
ess(data::InferenceData; kwargs...) -> Dataset
-ess(data::Dataset; kwargs...) -> Dataset

Calculate the effective sample size (ESS) for each parameter in the data.

source
ess(
+bfmi(energy::AbstractMatrix{<:Real}; dims::Int=1) -> AbstractVector{<:Real}

Calculate the estimated Bayesian fraction of missing information (BFMI).

When sampling with Hamiltonian Monte Carlo (HMC), BFMI quantifies how well momentum resampling matches the marginal energy distribution.

The current advice is that values smaller than 0.3 indicate poor sampling. However, this threshold is provisional and may change. A BFMI value below the threshold often indicates poor adaptation of sampling parameters or that the target distribution has heavy tails that were not well explored by the Markov chain.

For more information, see Section 6.1 of [Betancourt2018] or [Betancourt2016] for a complete account.

energy is either a vector of Hamiltonian energies of draws or a matrix of energies of draws for multiple chains. dims indicates the dimension in energy that contains the draws. The default dims=1 assumes energy has the shape draws or (draws, chains). If a different shape is provided, dims must be set accordingly.

If energy is a vector, a single BFMI value is returned. Otherwise, a vector of BFMI values for each chain is returned.

source

Effective sample size and $\widehat{R}$ diagnostic

MCMCDiagnosticTools.ess — Function
ess(
     samples::AbstractArray{<:Union{Missing,Real}};
     kind=:bulk,
     relative::Bool=false,
@@ -12,19 +11,15 @@
     split_chains::Int=2,
     maxlag::Int=250,
     kwargs...
-)

Estimate the effective sample size (ESS) of the samples of shape (draws, [chains[, parameters...]]) with the autocov_method.

Optionally, the kind of ESS estimate to be computed can be specified (see below). Some kinds accept additional kwargs.

If relative is true, the relative ESS is returned, i.e. ess / (draws * chains).

split_chains indicates the number of chains each chain is split into. When split_chains > 1, then the diagnostics check for within-chain convergence. When d = mod(draws, split_chains) > 0, i.e. the chains cannot be evenly split, then 1 draw is discarded after each of the first d splits within each chain. There must be at least 3 draws in each chain after splitting.

maxlag indicates the maximum lag for which autocovariance is computed and must be greater than 0.

For a given estimand, it is recommended that the ESS is at least 100 * chains and that $\widehat{R} < 1.01$.[VehtariGelman2021]

See also: AutocovMethod, FFTAutocovMethod, BDAAutocovMethod, rhat, ess_rhat, mcse

Kinds of ESS estimates

If kind isa a Symbol, it may take one of the following values:

  • :bulk: basic ESS computed on rank-normalized draws. This kind diagnoses poor convergence in the bulk of the distribution due to trends or different locations of the chains.
  • :tail: minimum of the quantile-ESS for the symmetric quantiles where tail_prob=0.1 is the probability in the tails. This kind diagnoses poor convergence in the tails of the distribution. If this kind is chosen, kwargs may contain a tail_prob keyword.
  • :basic: basic ESS, equivalent to specifying kind=Statistics.mean.
Note

While Bulk-ESS is conceptually related to basic ESS, it is well-defined even if the chains do not have finite variance.[VehtariGelman2021] For each parameter, rank-normalization proceeds by first ranking the inputs using "tied ranking" and then transforming the ranks to normal quantiles so that the result is standard normally distributed. This transform is monotonic.

Otherwise, kind specifies one of the following estimators, whose ESS is to be estimated:

  • Statistics.mean
  • Statistics.median
  • Statistics.std
  • StatsBase.mad
  • Base.Fix2(Statistics.quantile, p::Real)
source
MCMCDiagnosticTools.rhat — Function
rhat(data::InferenceData; kwargs...) -> Dataset
-rhat(data::Dataset; kwargs...) -> Dataset

Calculate the $\widehat{R}$ diagnostic for each parameter in the data.

source
rhat(samples::AbstractArray{Union{Real,Missing}}; kind::Symbol=:rank, split_chains=2)

Compute the $\widehat{R}$ diagnostics for each parameter in samples of shape (draws, [chains[, parameters...]]).[VehtariGelman2021]

kind indicates the kind of $\widehat{R}$ to compute (see below).

split_chains indicates the number of chains each chain is split into. When split_chains > 1, then the diagnostics check for within-chain convergence. When d = mod(draws, split_chains) > 0, i.e. the chains cannot be evenly split, then 1 draw is discarded after each of the first d splits within each chain.

See also ess, ess_rhat, rstar

Kinds of $\widehat{R}$

The following kinds are supported:

  • :rank: maximum of $\widehat{R}$ with kind=:bulk and kind=:tail.
  • :bulk: basic $\widehat{R}$ computed on rank-normalized draws. This kind diagnoses poor convergence in the bulk of the distribution due to trends or different locations of the chains.
  • :tail: $\widehat{R}$ computed on draws folded around the median and then rank-normalized. This kind diagnoses poor convergence in the tails of the distribution due to different scales of the chains.
  • :basic: Classic $\widehat{R}$.
source
MCMCDiagnosticTools.ess_rhat — Function
ess_rhat(data::InferenceData; kwargs...) -> Dataset
-ess_rhat(data::Dataset; kwargs...) -> Dataset

Calculate the effective sample size (ESS) and $\widehat{R}$ diagnostic for each parameter in the data.

source
ess_rhat(
+)

Estimate the effective sample size (ESS) of the samples of shape (draws, [chains[, parameters...]]) with the autocov_method.

Optionally, the kind of ESS estimate to be computed can be specified (see below). Some kinds accept additional kwargs.

If relative is true, the relative ESS is returned, i.e. ess / (draws * chains).

split_chains indicates the number of chains each chain is split into. When split_chains > 1, then the diagnostics check for within-chain convergence. When d = mod(draws, split_chains) > 0, i.e. the chains cannot be evenly split, then 1 draw is discarded after each of the first d splits within each chain. There must be at least 3 draws in each chain after splitting.

maxlag indicates the maximum lag for which autocovariance is computed and must be greater than 0.

For a given estimand, it is recommended that the ESS is at least 100 * chains and that $\widehat{R} < 1.01$.[VehtariGelman2021]

See also: AutocovMethod, FFTAutocovMethod, BDAAutocovMethod, rhat, ess_rhat, mcse

Kinds of ESS estimates

If kind isa a Symbol, it may take one of the following values:

  • :bulk: basic ESS computed on rank-normalized draws. This kind diagnoses poor convergence in the bulk of the distribution due to trends or different locations of the chains.
  • :tail: minimum of the quantile-ESS for the symmetric quantiles where tail_prob=0.1 is the probability in the tails. This kind diagnoses poor convergence in the tails of the distribution. If this kind is chosen, kwargs may contain a tail_prob keyword.
  • :basic: basic ESS, equivalent to specifying kind=Statistics.mean.
Note

While Bulk-ESS is conceptually related to basic ESS, it is well-defined even if the chains do not have finite variance.[VehtariGelman2021] For each parameter, rank-normalization proceeds by first ranking the inputs using "tied ranking" and then transforming the ranks to normal quantiles so that the result is standard normally distributed. This transform is monotonic.

Otherwise, kind specifies one of the following estimators, whose ESS is to be estimated:

  • Statistics.mean
  • Statistics.median
  • Statistics.std
  • StatsBase.mad
  • Base.Fix2(Statistics.quantile, p::Real)
source
ess(data::InferenceData; kwargs...) -> Dataset
+ess(data::Dataset; kwargs...) -> Dataset

Calculate the effective sample size (ESS) for each parameter in the data.

source
MCMCDiagnosticTools.rhat — Function
rhat(samples::AbstractArray{Union{Real,Missing}}; kind::Symbol=:rank, split_chains=2)

Compute the $\widehat{R}$ diagnostics for each parameter in samples of shape (draws, [chains[, parameters...]]).[VehtariGelman2021]

kind indicates the kind of $\widehat{R}$ to compute (see below).

split_chains indicates the number of chains each chain is split into. When split_chains > 1, then the diagnostics check for within-chain convergence. When d = mod(draws, split_chains) > 0, i.e. the chains cannot be evenly split, then 1 draw is discarded after each of the first d splits within each chain.

See also ess, ess_rhat, rstar

Kinds of $\widehat{R}$

The following kinds are supported:

  • :rank: maximum of $\widehat{R}$ with kind=:bulk and kind=:tail.
  • :bulk: basic $\widehat{R}$ computed on rank-normalized draws. This kind diagnoses poor convergence in the bulk of the distribution due to trends or different locations of the chains.
  • :tail: $\widehat{R}$ computed on draws folded around the median and then rank-normalized. This kind diagnoses poor convergence in the tails of the distribution due to different scales of the chains.
  • :basic: Classic $\widehat{R}$.
source
rhat(data::InferenceData; kwargs...) -> Dataset
+rhat(data::Dataset; kwargs...) -> Dataset

Calculate the $\widehat{R}$ diagnostic for each parameter in the data.

source
MCMCDiagnosticTools.ess_rhat — Function
ess_rhat(
     samples::AbstractArray{<:Union{Missing,Real}};
     kind::Symbol=:rank,
     kwargs...,
-) -> NamedTuple{(:ess, :rhat)}

Estimate the effective sample size and $\widehat{R}$ of the samples of shape (draws, [chains[, parameters...]]).

When both ESS and $\widehat{R}$ are needed, this method is often more efficient than calling ess and rhat separately.

See rhat for a description of supported kinds and ess for a description of kwargs.

source

The following autocovariance methods are supported:

MCMCDiagnosticTools.FFTAutocovMethod — Type
FFTAutocovMethod <: AbstractAutocovMethod

The FFTAutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains.

The algorithm is the same as the one of AutocovMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation.

Info

To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl.

source
MCMCDiagnosticTools.BDAAutocovMethod — Type
BDAAutocovMethod <: AbstractAutocovMethod

The BDAAutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains.

It is is based on the discussion by [VehtariGelman2021]. and uses the variogram estimator of the autocorrelation function discussed by [BDA3].

source

Monte Carlo standard error

MCMCDiagnosticTools.mcse — Function
mcse(data::InferenceData; kwargs...) -> Dataset
-mcse(data::Dataset; kwargs...) -> Dataset

Calculate the Monte Carlo standard error (MCSE) for each parameter in the data.

source
mcse(samples::AbstractArray{<:Union{Missing,Real}}; kind=Statistics.mean, kwargs...)

Estimate the Monte Carlo standard errors (MCSE) of the estimator kind applied to samples of shape (draws, [chains[, parameters...]]).

See also: ess

Kinds of MCSE estimates

The estimator whose MCSE should be estimated is specified with kind. kind must accept a vector of the same eltype as samples and return a real estimate.

For the following estimators, the effective sample size ess and an estimate of the asymptotic variance are used to compute the MCSE, and kwargs are forwarded to ess:

  • Statistics.mean
  • Statistics.median
  • Statistics.std
  • Base.Fix2(Statistics.quantile, p::Real)

For other estimators, the subsampling bootstrap method (SBM)[FlegalJones2011][Flegal2012] is used as a fallback, and the only accepted kwargs are batch_size, which indicates the size of the overlapping batches used to estimate the MCSE, defaulting to floor(Int, sqrt(draws * chains)). Note that SBM tends to underestimate the MCSE, especially for highly autocorrelated chains. One should verify that autocorrelation is low by checking the bulk- and tail-ESS values.

source

$R^*$ diagnostic

MCMCDiagnosticTools.rstar — Function
rstar(
-    rng::Random.AbstractRNG=Random.default_rng(),
-    classifier,
-    data::Union{InferenceData,Dataset};
-    kwargs...,
-)

Calculate the $R^*$ diagnostic for the data.

source
rstar(
+) -> NamedTuple{(:ess, :rhat)}

Estimate the effective sample size and $\widehat{R}$ of the samples of shape (draws, [chains[, parameters...]]).

When both ESS and $\widehat{R}$ are needed, this method is often more efficient than calling ess and rhat separately.

See rhat for a description of supported kinds and ess for a description of kwargs.

source
ess_rhat(data::InferenceData; kwargs...) -> Dataset
+ess_rhat(data::Dataset; kwargs...) -> Dataset

Calculate the effective sample size (ESS) and $\widehat{R}$ diagnostic for each parameter in the data.

source

The following autocovariance methods are supported:

MCMCDiagnosticTools.FFTAutocovMethod — Type
FFTAutocovMethod <: AbstractAutocovMethod

The FFTAutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains.

The algorithm is the same as the one of AutocovMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation.

Info

To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl.

source
MCMCDiagnosticTools.BDAAutocovMethod — Type
BDAAutocovMethod <: AbstractAutocovMethod

The BDAAutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains.

It is is based on the discussion by [VehtariGelman2021]. and uses the variogram estimator of the autocorrelation function discussed by [BDA3].

source

Monte Carlo standard error

MCMCDiagnosticTools.mcse — Function
mcse(samples::AbstractArray{<:Union{Missing,Real}}; kind=Statistics.mean, kwargs...)

Estimate the Monte Carlo standard errors (MCSE) of the estimator kind applied to samples of shape (draws, [chains[, parameters...]]).

See also: ess

Kinds of MCSE estimates

The estimator whose MCSE should be estimated is specified with kind. kind must accept a vector of the same eltype as samples and return a real estimate.

For the following estimators, the effective sample size ess and an estimate of the asymptotic variance are used to compute the MCSE, and kwargs are forwarded to ess:

  • Statistics.mean
  • Statistics.median
  • Statistics.std
  • Base.Fix2(Statistics.quantile, p::Real)

For other estimators, the subsampling bootstrap method (SBM)[FlegalJones2011][Flegal2012] is used as a fallback, and the only accepted kwargs are batch_size, which indicates the size of the overlapping batches used to estimate the MCSE, defaulting to floor(Int, sqrt(draws * chains)). Note that SBM tends to underestimate the MCSE, especially for highly autocorrelated chains. One should verify that autocorrelation is low by checking the bulk- and tail-ESS values.

source
mcse(data::InferenceData; kwargs...) -> Dataset
+mcse(data::Dataset; kwargs...) -> Dataset

Calculate the Monte Carlo standard error (MCSE) for each parameter in the data.

source

$R^*$ diagnostic

MCMCDiagnosticTools.rstar — Function
rstar(
     rng::Random.AbstractRNG=Random.default_rng(),
     classifier,
     samples,
@@ -63,4 +58,9 @@
 julia> value = rstar(evotree_deterministic, samples);
 
 julia> round(value; digits=2)
-1.0

References

Lambert, B., & Vehtari, A. (2020). $R^*$: A robust MCMC convergence diagnostic with uncertainty using decision tree classifiers.

source
  • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
  • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
  • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
  • BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
  • FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf
  • Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18
\ No newline at end of file +1.0

References

Lambert, B., & Vehtari, A. (2020). $R^*$: A robust MCMC convergence diagnostic with uncertainty using decision tree classifiers.

source
rstar(
+    rng::Random.AbstractRNG=Random.default_rng(),
+    classifier,
+    data::Union{InferenceData,Dataset};
+    kwargs...,
+)

Calculate the $R^*$ diagnostic for the data.

source
\ No newline at end of file diff --git a/ArviZ/dev/api/index.html b/ArviZ/dev/api/index.html index 032cc129c..9dacbe96c 100644 --- a/ArviZ/dev/api/index.html +++ b/ArviZ/dev/api/index.html @@ -2,4 +2,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-W1G68W77YV', {'page_path': location.pathname + location.search + location.hash}); -
GitHub
\ No newline at end of file +
GitHub
\ No newline at end of file diff --git a/ArviZ/dev/api/inference_data/index.html b/ArviZ/dev/api/inference_data/index.html index 939e2c640..fe1eac6e7 100644 --- a/ArviZ/dev/api/inference_data/index.html +++ b/ArviZ/dev/api/inference_data/index.html @@ -3,7 +3,7 @@ gtag('js', new Date()); gtag('config', 'G-W1G68W77YV', {'page_path': location.pathname + location.search + location.hash});
GitHub

InferenceData

Type definition

InferenceObjects.InferenceData — Type
InferenceData{group_names,group_types}

Container for inference data storage using DimensionalData.

This object implements the InferenceData schema.

Internally, groups are stored in a NamedTuple, which can be accessed using parent(::InferenceData).

Constructors

InferenceData(groups::NamedTuple)
-InferenceData(; groups...)

Construct an inference data from either a NamedTuple or keyword arguments of groups.

Groups must be Dataset objects.

Instead of directly creating an InferenceData, use the exported from_xyz functions or convert_to_inference_data.

source

Property interface

Base.getproperty — Function
getproperty(data::InferenceData, name::Symbol) -> Dataset

Get group with the specified name.

source

Indexing interface

Base.getindex — Function
Base.getindex(data::InferenceData, groups::Symbol; coords...) -> Dataset
+InferenceData(; groups...)

Construct an inference data from either a NamedTuple or keyword arguments of groups.

Groups must be Dataset objects.

Instead of directly creating an InferenceData, use the exported from_xyz functions or convert_to_inference_data.

source

Property interface

Base.getproperty — Function
getproperty(data::InferenceData, name::Symbol) -> Dataset

Get group with the specified name.

source

Indexing interface

Base.getindex — Function
Base.getindex(data::InferenceData, groups::Symbol; coords...) -> Dataset
 Base.getindex(data::InferenceData, groups; coords...) -> InferenceData

Return a new InferenceData containing the specified groups sliced to the specified coords.

coords specifies a dimension name mapping to an index, a DimensionalData.Selector, or an IntervalSets.AbstractInterval.

If one or more groups lack the specified dimension, a warning is raised but can be ignored. All groups that contain the dimension must also contain the specified indices, or an exception will be raised.

Examples

Select data from all groups for just the specified id values.

julia> using InferenceObjects, DimensionalData
 
 julia> idata = from_namedtuple(
@@ -53,7 +53,7 @@
   :y Float64 dims: Dim{:id} (1)
 
 with metadata Dict{String, Any} with 1 entry:
-  "created_at" => "2022-08-11T11:19:25.982"

Note that if a single index is provided, the behavior is still to slice so that the dimension is preserved.

source
Base.setindex — Function
Base.setindex(data::InferenceData, group::Dataset, name::Symbol) -> InferenceData

Create a new InferenceData containing the group with the specified name.

If a group with name is already in data, it is replaced.

source

Iteration interface

InferenceData also implements the same iteration interface as its underlying NamedTuple. That is, iterating over an InferenceData iterates over its groups.

General conversion

InferenceObjects.convert_to_inference_data — Function
convert_to_inference_data(obj; group, kwargs...) -> InferenceData

Convert a supported object to an InferenceData object.

If obj converts to a single dataset, group specifies which dataset in the resulting InferenceData that is.

See convert_to_dataset

Arguments

  • obj can be many objects. Basic supported types are:
    • InferenceData: return unchanged
    • Dataset/DimensionalData.AbstractDimStack: add to InferenceData as the only group
    • NamedTuple/AbstractDict: create a Dataset as the only group
    • AbstractArray{<:Real}: create a Dataset as the only group, given an arbitrary name, if the name is not set

More specific types may be documented separately.

Keywords

  • group::Symbol = :posterior: If obj converts to a single dataset, assign the resulting dataset to this group.

  • dims: a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are:

    • Symbol: dimension name
    • Type{<:DimensionsionalData.Dimension}: dimension type
    • DimensionsionalData.Dimension: dimension, potentially with indices
    • Nothing: no dimension name provided, dimension name is automatically generated

  • coords: a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated.

  • kwargs: remaining keywords forwarded to converter functions

source
InferenceObjects.from_dict — Function
from_dict(posterior::AbstractDict; kwargs...) -> InferenceData

Convert a Dict to an InferenceData.

Arguments

  • posterior: The data to be converted. Its strings must be Symbol or AbstractString, and its values must be arrays.

Keywords

  • posterior_predictive::Any=nothing: Draws from the posterior predictive distribution
  • sample_stats::Any=nothing: Statistics of the posterior sampling process
  • predictions::Any=nothing: Out-of-sample predictions for the posterior.
  • prior::Dict=nothing: Draws from the prior
  • prior_predictive::Any=nothing: Draws from the prior predictive distribution
  • sample_stats_prior::Any=nothing: Statistics of the prior sampling process
  • observed_data::NamedTuple: Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values.
  • constant_data::NamedTuple: Model constants, data included in the model which is not modeled as a random variable. Keys are parameter names and values.
  • predictions_constant_data::NamedTuple: Constants relevant to the model predictions (i.e. new x values in a linear regression).
  • log_likelihood: Pointwise log-likelihood for the data. It is recommended to use this argument as a NamedTuple whose keys are observed variable names and whose values are log likelihood arrays.
  • library: Name of library that generated the draws
  • coords: Map from named dimension to named indices
  • dims: Map from variable name to names of its dimensions

Returns

  • InferenceData: The data with groups corresponding to the provided data

Examples

using InferenceObjects
+  "created_at" => "2022-08-11T11:19:25.982"

Note that if a single index is provided, the behavior is still to slice so that the dimension is preserved.

source
Base.setindex — Function
Base.setindex(data::InferenceData, group::Dataset, name::Symbol) -> InferenceData

Create a new InferenceData containing the group with the specified name.

If a group with name is already in data, it is replaced.

source

Iteration interface

InferenceData also implements the same iteration interface as its underlying NamedTuple. That is, iterating over an InferenceData iterates over its groups.

General conversion

InferenceObjects.convert_to_inference_data — Function
convert_to_inference_data(obj; group, kwargs...) -> InferenceData

Convert a supported object to an InferenceData object.

If obj converts to a single dataset, group specifies which dataset in the resulting InferenceData that is.

See convert_to_dataset

Arguments

  • obj can be many objects. Basic supported types are:
    • InferenceData: return unchanged
    • Dataset/DimensionalData.AbstractDimStack: add to InferenceData as the only group
    • NamedTuple/AbstractDict: create a Dataset as the only group
    • AbstractArray{<:Real}: create a Dataset as the only group, given an arbitrary name, if the name is not set

More specific types may be documented separately.

Keywords

  • group::Symbol = :posterior: If obj converts to a single dataset, assign the resulting dataset to this group.

  • dims: a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are:

    • Symbol: dimension name
    • Type{<:DimensionsionalData.Dimension}: dimension type
    • DimensionsionalData.Dimension: dimension, potentially with indices
    • Nothing: no dimension name provided, dimension name is automatically generated

  • coords: a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated.

  • kwargs: remaining keywords forwarded to converter functions

source
InferenceObjects.from_dict — Function
from_dict(posterior::AbstractDict; kwargs...) -> InferenceData

Convert a Dict to an InferenceData.

Arguments

  • posterior: The data to be converted. Its strings must be Symbol or AbstractString, and its values must be arrays.

Keywords

  • posterior_predictive::Any=nothing: Draws from the posterior predictive distribution
  • sample_stats::Any=nothing: Statistics of the posterior sampling process
  • predictions::Any=nothing: Out-of-sample predictions for the posterior.
  • prior::Dict=nothing: Draws from the prior
  • prior_predictive::Any=nothing: Draws from the prior predictive distribution
  • sample_stats_prior::Any=nothing: Statistics of the prior sampling process
  • observed_data::NamedTuple: Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values.
  • constant_data::NamedTuple: Model constants, data included in the model which is not modeled as a random variable. Keys are parameter names and values.
  • predictions_constant_data::NamedTuple: Constants relevant to the model predictions (i.e. new x values in a linear regression).
  • log_likelihood: Pointwise log-likelihood for the data. It is recommended to use this argument as a NamedTuple whose keys are observed variable names and whose values are log likelihood arrays.
  • library: Name of library that generated the draws
  • coords: Map from named dimension to named indices
  • dims: Map from variable name to names of its dimensions

Returns

  • InferenceData: The data with groups corresponding to the provided data

Examples

using InferenceObjects
 nchains = 2
 ndraws = 100
 
@@ -62,7 +62,7 @@
     :y => randn(2, ndraws, nchains),
     :z => randn(3, 2, ndraws, nchains),
 )
-idata = from_dict(data)
source
InferenceObjects.from_namedtuple — Function
from_namedtuple(posterior::NamedTuple; kwargs...) -> InferenceData
 from_namedtuple(posterior::Vector{Vector{<:NamedTuple}}; kwargs...) -> InferenceData
 from_namedtuple(
     posterior::NamedTuple,
@@ -81,7 +81,7 @@
 idata1 = from_namedtuple(data1)
 
 data2 = [[(x=rand(), y=randn(2), z=randn(3, 2)) for _ in 1:ndraws] for _ in 1:nchains];
-idata2 = from_namedtuple(data2)
source

General functions

Base.cat — Function
cat(data::InferenceData...; [groups=keys(data[1]),] dims) -> InferenceData

Concatenate InferenceData objects along the specified dimension dims.

Only the groups in groups are concatenated. Remaining groups are merged into the new InferenceData object.

Examples

Here is how we can concatenate all groups of two InferenceData objects along the existing chain dimension:

julia> coords = (; a_dim=["x", "y", "z"]);
+idata2 = from_namedtuple(data2)
source

General functions

Base.cat — Function
cat(data::InferenceData...; [groups=keys(data[1]),] dims) -> InferenceData

Concatenate InferenceData objects along the specified dimension dims.

Only the groups in groups are concatenated. Remaining groups are merged into the new InferenceData object.

Examples

Here is how we can concatenate all groups of two InferenceData objects along the existing chain dimension:

julia> coords = (; a_dim=["x", "y", "z"]);
 
 julia> dims = dims=(; a=[:a_dim]);
 
@@ -151,7 +151,7 @@
   :y Float64 dims: Dim{:y_dim_1} (10)
 
 with metadata Dict{String, Any} with 1 entry:
-  "created_at" => "2023-02-17T15:11:00.59"
source
Base.merge — Function
merge(data::InferenceData...) -> InferenceData

Merge InferenceData objects.

The result contains all groups in data and others. If a group appears more than once, the one that occurs last is kept.

See also: cat

Examples

Here we merge an InferenceData containing only a posterior group with one containing only a prior group to create a new one containing both groups.

julia> idata1 = from_dict(Dict(:a => randn(100, 4, 3), :b => randn(100, 4)))
+  "created_at" => "2023-02-17T15:11:00.59"
source
Base.merge — Function
merge(data::InferenceData...) -> InferenceData

Merge InferenceData objects.

The result contains all groups in data and others. If a group appears more than once, the one that occurs last is kept.

See also: cat

Examples

Here we merge an InferenceData containing only a posterior group with one containing only a prior group to create a new one containing both groups.

julia> idata1 = from_dict(Dict(:a => randn(100, 4, 3), :b => randn(100, 4)))
 InferenceData with groups:
   > posterior
 
@@ -162,4 +162,4 @@
 julia> idata_merged = merge(idata1, idata2)
 InferenceData with groups:
   > posterior
-  > prior
source
\ No newline at end of file + > priorsource \ No newline at end of file diff --git a/ArviZ/dev/api/stats/index.html b/ArviZ/dev/api/stats/index.html index 6280ad58a..e560d584b 100644 --- a/ArviZ/dev/api/stats/index.html +++ b/ArviZ/dev/api/stats/index.html @@ -2,7 +2,8 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-W1G68W77YV', {'page_path': location.pathname + location.search + location.hash}); -
GitHub

Stats

Summary statistics

PosteriorStats.SummaryStats — Type

A container for a column table of values computed by summarize.

This object implements the Tables and TableTraits interfaces and has a custom show method.

  • name: The name of the collection of summary statistics, used as the table title in display.

  • data: The summary statistics for each parameter, with an optional first column parameter containing the parameter names.

source
PosteriorStats.default_stats — Function
default_stats(focus=Statistics.mean; prob_interval=0.94, kwargs...)

Default statistics to be computed with summarize.

The value of focus determines the statistics to be returned:

  • Statistics.mean: mean, std, hdi_3%, hdi_97%
  • Statistics.median: median, mad, eti_3%, eti_97%

If prob_interval is set to a different value than the default, then different HDI and ETI statistics are computed accordingly. hdi refers to the highest-density interval, while eti refers to the equal-tailed interval (i.e. the credible interval computed from symmetric quantiles).

See also: hdi

source
PosteriorStats.default_diagnostics — Function
default_diagnostics(focus=Statistics.mean; kwargs...)

Default diagnostics to be computed with summarize.

The value of focus determines the diagnostics to be returned:

  • Statistics.mean: mcse_mean, mcse_std, ess_tail, ess_bulk, rhat
  • Statistics.median: mcse_median, ess_tail, ess_bulk, rhat
source
PosteriorStats.summarize — Function
summarize(data, stats_funs...; name="SummaryStats", [var_names]) -> SummaryStats

Compute the summary statistics in stats_funs on each param in data.

stats_funs is a collection of functions that reduces a matrix with shape (draws, chains) to a scalar or a collection of scalars. Alternatively, an item in stats_funs may be a Pair of the form name => fun specifying the name to be used for the statistic or of the form (name1, ...) => fun when the function returns a collection. When the function returns a collection, the names in this latter format must be provided.

If no stats functions are provided, then those specified in default_summary_stats are computed.

var_names specifies the names of the parameters in data. If not provided, the names are inferred from data.

To support computing summary statistics from a custom object, overload this method specifying the type of data.

See also SummaryStats, default_summary_stats, default_stats, default_diagnostics.

Examples

Compute mean, std and the Monte Carlo standard error (MCSE) of the mean estimate:

julia> using Statistics, StatsBase
+
GitHub
Stats
Summary statistics
PosteriorStats.SummaryStats — Type
struct SummaryStats{D, V<:(AbstractVector)}
A container for a column table of values computed by summarize.
This object implements the Tables and TableTraits column table interfaces. It has a custom show method.
SummaryStats behaves like an OrderedDict of columns, where the columns can be accessed using either Symbols or a 1-based integer index.
  • name::String: The name of the collection of summary statistics, used as the table title in display.
  • data::Any: The summary statistics for each parameter. It must implement the Tables interface.
  • parameter_names::AbstractVector: Names of the parameters
SummaryStats([name::String,] data[, parameter_names])
+SummaryStats(data[, parameter_names]; name::String="SummaryStats")
Construct a SummaryStats from tabular data with optional stats name and param_names.
data must not contain a column :parameter, as this is reserved for the parameter names, which are always in the first column.
source
PosteriorStats.default_stats — Function
default_stats(focus=Statistics.mean; prob_interval=0.94, kwargs...)
Default statistics to be computed with summarize.
The value of focus determines the statistics to be returned:
  • Statistics.mean: mean, std, hdi_3%, hdi_97%
  • Statistics.median: median, mad, eti_3%, eti_97%
If prob_interval is set to a different value than the default, then different HDI and ETI statistics are computed accordingly. hdi refers to the highest-density interval, while eti refers to the equal-tailed interval (i.e. the credible interval computed from symmetric quantiles).
See also: hdi
source
PosteriorStats.default_diagnostics — Function
default_diagnostics(focus=Statistics.mean; kwargs...)
Default diagnostics to be computed with summarize.
The value of focus determines the diagnostics to be returned:
  • Statistics.mean: mcse_mean, mcse_std, ess_tail, ess_bulk, rhat
  • Statistics.median: mcse_median, ess_tail, ess_bulk, rhat
source
PosteriorStats.summarize — Function
summarize(data, stats_funs...; name="SummaryStats", [var_names]) -> SummaryStats
Compute the summary statistics in stats_funs on each param in data.
stats_funs is a collection of functions that reduces a matrix with shape (draws, chains) to a scalar or a collection of scalars. Alternatively, an item in stats_funs may be a Pair of the form name => fun specifying the name to be used for the statistic or of the form (name1, ...) => fun when the function returns a collection. When the function returns a collection, the names in this latter format must be provided.
If no stats functions are provided, then those specified in default_summary_stats are computed.
var_names specifies the names of the parameters in data. If not provided, the names are inferred from data.
To support computing summary statistics from a custom object, overload this method specifying the type of data.
See also SummaryStats, default_summary_stats, default_stats, default_diagnostics.
Examples
Compute mean, std and the Monte Carlo standard error (MCSE) of the mean estimate:
julia> using Statistics, StatsBase
 
 julia> x = randn(1000, 4, 3) .+ reshape(0:10:20, 1, 1, :);
 
@@ -32,8 +33,9 @@
     median    mad  eti_3%  eti_97%  mcse_median  ess_tail  ess_median  rhat
  a   0.004  0.978   -1.83     1.89        0.020      3567        3336  1.00
  b  10.02   0.995    8.17    11.9         0.023      3841        3787  1.00
- c  19.99   0.979   18.1     21.9         0.020      3892        3829  1.00
source
StatsBase.summarystats — Function
summarystats(data::InferenceData; group=:posterior, kwargs...) -> SummaryStats
-summarystats(data::Dataset; kwargs...) -> SummaryStats
Compute default summary statistics for the data using summarize.
source
General statistics
PosteriorStats.hdi — Function
hdi(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper)
Estimate the unimodal highest density interval (HDI) of samples for the probability prob.
The HDI is the minimum width Bayesian credible interval (BCI). That is, it is the smallest possible interval containing (100*prob)% of the probability mass.[Hyndman1996]
samples is an array of shape (draws[, chains[, params...]]). If multiple parameters are present, then lower and upper are arrays with the shape (params...,), computed separately for each marginal.
This implementation uses the algorithm of [ChenShao1999].
Note
Any default value of prob is arbitrary. The default value of prob=0.94 instead of a more common default like prob=0.95 is chosen to reminder the user of this arbitrariness.
Examples
Here we calculate the 83% HDI for a normal random variable:
julia> x = randn(2_000);
+ c  19.99   0.979   18.1     21.9         0.020      3892        3829  1.00
source
StatsBase.summarystats — Function
summarystats(data::InferenceData; group=:posterior, kwargs...) -> SummaryStats
+summarystats(data::Dataset; kwargs...) -> SummaryStats
Compute default summary statistics for the data using summarize.
source
General statistics
PosteriorStats.hdi — Function
hdi(data::InferenceData; kwargs...) -> Dataset
+hdi(data::Dataset; kwargs...) -> Dataset
Calculate the highest density interval (HDI) for each parameter in the data.
source
hdi(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper)
Estimate the unimodal highest density interval (HDI) of samples for the probability prob.
The HDI is the minimum width Bayesian credible interval (BCI). That is, it is the smallest possible interval containing (100*prob)% of the probability mass.[Hyndman1996]
samples is an array of shape (draws[, chains[, params...]]). If multiple parameters are present, then lower and upper are arrays with the shape (params...,), computed separately for each marginal.
This implementation uses the algorithm of [ChenShao1999].
Note
Any default value of prob is arbitrary. The default value of prob=0.94 instead of a more common default like prob=0.95 is chosen to reminder the user of this arbitrariness.
Examples
Here we calculate the 83% HDI for a normal random variable:
julia> x = randn(2_000);
 
 julia> hdi(x; prob=0.83) |> pairs
 pairs(::NamedTuple) with 2 entries:
@@ -43,8 +45,14 @@
 julia> hdi(x) |> pairs
 pairs(::NamedTuple) with 2 entries:
   :lower => [-1.9674, 3.0326, 8.0326]
-  :upper => [1.90028, 6.90028, 11.9003]
source
hdi(data::InferenceData; kwargs...) -> Dataset
-hdi(data::Dataset; kwargs...) -> Dataset
Calculate the highest density interval (HDI) for each parameter in the data.
source
PosteriorStats.hdi! — Function
hdi!(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper)
A version of hdi that sorts samples in-place while computing the HDI.
source
PosteriorStats.r2_score — Function
r2_score(y_true::AbstractVector, y_pred::AbstractVecOrMat) -> (; r2, r2_std)
$R²$ for linear Bayesian regression models.[GelmanGoodrich2019]
Arguments
  • y_true: Observed data of length noutputs
  • y_pred: Predicted data with size (ndraws[, nchains], noutputs)
Examples
julia> using ArviZExampleData
+  :upper => [1.90028, 6.90028, 11.9003]
source
PosteriorStats.hdi! — Function
hdi!(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper)
A version of hdi that sorts samples in-place while computing the HDI.
source
PosteriorStats.r2_score — Function
r2_score(idata::InferenceData; y_name, y_pred_name) -> (; r2, r2_std)
Compute $R²$ from idata, automatically formatting the predictions to the correct shape.
Keywords
  • y_name: Name of observed data variable in idata.observed_data. If not provided, then the only observed data variable is used.
  • y_pred_name: Name of posterior predictive variable in idata.posterior_predictive. If not provided, then y_name is used.
Examples
julia> using ArviZExampleData, PosteriorStats
+
+julia> idata = load_example_data("regression10d");
+
+julia> r2_score(idata) |> pairs
+pairs(::NamedTuple) with 2 entries:
+  :r2     => 0.998385
+  :r2_std => 0.000100621
source
r2_score(y_true::AbstractVector, y_pred::AbstractArray) -> (; r2, r2_std)
$R²$ for linear Bayesian regression models.[GelmanGoodrich2019]
Arguments
  • y_true: Observed data of length noutputs
  • y_pred: Predicted data with size (ndraws[, nchains], noutputs)
Examples
julia> using ArviZExampleData
 
 julia> idata = load_example_data("regression1d");
 
@@ -55,14 +63,7 @@
 julia> r2_score(y_true, y_pred) |> pairs
 pairs(::NamedTuple) with 2 entries:
   :r2     => 0.683197
-  :r2_std => 0.0368838
source
r2_score(idata::InferenceData; y_name, y_pred_name) -> (; r2, r2_std)
Compute $R²$ from idata, automatically formatting the predictions to the correct shape.
Keywords
  • y_name: Name of observed data variable in idata.observed_data. If not provided, then the only observed data variable is used.
  • y_pred_name: Name of posterior predictive variable in idata.posterior_predictive. If not provided, then y_name is used.
Examples
julia> using ArviZExampleData, PosteriorStats
-
-julia> idata = load_example_data("regression10d");
-
-julia> r2_score(idata) |> pairs
-pairs(::NamedTuple) with 2 entries:
-  :r2     => 0.998385
-  :r2_std => 0.000100621
source
Pareto-smoothed importance sampling
PSIS.PSISResult — Type
PSISResult
Result of Pareto-smoothed importance sampling (PSIS) using psis.
Properties
  • log_weights: un-normalized Pareto-smoothed log weights
  • weights: normalized Pareto-smoothed weights (allocates a copy)
  • pareto_shape: Pareto $k=ξ$ shape parameter
  • nparams: number of parameters in log_weights
  • ndraws: number of draws in log_weights
  • nchains: number of chains in log_weights
  • reff: the ratio of the effective sample size of the unsmoothed importance ratios and the actual sample size.
  • ess: estimated effective sample size of estimate of mean using smoothed importance samples (see ess_is)
  • tail_length: length of the upper tail of log_weights that was smoothed
  • tail_dist: the generalized Pareto distribution that was fit to the tail of log_weights. Note that the tail weights are scaled to have a maximum of 1, so tail_dist * exp(maximum(log_ratios)) is the corresponding fit directly to the tail of log_ratios.
  • normalized::Bool:indicates whether log_weights are log-normalized along the sample dimensions.
Diagnostic
The pareto_shape parameter $k=ξ$ of the generalized Pareto distribution tail_dist can be used to diagnose reliability and convergence of estimates using the importance weights [VehtariSimpson2021].
  • if $k < \frac{1}{3}$, importance sampling is stable, and importance sampling (IS) and PSIS both are reliable.
  • if $k ≤ \frac{1}{2}$, then the importance ratio distributon has finite variance, and the central limit theorem holds. As $k$ approaches the upper bound, IS becomes less reliable, while PSIS still works well but with a higher RMSE.
  • if $\frac{1}{2} < k ≤ 0.7$, then the variance is infinite, and IS can behave quite poorly. However, PSIS works well in this regime.
  • if $0.7 < k ≤ 1$, then it quickly becomes impractical to collect enough importance weights to reliably compute estimates, and importance sampling is not recommended.
  • if $k > 1$, then neither the variance nor the mean of the raw importance ratios exists. The convergence rate is close to zero, and bias can be large with practical sample sizes.
See PSISPlots.paretoshapeplot for a diagnostic plot.
source
PSIS.ess_is — Function
ess_is(weights; reff=1)
Estimate effective sample size (ESS) for importance sampling over the sample dimensions.
Given normalized weights $w_{1:n}$, the ESS is estimated using the L2-norm of the weights:
\[\mathrm{ESS}(w_{1:n}) = \frac{r_{\mathrm{eff}}}{\sum_{i=1}^n w_i^2}\]
where $r_{\mathrm{eff}}$ is the relative efficiency of the log_weights.
ess_is(result::PSISResult; bad_shape_nan=true)
Estimate ESS for Pareto-smoothed importance sampling.
Note
ESS estimates for Pareto shape values $k > 0.7$, which are unreliable and misleadingly high, are set to NaN. To avoid this, set bad_shape_nan=false.
source
Pareto-smoothed importance sampling
PSIS.PSISResult — Type
PSISResult
Result of Pareto-smoothed importance sampling (PSIS) using psis.
Properties
  • log_weights: un-normalized Pareto-smoothed log weights
  • weights: normalized Pareto-smoothed weights (allocates a copy)
  • pareto_shape: Pareto $k=ξ$ shape parameter
  • nparams: number of parameters in log_weights
  • ndraws: number of draws in log_weights
  • nchains: number of chains in log_weights
  • reff: the ratio of the effective sample size of the unsmoothed importance ratios and the actual sample size.
  • ess: estimated effective sample size of estimate of mean using smoothed importance samples (see ess_is)
  • tail_length: length of the upper tail of log_weights that was smoothed
  • tail_dist: the generalized Pareto distribution that was fit to the tail of log_weights. Note that the tail weights are scaled to have a maximum of 1, so tail_dist * exp(maximum(log_ratios)) is the corresponding fit directly to the tail of log_ratios.
  • normalized::Bool:indicates whether log_weights are log-normalized along the sample dimensions.
Diagnostic
The pareto_shape parameter $k=ξ$ of the generalized Pareto distribution tail_dist can be used to diagnose reliability and convergence of estimates using the importance weights [VehtariSimpson2021].
  • if $k < \frac{1}{3}$, importance sampling is stable, and importance sampling (IS) and PSIS both are reliable.
  • if $k ≤ \frac{1}{2}$, then the importance ratio distributon has finite variance, and the central limit theorem holds. As $k$ approaches the upper bound, IS becomes less reliable, while PSIS still works well but with a higher RMSE.
  • if $\frac{1}{2} < k ≤ 0.7$, then the variance is infinite, and IS can behave quite poorly. However, PSIS works well in this regime.
  • if $0.7 < k ≤ 1$, then it quickly becomes impractical to collect enough importance weights to reliably compute estimates, and importance sampling is not recommended.
  • if $k > 1$, then neither the variance nor the mean of the raw importance ratios exists. The convergence rate is close to zero, and bias can be large with practical sample sizes.
See PSISPlots.paretoshapeplot for a diagnostic plot.
source
PSIS.ess_is — Function
ess_is(weights; reff=1)
Estimate effective sample size (ESS) for importance sampling over the sample dimensions.
Given normalized weights $w_{1:n}$, the ESS is estimated using the L2-norm of the weights:
\[\mathrm{ESS}(w_{1:n}) = \frac{r_{\mathrm{eff}}}{\sum_{i=1}^n w_i^2}\]
where $r_{\mathrm{eff}}$ is the relative efficiency of the log_weights.
ess_is(result::PSISResult; bad_shape_nan=true)
Estimate ESS for Pareto-smoothed importance sampling.
Note
ESS estimates for Pareto shape values $k > 0.7$, which are unreliable and misleadingly high, are set to NaN. To avoid this, set bad_shape_nan=false.
source
PSIS.PSISPlots.paretoshapeplot — Function
paretoshapeplot(values; showlines=false, ...)
 paretoshapeplot!(values; showlines=false, kwargs...)
Plot shape parameters of fitted Pareto tail distributions for diagnosing convergence.
values may be either a vector of Pareto shape parameters or a PSIS.PSISResult.
If showlines==true, horizontal lines indicating relevant Pareto shape thresholds are drawn. See PSIS.PSISResult for an explanation of the thresholds.
All remaining kwargs are forwarded to the plotting function.
See psis, PSISResult.
Examples
using PSIS, Distributions, Plots
 proposal = Normal()
 target = TDist(7)
@@ -71,15 +72,12 @@
 result = psis(log_ratios)
 paretoshapeplot(result)
We can also plot the Pareto shape parameters directly:
paretoshapeplot(result.pareto_shape)
We can also use plot directly:
plot(result.pareto_shape; showlines=true)
source
PSIS.psis — Function
psis(log_ratios, reff = 1.0; kwargs...) -> PSISResult
 psis!(log_ratios, reff = 1.0; kwargs...) -> PSISResult
Compute Pareto smoothed importance sampling (PSIS) log weights [VehtariSimpson2021].
While psis computes smoothed log weights out-of-place, psis! smooths them in-place.
Arguments
  • log_ratios: an array of logarithms of importance ratios, with size (draws, [chains, [parameters...]]), where chains>1 would be used when chains are generated using Markov chain Monte Carlo.
  • reff::Union{Real,AbstractArray}: the ratio(s) of effective sample size of log_ratios and the actual sample size reff = ess/(draws * chains), used to account for autocorrelation, e.g. due to Markov chain Monte Carlo. If an array, it must have the size (parameters...,) to match log_ratios.
Keywords
  • warn=true: If true, warning messages are delivered
  • normalize=true: If true, the log-weights will be log-normalized so that exp.(log_weights) sums to 1 along the sample dimensions.
Returns
  • result: a PSISResult object containing the results of the Pareto-smoothing.
A warning is raised if the Pareto shape parameter $k ≥ 0.7$. See PSISResult for details and PSISPlots.paretoshapeplot for a diagnostic plot.
source
PSIS.psis! — Function
psis(log_ratios, reff = 1.0; kwargs...) -> PSISResult
-psis!(log_ratios, reff = 1.0; kwargs...) -> PSISResult
Compute Pareto smoothed importance sampling (PSIS) log weights [VehtariSimpson2021].
While psis computes smoothed log weights out-of-place, psis! smooths them in-place.
Arguments
  • log_ratios: an array of logarithms of importance ratios, with size (draws, [chains, [parameters...]]), where chains>1 would be used when chains are generated using Markov chain Monte Carlo.
  • reff::Union{Real,AbstractArray}: the ratio(s) of effective sample size of log_ratios and the actual sample size reff = ess/(draws * chains), used to account for autocorrelation, e.g. due to Markov chain Monte Carlo. If an array, it must have the size (parameters...,) to match log_ratios.
Keywords
  • warn=true: If true, warning messages are delivered
  • normalize=true: If true, the log-weights will be log-normalized so that exp.(log_weights) sums to 1 along the sample dimensions.
Returns
  • result: a PSISResult object containing the results of the Pareto-smoothing.
A warning is raised if the Pareto shape parameter $k ≥ 0.7$. See PSISResult for details and PSISPlots.paretoshapeplot for a diagnostic plot.
source
LOO and WAIC
PosteriorStats.AbstractELPDResult — Type
abstract type AbstractELPDResult
An abstract type representing the result of an ELPD computation.
Every subtype stores estimates of both the expected log predictive density (elpd) and the effective number of parameters p, as well as standard errors and pointwise estimates of each, from which other relevant estimates can be computed.
Subtypes implement the following functions:
source
PosteriorStats.PSISLOOResult — Type
Results of Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO).
See also: loo, AbstractELPDResult
  • estimates: Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p)
  • pointwise: Pointwise estimates
  • psis_result: Pareto-smoothed importance sampling (PSIS) results
source
PosteriorStats.WAICResult — Type
Results of computing the widely applicable information criterion (WAIC).
See also: waic, AbstractELPDResult
  • estimates: Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p)
  • pointwise: Pointwise estimates
source
PosteriorStats.elpd_estimates — Function
elpd_estimates(result::AbstractELPDResult; pointwise=false) -> (; elpd, elpd_mcse, lpd)
Return the (E)LPD estimates from the result.
source
PosteriorStats.information_criterion — Function
information_criterion(elpd, scale::Symbol)
Compute the information criterion for the given scale from the elpd estimate.
scale must be one of (:deviance, :log, :negative_log).
See also: loo, waic
source
information_criterion(result::AbstractELPDResult, scale::Symbol; pointwise=false)
Compute information criterion for the given scale from the existing ELPD result.
scale must be one of (:deviance, :log, :negative_log).
If pointwise=true, then pointwise estimates are returned.
source
PosteriorStats.loo — Function
loo(log_likelihood; reff=nothing, kwargs...) -> PSISLOOResult{<:NamedTuple,<:NamedTuple}
Compute the Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO). [Vehtari2017][LOOFAQ]
log_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]).
Keywords
  • reff::Union{Real,AbstractArray{<:Real}}: The relative effective sample size(s) of the likelihood values. If an array, it must have the same data dimensions as the corresponding log-likelihood variable. If not provided, then this is estimated using MCMCDiagnosticTools.ess.
  • kwargs: Remaining keywords are forwarded to [PSIS.psis].
See also: PSISLOOResult, waic
Examples
Manually compute $R_\mathrm{eff}$ and calculate PSIS-LOO of a model:
julia> using ArviZExampleData, MCMCDiagnosticTools
+psis!(log_ratios, reff = 1.0; kwargs...) -> PSISResult
Compute Pareto smoothed importance sampling (PSIS) log weights [VehtariSimpson2021].
While psis computes smoothed log weights out-of-place, psis! smooths them in-place.
Arguments
  • log_ratios: an array of logarithms of importance ratios, with size (draws, [chains, [parameters...]]), where chains>1 would be used when chains are generated using Markov chain Monte Carlo.
  • reff::Union{Real,AbstractArray}: the ratio(s) of effective sample size of log_ratios and the actual sample size reff = ess/(draws * chains), used to account for autocorrelation, e.g. due to Markov chain Monte Carlo. If an array, it must have the size (parameters...,) to match log_ratios.
Keywords
  • warn=true: If true, warning messages are delivered
  • normalize=true: If true, the log-weights will be log-normalized so that exp.(log_weights) sums to 1 along the sample dimensions.
Returns
  • result: a PSISResult object containing the results of the Pareto-smoothing.
A warning is raised if the Pareto shape parameter $k ≥ 0.7$. See PSISResult for details and PSISPlots.paretoshapeplot for a diagnostic plot.
source
LOO and WAIC
PosteriorStats.AbstractELPDResult — Type
abstract type AbstractELPDResult
An abstract type representing the result of an ELPD computation.
Every subtype stores estimates of both the expected log predictive density (elpd) and the effective number of parameters p, as well as standard errors and pointwise estimates of each, from which other relevant estimates can be computed.
Subtypes implement the following functions:
source
PosteriorStats.PSISLOOResult — Type
Results of Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO).
See also: loo, AbstractELPDResult
  • estimates: Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p)
  • pointwise: Pointwise estimates
  • psis_result: Pareto-smoothed importance sampling (PSIS) results
source
PosteriorStats.WAICResult — Type
Results of computing the widely applicable information criterion (WAIC).
See also: waic, AbstractELPDResult
  • estimates: Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p)
  • pointwise: Pointwise estimates
source
PosteriorStats.elpd_estimates — Function
elpd_estimates(result::AbstractELPDResult; pointwise=false) -> (; elpd, elpd_mcse, lpd)
Return the (E)LPD estimates from the result.
source
PosteriorStats.information_criterion — Function
information_criterion(elpd, scale::Symbol)
Compute the information criterion for the given scale from the elpd estimate.
scale must be one of (:deviance, :log, :negative_log).
See also: loo, waic
source
information_criterion(result::AbstractELPDResult, scale::Symbol; pointwise=false)
Compute information criterion for the given scale from the existing ELPD result.
scale must be one of (:deviance, :log, :negative_log).
If pointwise=true, then pointwise estimates are returned.
source
PosteriorStats.loo — Function
loo(data::Dataset; [var_name::Symbol,] kwargs...) -> PSISLOOResult{<:NamedTuple,<:Dataset}
+loo(data::InferenceData; [var_name::Symbol,] kwargs...) -> PSISLOOResult{<:NamedTuple,<:Dataset}
Compute PSIS-LOO from log-likelihood values in data.
If more than one log-likelihood variable is present, then var_name must be provided.
Examples
Calculate PSIS-LOO of a model:
julia> using ArviZExampleData, PosteriorStats
 
 julia> idata = load_example_data("centered_eight");
 
-julia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));
-
-julia> reff = ess(log_like; kind=:basic, split_chains=1, relative=true);
-
-julia> loo(log_like; reff)
+julia> loo(idata)
 PSISLOOResult with estimates
  elpd  elpd_mcse    p  p_mcse
   -31        1.4  0.9    0.34
@@ -87,13 +85,16 @@
 and PSISResult with 500 draws, 4 chains, and 8 parameters
 Pareto shape (k) diagnostic values:
                     Count      Min. ESS
- (-Inf, 0.5]  good  7 (87.5%)  151
-  (0.5, 0.7]  okay  1 (12.5%)  446
source
loo(data::Dataset; [var_name::Symbol,] kwargs...) -> PSISLOOResult{<:NamedTuple,<:Dataset}
-loo(data::InferenceData; [var_name::Symbol,] kwargs...) -> PSISLOOResult{<:NamedTuple,<:Dataset}
Compute PSIS-LOO from log-likelihood values in data.
If more than one log-likelihood variable is present, then var_name must be provided.
Examples
Calculate PSIS-LOO of a model:
julia> using ArviZExampleData, PosteriorStats
+ (-Inf, 0.5]  good  6 (75.0%)  135
+  (0.5, 0.7]  okay  2 (25.0%)  421
source
loo(log_likelihood; reff=nothing, kwargs...) -> PSISLOOResult{<:NamedTuple,<:NamedTuple}
Compute the Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO). [Vehtari2017][LOOFAQ]
log_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]).
Keywords
  • reff::Union{Real,AbstractArray{<:Real}}: The relative effective sample size(s) of the likelihood values. If an array, it must have the same data dimensions as the corresponding log-likelihood variable. If not provided, then this is estimated using MCMCDiagnosticTools.ess.
  • kwargs: Remaining keywords are forwarded to [PSIS.psis].
See also: PSISLOOResult, waic
Examples
Manually compute $R_\mathrm{eff}$ and calculate PSIS-LOO of a model:
julia> using ArviZExampleData, MCMCDiagnosticTools
 
 julia> idata = load_example_data("centered_eight");
 
-julia> loo(idata)
+julia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));
+
+julia> reff = ess(log_like; kind=:basic, split_chains=1, relative=true);
+
+julia> loo(log_like; reff)
 PSISLOOResult with estimates
  elpd  elpd_mcse    p  p_mcse
   -31        1.4  0.9    0.34
@@ -101,25 +102,25 @@
 and PSISResult with 500 draws, 4 chains, and 8 parameters
 Pareto shape (k) diagnostic values:
                     Count      Min. ESS
- (-Inf, 0.5]  good  6 (75.0%)  135
-  (0.5, 0.7]  okay  2 (25.0%)  421
source
PosteriorStats.waic — Function
waic(log_likelihood::AbstractArray) -> WAICResult{<:NamedTuple,<:NamedTuple}
Compute the widely applicable information criterion (WAIC).[Watanabe2010][Vehtari2017][LOOFAQ]
log_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]).
See also: WAICResult, loo
Examples
Calculate WAIC of a model:
julia> using ArviZExampleData
+ (-Inf, 0.5]  good  7 (87.5%)  151
+  (0.5, 0.7]  okay  1 (12.5%)  446
source
PosteriorStats.waic — Function
waic(data::Dataset; [var_name::Symbol]) -> WAICResult{<:NamedTuple,<:Dataset}
+waic(data::InferenceData; [var_name::Symbol]) -> WAICResult{<:NamedTuple,<:Dataset}
Compute WAIC from log-likelihood values in data.
If more than one log-likelihood variable is present, then var_name must be provided.
Examples
Calculate WAIC of a model:
julia> using ArviZExampleData, PosteriorStats
 
 julia> idata = load_example_data("centered_eight");
 
-julia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));
-
-julia> waic(log_like)
+julia> waic(idata)
 WAICResult with estimates
  elpd  elpd_mcse    p  p_mcse
-  -31        1.4  0.9    0.33
source
waic(data::Dataset; [var_name::Symbol]) -> WAICResult{<:NamedTuple,<:Dataset}
-waic(data::InferenceData; [var_name::Symbol]) -> WAICResult{<:NamedTuple,<:Dataset}
Compute WAIC from log-likelihood values in data.
If more than one log-likelihood variable is present, then var_name must be provided.
Examples
Calculate WAIC of a model:
julia> using ArviZExampleData, PosteriorStats
+  -31        1.4  0.9    0.33
source
waic(log_likelihood::AbstractArray) -> WAICResult{<:NamedTuple,<:NamedTuple}
Compute the widely applicable information criterion (WAIC).[Watanabe2010][Vehtari2017][LOOFAQ]
log_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]).
See also: WAICResult, loo
Examples
Calculate WAIC of a model:
julia> using ArviZExampleData
 
 julia> idata = load_example_data("centered_eight");
 
-julia> waic(idata)
+julia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));
+
+julia> waic(log_like)
 WAICResult with estimates
  elpd  elpd_mcse    p  p_mcse
-  -31        1.4  0.9    0.33
source
Model comparison
PosteriorStats.ModelComparisonResult — Type
ModelComparisonResult
Result of model comparison using ELPD.
This struct implements the Tables and TableTraits interfaces.
Each field returns a collection of the corresponding entry for each model:
  • name: Names of the models, if provided.
  • rank: Ranks of the models (ordered by decreasing ELPD)
  • elpd_diff: ELPD of a model subtracted from the largest ELPD of any model
  • elpd_diff_mcse: Monte Carlo standard error of the ELPD difference
  • weight: Model weights computed with weights_method
  • elpd_result: AbstactELPDResults for each model, which can be used to access useful stats like ELPD estimates, pointwise estimates, and Pareto shape values for PSIS-LOO
  • weights_method: Method used to compute model weights with model_weights
source
PosteriorStats.compare — Function
compare(models; kwargs...) -> ModelComparisonResult
Compare models based on their expected log pointwise predictive density (ELPD).
The ELPD is estimated either by Pareto smoothed importance sampling leave-one-out cross-validation (LOO) or using the widely applicable information criterion (WAIC). We recommend loo. Read more theory here - in a paper by some of the leading authorities on model comparison dx.doi.org/10.1111/1467-9868.00353
Arguments
  • models: a Tuple, NamedTuple, or AbstractVector whose values are either AbstractELPDResult entries or any argument to elpd_method.
Keywords
  • weights_method::AbstractModelWeightsMethod=Stacking(): the method to be used to weight the models. See model_weights for details
  • elpd_method=loo: a method that computes an AbstractELPDResult from an argument in models.
  • sort::Bool=true: Whether to sort models by decreasing ELPD.
Returns
  • ModelComparisonResult: A container for the model comparison results. The fields contain a similar collection to models.
Examples
Compare the centered and non centered models of the eight school problem using the defaults: loo and Stacking weights. A custom myloo method formates the inputs as expected by loo.
julia> using ArviZExampleData
+  -31        1.4  0.9    0.33
source
Model comparison
PosteriorStats.ModelComparisonResult — Type
ModelComparisonResult
Result of model comparison using ELPD.
This struct implements the Tables and TableTraits interfaces.
Each field returns a collection of the corresponding entry for each model:
  • name: Names of the models, if provided.
  • rank: Ranks of the models (ordered by decreasing ELPD)
  • elpd_diff: ELPD of a model subtracted from the largest ELPD of any model
  • elpd_diff_mcse: Monte Carlo standard error of the ELPD difference
  • weight: Model weights computed with weights_method
  • elpd_result: AbstactELPDResults for each model, which can be used to access useful stats like ELPD estimates, pointwise estimates, and Pareto shape values for PSIS-LOO
  • weights_method: Method used to compute model weights with model_weights
source
PosteriorStats.compare — Function
compare(models; kwargs...) -> ModelComparisonResult
Compare models based on their expected log pointwise predictive density (ELPD).
The ELPD is estimated either by Pareto smoothed importance sampling leave-one-out cross-validation (LOO) or using the widely applicable information criterion (WAIC). We recommend loo. Read more theory here - in a paper by some of the leading authorities on model comparison dx.doi.org/10.1111/1467-9868.00353
Arguments
  • models: a Tuple, NamedTuple, or AbstractVector whose values are either AbstractELPDResult entries or any argument to elpd_method.
Keywords
  • weights_method::AbstractModelWeightsMethod=Stacking(): the method to be used to weight the models. See model_weights for details
  • elpd_method=loo: a method that computes an AbstractELPDResult from an argument in models.
  • sort::Bool=true: Whether to sort models by decreasing ELPD.
Returns
  • ModelComparisonResult: A container for the model comparison results. The fields contain a similar collection to models.
Examples
Compare the centered and non centered models of the eight school problem using the defaults: loo and Stacking weights. A custom myloo method formates the inputs as expected by loo.
julia> using ArviZExampleData
 
 julia> models = (
            centered=load_example_data("centered_eight"),
@@ -149,7 +150,7 @@
                rank  elpd  elpd_mcse  elpd_diff  elpd_diff_mcse  weight    p   ⋯
  non_centered     1   -31        1.4       0              0.0      0.52  0.9   ⋯
  centered         2   -31        1.4       0.06           0.067    0.48  0.9   ⋯
-                                                                1 column omitted
source
PosteriorStats.model_weights — Function
model_weights(elpd_results; method=Stacking())
 model_weights(method::AbstractModelWeightsMethod, elpd_results)
Compute weights for each model in elpd_results using method.
elpd_results is a Tuple, NamedTuple, or AbstractVector with AbstractELPDResult entries. The weights are returned in the same type of collection.
Stacking is the recommended approach, as it performs well even when the true data generating process is not included among the candidate models. See [YaoVehtari2018] for details.
See also: AbstractModelWeightsMethod, compare
Examples
Compute Stacking weights for two models:
julia> using ArviZExampleData
 
 julia> models = (
@@ -170,10 +171,40 @@
   :non_centered => 1.0
Now we compute BootstrappedPseudoBMA weights for the same models:
julia> model_weights(elpd_results; method=BootstrappedPseudoBMA()) |> pairs
 pairs(::NamedTuple) with 2 entries:
   :centered     => 0.483723
-  :non_centered => 0.516277
source
The following model weighting methods are available
PosteriorStats.BootstrappedPseudoBMA — Type
struct BootstrappedPseudoBMA{R<:Random.AbstractRNG, T<:Real} <: AbstractModelWeightsMethod
Model weighting method using pseudo Bayesian Model Averaging using Akaike-type weighting with the Bayesian bootstrap (pseudo-BMA+)[YaoVehtari2018].
The Bayesian bootstrap stabilizes the model weights.
BootstrappedPseudoBMA(; rng=Random.default_rng(), samples=1_000, alpha=1)
-BootstrappedPseudoBMA(rng, samples, alpha)
Construct the method.
  • rng::Random.AbstractRNG: The random number generator to use for the Bayesian bootstrap
  • samples::Int64: The number of samples to draw for bootstrapping
  • alpha::Real: The shape parameter in the Dirichlet distribution used for the Bayesian bootstrap. The default (1) corresponds to a uniform distribution on the simplex.
See also: Stacking
source
PosteriorStats.PseudoBMA — Type
struct PseudoBMA <: AbstractModelWeightsMethod
Model weighting method using pseudo Bayesian Model Averaging (pseudo-BMA) and Akaike-type weighting.
PseudoBMA(; regularize=false)
-PseudoBMA(regularize)
Construct the method with optional regularization of the weights using the standard error of the ELPD estimate.
Note
This approach is not recommended, as it produces unstable weight estimates. It is recommended to instead use BootstrappedPseudoBMA to stabilize the weights or Stacking. For details, see [YaoVehtari2018].
See also: Stacking
source
PosteriorStats.Stacking — Type
struct Stacking{O<:Optim.AbstractOptimizer} <: AbstractModelWeightsMethod
Model weighting using stacking of predictive distributions[YaoVehtari2018].
Stacking(; optimizer=Optim.LBFGS(), options=Optim.Options()
-Stacking(optimizer[, options])
Construct the method, optionally customizing the optimization.
  • optimizer::Optim.AbstractOptimizer: The optimizer to use for the optimization of the weights. The optimizer must support projected gradient optimization via a manifold field.
  • options::Optim.Options: The Optim options to use for the optimization of the weights.
See also: BootstrappedPseudoBMA
source
Predictive checks
PosteriorStats.loo_pit — Function
loo_pit(y, y_pred, log_weights; kwargs...) -> Union{Real,AbstractArray}
Compute leave-one-out probability integral transform (LOO-PIT) checks.
Arguments
  • y: array of observations with shape (params...,)
  • y_pred: array of posterior predictive samples with shape (draws, chains, params...).
  • log_weights: array of normalized log LOO importance weights with shape (draws, chains, params...).
Keywords
  • is_discrete: If not provided, then it is set to true iff elements of y and y_pred are all integer-valued. If true, then data are smoothed using smooth_data to make them non-discrete before estimating LOO-PIT values.
  • kwargs: Remaining keywords are forwarded to smooth_data if data is discrete.
Returns
  • pitvals: LOO-PIT values with same size as y. If y is a scalar, then pitvals is a scalar.
LOO-PIT is a marginal posterior predictive check. If $y_{-i}$ is the array $y$ of observations with the $i$th observation left out, and $y_i^*$ is a posterior prediction of the $i$th observation, then the LOO-PIT value for the $i$th observation is defined as
\[P(y_i^* \le y_i \mid y_{-i}) = \int_{-\infty}^{y_i} p(y_i^* \mid y_{-i}) \mathrm{d} y_i^*\]
The LOO posterior predictions and the corresponding observations should have similar distributions, so if conditional predictive distributions are well-calibrated, then all LOO-PIT values should be approximately uniformly distributed on $[0, 1]$.[Gabry2019]
Examples
Calculate LOO-PIT values using as test quantity the observed values themselves.
julia> using ArviZExampleData
+  :non_centered => 0.516277
source
The following model weighting methods are available
PosteriorStats.BootstrappedPseudoBMA — Type
struct BootstrappedPseudoBMA{R<:Random.AbstractRNG, T<:Real} <: AbstractModelWeightsMethod
Model weighting method using pseudo Bayesian Model Averaging using Akaike-type weighting with the Bayesian bootstrap (pseudo-BMA+)[YaoVehtari2018].
The Bayesian bootstrap stabilizes the model weights.
BootstrappedPseudoBMA(; rng=Random.default_rng(), samples=1_000, alpha=1)
+BootstrappedPseudoBMA(rng, samples, alpha)
Construct the method.
  • rng::Random.AbstractRNG: The random number generator to use for the Bayesian bootstrap
  • samples::Int64: The number of samples to draw for bootstrapping
  • alpha::Real: The shape parameter in the Dirichlet distribution used for the Bayesian bootstrap. The default (1) corresponds to a uniform distribution on the simplex.
See also: Stacking
source
PosteriorStats.PseudoBMA — Type
struct PseudoBMA <: AbstractModelWeightsMethod
Model weighting method using pseudo Bayesian Model Averaging (pseudo-BMA) and Akaike-type weighting.
PseudoBMA(; regularize=false)
+PseudoBMA(regularize)
Construct the method with optional regularization of the weights using the standard error of the ELPD estimate.
Note
This approach is not recommended, as it produces unstable weight estimates. It is recommended to instead use BootstrappedPseudoBMA to stabilize the weights or Stacking. For details, see [YaoVehtari2018].
See also: Stacking
source
PosteriorStats.Stacking — Type
struct Stacking{O<:Optim.AbstractOptimizer} <: AbstractModelWeightsMethod
Model weighting using stacking of predictive distributions[YaoVehtari2018].
Stacking(; optimizer=Optim.LBFGS(), options=Optim.Options()
+Stacking(optimizer[, options])
Construct the method, optionally customizing the optimization.
  • optimizer::Optim.AbstractOptimizer: The optimizer to use for the optimization of the weights. The optimizer must support projected gradient optimization via a manifold field.
  • options::Optim.Options: The Optim options to use for the optimization of the weights.
See also: BootstrappedPseudoBMA
source
Predictive checks
PosteriorStats.loo_pit — Function
loo_pit(idata::InferenceData, log_weights; kwargs...) -> DimArray
Compute LOO-PIT values using existing normalized log LOO importance weights.
Keywords
  • y_name: Name of observed data variable in idata.observed_data. If not provided, then the only observed data variable is used.
  • y_pred_name: Name of posterior predictive variable in idata.posterior_predictive. If not provided, then y_name is used.
  • kwargs: Remaining keywords are forwarded to the base method of loo_pit.
Examples
Calculate LOO-PIT values using already computed log weights.
julia> using ArviZExampleData, PosteriorStats
+
+julia> idata = load_example_data("centered_eight");
+
+julia> loo_result = loo(idata; var_name=:obs);
+
+julia> loo_pit(idata, loo_result.psis_result.log_weights; y_name=:obs)
+8-element DimArray{Float64,1} loo_pit_obs with dimensions:
+  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered
+ "Choate"            0.943511
+ "Deerfield"         0.63797
+ "Phillips Andover"  0.316697
+ "Phillips Exeter"   0.582252
+ "Hotchkiss"         0.295321
+ "Lawrenceville"     0.403318
+ "St. Paul's"        0.902508
+ "Mt. Hermon"        0.655275
source
loo_pit(idata::InferenceData; kwargs...) -> DimArray
Compute LOO-PIT from groups in idata using PSIS-LOO.
Keywords
  • y_name: Name of observed data variable in idata.observed_data. If not provided, then the only observed data variable is used.
  • y_pred_name: Name of posterior predictive variable in idata.posterior_predictive. If not provided, then y_name is used.
  • log_likelihood_name: Name of log-likelihood variable in idata.log_likelihood. If not provided, then y_name is used if idata has a log_likelihood group, otherwise the only variable is used.
  • reff::Union{Real,AbstractArray{<:Real}}: The relative effective sample size(s) of the likelihood values. If an array, it must have the same data dimensions as the corresponding log-likelihood variable. If not provided, then this is estimated using ess.
  • kwargs: Remaining keywords are forwarded to the base method of loo_pit.
Examples
Calculate LOO-PIT values using as test quantity the observed values themselves.
julia> using ArviZExampleData, PosteriorStats
+
+julia> idata = load_example_data("centered_eight");
+
+julia> loo_pit(idata; y_name=:obs)
+8-element DimArray{Float64,1} loo_pit_obs with dimensions:
+  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered
+ "Choate"            0.943511
+ "Deerfield"         0.63797
+ "Phillips Andover"  0.316697
+ "Phillips Exeter"   0.582252
+ "Hotchkiss"         0.295321
+ "Lawrenceville"     0.403318
+ "St. Paul's"        0.902508
+ "Mt. Hermon"        0.655275
source
loo_pit(y, y_pred, log_weights; kwargs...) -> Union{Real,AbstractArray}
Compute leave-one-out probability integral transform (LOO-PIT) checks.
Arguments
  • y: array of observations with shape (params...,)
  • y_pred: array of posterior predictive samples with shape (draws, chains, params...).
  • log_weights: array of normalized log LOO importance weights with shape (draws, chains, params...).
Keywords
  • is_discrete: If not provided, then it is set to true iff elements of y and y_pred are all integer-valued. If true, then data are smoothed using smooth_data to make them non-discrete before estimating LOO-PIT values.
  • kwargs: Remaining keywords are forwarded to smooth_data if data is discrete.
Returns
  • pitvals: LOO-PIT values with same size as y. If y is a scalar, then pitvals is a scalar.
LOO-PIT is a marginal posterior predictive check. If $y_{-i}$ is the array $y$ of observations with the $i$th observation left out, and $y_i^*$ is a posterior prediction of the $i$th observation, then the LOO-PIT value for the $i$th observation is defined as
\[P(y_i^* \le y_i \mid y_{-i}) = \int_{-\infty}^{y_i} p(y_i^* \mid y_{-i}) \mathrm{d} y_i^*\]
The LOO posterior predictions and the corresponding observations should have similar distributions, so if conditional predictive distributions are well-calibrated, then all LOO-PIT values should be approximately uniformly distributed on $[0, 1]$.[Gabry2019]
Examples
Calculate LOO-PIT values using as test quantity the observed values themselves.
julia> using ArviZExampleData
 
 julia> idata = load_example_data("centered_eight");
 
@@ -213,34 +244,4 @@
  "Hotchkiss"         0.435094
  "Lawrenceville"     0.220627
  "St. Paul's"        0.775086
- "Mt. Hermon"        0.296706
source
loo_pit(idata::InferenceData, log_weights; kwargs...) -> DimArray
Compute LOO-PIT values using existing normalized log LOO importance weights.
Keywords
  • y_name: Name of observed data variable in idata.observed_data. If not provided, then the only observed data variable is used.
  • y_pred_name: Name of posterior predictive variable in idata.posterior_predictive. If not provided, then y_name is used.
  • kwargs: Remaining keywords are forwarded to the base method of loo_pit.
Examples
Calculate LOO-PIT values using already computed log weights.
julia> using ArviZExampleData, PosteriorStats
-
-julia> idata = load_example_data("centered_eight");
-
-julia> loo_result = loo(idata; var_name=:obs);
-
-julia> loo_pit(idata, loo_result.psis_result.log_weights; y_name=:obs)
-8-element DimArray{Float64,1} loo_pit_obs with dimensions:
-  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered
- "Choate"            0.943511
- "Deerfield"         0.63797
- "Phillips Andover"  0.316697
- "Phillips Exeter"   0.582252
- "Hotchkiss"         0.295321
- "Lawrenceville"     0.403318
- "St. Paul's"        0.902508
- "Mt. Hermon"        0.655275
source
loo_pit(idata::InferenceData; kwargs...) -> DimArray
Compute LOO-PIT from groups in idata using PSIS-LOO.
Keywords
  • y_name: Name of observed data variable in idata.observed_data. If not provided, then the only observed data variable is used.
  • y_pred_name: Name of posterior predictive variable in idata.posterior_predictive. If not provided, then y_name is used.
  • log_likelihood_name: Name of log-likelihood variable in idata.log_likelihood. If not provided, then y_name is used if idata has a log_likelihood group, otherwise the only variable is used.
  • reff::Union{Real,AbstractArray{<:Real}}: The relative effective sample size(s) of the likelihood values. If an array, it must have the same data dimensions as the corresponding log-likelihood variable. If not provided, then this is estimated using ess.
  • kwargs: Remaining keywords are forwarded to the base method of loo_pit.
Examples
Calculate LOO-PIT values using as test quantity the observed values themselves.
julia> using ArviZExampleData, PosteriorStats
-
-julia> idata = load_example_data("centered_eight");
-
-julia> loo_pit(idata; y_name=:obs)
-8-element DimArray{Float64,1} loo_pit_obs with dimensions:
-  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered
- "Choate"            0.943511
- "Deerfield"         0.63797
- "Phillips Andover"  0.316697
- "Phillips Exeter"   0.582252
- "Hotchkiss"         0.295321
- "Lawrenceville"     0.403318
- "St. Paul's"        0.902508
- "Mt. Hermon"        0.655275
source
Utilities
PosteriorStats.smooth_data — Function
smooth_data(y; dims=:, interp_method=CubicSpline, offset_frac=0.01)
Smooth y along dims using interp_method.
interp_method is a 2-argument callabale that takes the arguments y and x and returns a DataInterpolations.jl interpolation method, defaulting to a cubic spline interpolator.
offset_frac is the fraction of the length of y to use as an offset when interpolating.
source
  • Hyndman1996Rob J. Hyndman (1996) Computing and Graphing Highest Density Regions,             Amer. Stat., 50(2): 120-6.             DOI: 10.1080/00031305.1996.10474359jstor.
  • ChenShao1999Ming-Hui Chen & Qi-Man Shao (1999)              Monte Carlo Estimation of Bayesian Credible and HPD Intervals,              J Comput. Graph. Stat., 8:1, 69-92.              DOI: 10.1080/10618600.1999.10474802jstor.
  • GelmanGoodrich2019Andrew Gelman, Ben Goodrich, Jonah Gabry & Aki Vehtari (2019) R-squared for Bayesian Regression Models, The American Statistician, 73:3, 307-9, DOI: 10.1080/00031305.2018.1549100.
  • VehtariSimpson2021Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO]
  • VehtariSimpson2021Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO]
  • VehtariSimpson2021Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO]
  • Vehtari2017Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544
  • LOOFAQAki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html
  • Watanabe2010Watanabe, S. Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory. 11(116):3571−3594, 2010. https://jmlr.csail.mit.edu/papers/v11/watanabe10a.html
  • Vehtari2017Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544
  • LOOFAQAki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html
  • YaoVehtari2018Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman.                Using Stacking to Average Bayesian Predictive Distributions.                2018. Bayesian Analysis. 13, 3, 917–1007.                doi: 10.1214/17-BA1091                arXiv: 1704.02030
  • YaoVehtari2018Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman.                Using Stacking to Average Bayesian Predictive Distributions.                2018. Bayesian Analysis. 13, 3, 917–1007.                doi: 10.1214/17-BA1091                arXiv: 1704.02030
  • YaoVehtari2018Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman.                Using Stacking to Average Bayesian Predictive Distributions.                2018. Bayesian Analysis. 13, 3, 917–1007.                doi: 10.1214/17-BA1091                arXiv: 1704.02030
  • YaoVehtari2018Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman.                Using Stacking to Average Bayesian Predictive Distributions.                2018. Bayesian Analysis. 13, 3, 917–1007.                doi: 10.1214/17-BA1091                arXiv: 1704.02030
  • Gabry2019Gabry, J., Simpson, D., Vehtari, A., Betancourt, M. & Gelman, A. Visualization in Bayesian Workflow. J. R. Stat. Soc. Ser. A Stat. Soc. 182, 389–402 (2019). doi: 10.1111/rssa.12378 arXiv: 1709.01449

\ No newline at end of file
+ "Mt. Hermon"        0.296706
source

Utilities

PosteriorStats.smooth_data — Function
smooth_data(y; dims=:, interp_method=CubicSpline, offset_frac=0.01)

Smooth y along dims using interp_method.

interp_method is a 2-argument callabale that takes the arguments y and x and returns a DataInterpolations.jl interpolation method, defaulting to a cubic spline interpolator.

offset_frac is the fraction of the length of y to use as an offset when interpolating.

source
  • Hyndman1996Rob J. Hyndman (1996) Computing and Graphing Highest Density Regions, Amer. Stat., 50(2): 120-6. DOI: 10.1080/00031305.1996.10474359jstor.
  • ChenShao1999Ming-Hui Chen & Qi-Man Shao (1999) Monte Carlo Estimation of Bayesian Credible and HPD Intervals, J Comput. Graph. Stat., 8:1, 69-92. DOI: 10.1080/10618600.1999.10474802jstor.
  • GelmanGoodrich2019Andrew Gelman, Ben Goodrich, Jonah Gabry & Aki Vehtari (2019) R-squared for Bayesian Regression Models, The American Statistician, 73:3, 307-9, DOI: 10.1080/00031305.2018.1549100.
  • VehtariSimpson2021Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO]
  • VehtariSimpson2021Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO]
  • VehtariSimpson2021Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO]
  • Vehtari2017Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544
  • LOOFAQAki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html
  • Watanabe2010Watanabe, S. Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory. 11(116):3571−3594, 2010. https://jmlr.csail.mit.edu/papers/v11/watanabe10a.html
  • Vehtari2017Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544
  • LOOFAQAki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html
  • YaoVehtari2018Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030
  • YaoVehtari2018Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030
  • YaoVehtari2018Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030
  • YaoVehtari2018Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030
  • Gabry2019Gabry, J., Simpson, D., Vehtari, A., Betancourt, M. & Gelman, A. Visualization in Bayesian Workflow. J. R. Stat. Soc. Ser. A Stat. Soc. 182, 389–402 (2019). doi: 10.1111/rssa.12378 arXiv: 1709.01449
\ No newline at end of file diff --git a/ArviZ/dev/creating_custom_plots/index.html b/ArviZ/dev/creating_custom_plots/index.html index 8ce2cd88e..16003dd94 100644 --- a/ArviZ/dev/creating_custom_plots/index.html +++ b/ArviZ/dev/creating_custom_plots/index.html @@ -187,7 +187,7 @@ ) end

Environment

using Pkg, InteractiveUtils
using PlutoUI
with_terminal(Pkg.status; color=false)
Status `~/work/ArviZ.jl/ArviZ.jl/docs/Project.toml`
   [cbdf2221] AlgebraOfGraphics v0.6.17
-  [131c737c] ArviZ v0.10.3 `~/work/ArviZ.jl/ArviZ.jl`
+  [131c737c] ArviZ v0.10.4 `~/work/ArviZ.jl/ArviZ.jl`
   [2f96bb34] ArviZExampleData v0.1.8
   [4a6e88f0] ArviZPythonPlots v0.1.3
   [13f3f980] CairoMakie v0.11.4
@@ -196,14 +196,14 @@
   [31c24e10] Distributions v0.25.104
   [e30172f5] Documenter v1.2.1
   [f6006082] EvoTrees v0.16.5
-  [b5cf5a8d] InferenceObjects v0.3.14
+  [b5cf5a8d] InferenceObjects v0.3.15
   [be115224] MCMCDiagnosticTools v0.3.8
   [a7f614a8] MLJBase v1.0.1
   [614be32b] MLJIteration v0.6.0
   [ce719bf2] PSIS v0.9.4
   [359b1769] PlutoStaticHTML v6.0.18
   [7f904dfe] PlutoUI v0.7.54
-  [7f36be82] PosteriorStats v0.1.4
+  [7f36be82] PosteriorStats v0.2.0
   [c1514b29] StanSample v7.6.0
   [a19d573c] StatisticalMeasures v0.1.3
   [2913bbd2] StatsBase v0.34.2
@@ -231,4 +231,4 @@
   JULIA_LOAD_PATH = @:@v#.#:@stdlib
   JULIA_CMDSTAN_HOME = /home/runner/work/ArviZ.jl/ArviZ.jl/.cmdstan//cmdstan-2.33.1/
   JULIA_REVISE_WORKER_ONLY = 1
-
\ No newline at end of file + \ No newline at end of file diff --git a/ArviZ/dev/index.html b/ArviZ/dev/index.html index 70025fd33..83f2aded0 100644 --- a/ArviZ/dev/index.html +++ b/ArviZ/dev/index.html @@ -2,4 +2,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-W1G68W77YV', {'page_path': location.pathname + location.search + location.hash}); -
GitHub

ArviZ.jl: Exploratory analysis of Bayesian models in Julia

ArviZ.jl is a Julia meta-package for exploratory analysis of Bayesian models. It is part of the ArviZ project, which also includes a related Python package.

ArviZ consists of and re-exports the following subpackages, along with extensions integrating them with InferenceObjects:

Additional functionality can be loaded with the following packages:

See the navigation bar for more useful packages.

Installation

From the Julia REPL, type ] to enter the Pkg REPL mode and run

pkg> add ArviZ

Usage

See the Quickstart for example usage and the API Overview for description of functions.

Extending ArviZ.jl

To use a custom data type with ArviZ.jl, simply overload InferenceObjects.convert_to_inference_data to convert your input(s) to an InferenceObjects.InferenceData.

\ No newline at end of file +
GitHub

ArviZ.jl: Exploratory analysis of Bayesian models in Julia

ArviZ.jl is a Julia meta-package for exploratory analysis of Bayesian models. It is part of the ArviZ project, which also includes a related Python package.

ArviZ consists of and re-exports the following subpackages, along with extensions integrating them with InferenceObjects:

Additional functionality can be loaded with the following packages:

See the navigation bar for more useful packages.

Installation

From the Julia REPL, type ] to enter the Pkg REPL mode and run

pkg> add ArviZ

Usage

See the Quickstart for example usage and the API Overview for description of functions.

Extending ArviZ.jl

To use a custom data type with ArviZ.jl, simply overload InferenceObjects.convert_to_inference_data to convert your input(s) to an InferenceObjects.InferenceData.

\ No newline at end of file diff --git a/ArviZ/dev/quickstart/index.html b/ArviZ/dev/quickstart/index.html index b59608b5e..60c5b452e 100644 --- a/ArviZ/dev/quickstart/index.html +++ b/ArviZ/dev/quickstart/index.html @@ -64,7 +64,7 @@ :θ Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8) with metadata Dict{String, Any} with 2 entries: - "created_at" => "2023-12-22T04:14:27.911" + "created_at" => "2023-12-23T22:52:52.783" "inference_library" => "Turing"
sample_stats
Dataset with dimensions: Dim{:draw}, Dim{:chain}
 and 12 layers:
   :energy           Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)
@@ -81,7 +81,7 @@
   :step_size_nom    Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)
 
 with metadata Dict{String, Any} with 2 entries:
-  "created_at" => "2023-12-22T04:14:27.823"
+  "created_at" => "2023-12-23T22:52:52.666"
   "inference_library" => "Turing"

Each group is an ArviZ.Dataset, a DimensionalData.AbstractDimStack that can be used identically to a DimensionalData.Dimstack. We can view a summary of the dataset.

idata_turing_post.posterior
Dataset with dimensions: 
   Dim{:draw},
   Dim{:chain},
@@ -92,11 +92,11 @@
   :θ Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)
 
 with metadata Dict{String, Any} with 2 entries:
-  "created_at"        => "2023-12-22T04:14:27.911"
+  "created_at"        => "2023-12-23T22:52:52.783"
   "inference_library" => "Turing"

Here is a plot of the trace. Note the intelligent labels.

begin
     plot_trace(idata_turing_post)
     gcf()
-end

We can also generate summary stats...

summarystats(idata_turing_post)
parametermeanstdhdi_3%hdi_97%mcse_meanmcse_stdess_tailess_bulkrhat
1"μ"4.263363.32219-1.8079110.51890.1149250.06222581191.94845.3211.00722
2"τ"4.36183.305250.67284310.42530.2023870.11768108.703115.1631.04819
3"θ[Choate]"6.605916.1128-4.0124617.99780.2079080.1929711626.68749.9241.00779
4"θ[Deerfield]"5.049345.0379-4.8064514.17990.1352670.1387131951.991277.111.00555
5"θ[Phillips Andover]"3.662795.65126-7.0725514.63860.1412230.1569931979.181429.091.00626
6"θ[Phillips Exeter]"4.761025.08264-4.601514.4410.1416990.1365662064.01178.231.00229
7"θ[Hotchkiss]"3.32714.92716-6.0833712.63570.1455870.1098251804.291097.651.00571
8"θ[Lawrenceville]"3.828345.16045-6.1173513.30490.1349910.1393971964.791331.421.00486
9"θ[St. Paul's]"6.644895.3885-2.6812917.35930.1800310.1443071841.62853.4921.0055
10"θ[Mt. Hermon]"4.943715.57785-5.7056514.83970.139630.1870221793.721392.591.00363

...and examine the energy distribution of the Hamiltonian sampler.

begin
+end

We can also generate summary stats...

summarystats(idata_turing_post)
SummaryStats
meanstdhdi_3%hdi_97%mcse_meanmcse_stdess_tailess_bulkrhat
μ4.33.3-1.8110.50.110.06211928451.01
τ4.43.30.67310.40.200.121091151.05
θ[Choate]6.66.1-4.0118.00.210.1916277501.01
θ[Deerfield]5.05.0-4.8114.20.140.14195212771.01
θ[Phillips Andover]3.75.7-7.0714.60.140.16197914291.01
θ[Phillips Exeter]4.85.1-4.6014.40.140.14206411781.00
θ[Hotchkiss]3.34.9-6.0812.60.150.11180410981.01
θ[Lawrenceville]3.85.2-6.1213.30.130.14196513311.00
θ[St. Paul's]6.65.4-2.6817.40.180.1418428531.01
θ[Mt. Hermon]4.95.6-5.7114.80.140.19179413931.00

...and examine the energy distribution of the Hamiltonian sampler.

begin
     plot_energy(idata_turing_post)
     gcf()
 end

Additional information in Turing.jl

With a few more steps, we can use Turing to compute additional useful groups to add to the InferenceData.

To sample from the prior, one simply calls sample but with the Prior sampler:

prior = Turing.sample(rng2, param_mod_turing, Prior(), ndraws);

To draw from the prior and posterior predictive distributions we can instantiate a "predictive model", i.e. a Turing model but with the observations set to missing, and then calling predict on the predictive model and the previously drawn samples:

begin
@@ -133,7 +133,7 @@
   :θ Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)
 
 with metadata Dict{String, Any} with 3 entries:
-  "created_at" => "2023-12-22T04:14:57.998"
+  "created_at" => "2023-12-23T22:53:24.667"
   "inference_library_version" => "0.30.0"
   "inference_library" => "Turing"
posterior_predictive
Dataset with dimensions: 
   Dim{:draw},
@@ -143,7 +143,7 @@
   :y Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)
 
 with metadata Dict{String, Any} with 3 entries:
-  "created_at" => "2023-12-22T04:14:57.366"
+  "created_at" => "2023-12-23T22:53:23.998"
   "inference_library_version" => "0.30.0"
   "inference_library" => "Turing"
log_likelihood
Dataset with dimensions: 
   Dim{:draw},
@@ -153,7 +153,7 @@
   :y Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)
 
 with metadata Dict{String, Any} with 3 entries:
-  "created_at" => "2023-12-22T04:14:57.833"
+  "created_at" => "2023-12-23T22:53:24.498"
   "inference_library_version" => "0.30.0"
   "inference_library" => "Turing"
sample_stats
Dataset with dimensions: Dim{:draw}, Dim{:chain}
 and 12 layers:
@@ -171,7 +171,7 @@
   :step_size_nom    Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)
 
 with metadata Dict{String, Any} with 3 entries:
-  "created_at" => "2023-12-22T04:14:57.997"
+  "created_at" => "2023-12-23T22:53:24.666"
   "inference_library_version" => "0.30.0"
   "inference_library" => "Turing"
prior
Dataset with dimensions: 
   Dim{:draw},
@@ -183,7 +183,7 @@
   :θ Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×1×8)
 
 with metadata Dict{String, Any} with 3 entries:
-  "created_at" => "2023-12-22T04:14:58.695"
+  "created_at" => "2023-12-23T22:53:25.381"
   "inference_library_version" => "0.30.0"
   "inference_library" => "Turing"
prior_predictive
Dataset with dimensions: 
   Dim{:draw},
@@ -193,14 +193,14 @@
   :y Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×1×8)
 
 with metadata Dict{String, Any} with 3 entries:
-  "created_at" => "2023-12-22T04:14:58.479"
+  "created_at" => "2023-12-23T22:53:25.163"
   "inference_library_version" => "0.30.0"
   "inference_library" => "Turing"
sample_stats_prior
Dataset with dimensions: Dim{:draw}, Dim{:chain}
 and 1 layer:
   :lp Float64 dims: Dim{:draw}, Dim{:chain} (1000×1)
 
 with metadata Dict{String, Any} with 3 entries:
-  "created_at" => "2023-12-22T04:14:58.587"
+  "created_at" => "2023-12-23T22:53:25.275"
   "inference_library_version" => "0.30.0"
   "inference_library" => "Turing"
observed_data
Dataset with dimensions: 
   Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered
@@ -208,7 +208,7 @@
   :y Float64 dims: Dim{:school} (8)
 
 with metadata Dict{String, Any} with 3 entries:
-  "created_at" => "2023-12-22T04:14:58.986"
+  "created_at" => "2023-12-23T22:53:25.662"
   "inference_library_version" => "0.30.0"
   "inference_library" => "Turing"

Then we can for example compute the expected leave-one-out (LOO) predictive density, which is an estimate of the out-of-distribution predictive fit of the model:

loo(idata_turing) # higher ELPD is better
PSISLOOResult with estimates
  elpd  elpd_mcse    p  p_mcse
@@ -285,7 +285,7 @@
   :theta Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)
 
 with metadata Dict{String, Any} with 1 entry:
-  "created_at" => "2023-12-22T04:15:38.213"
posterior_predictive
Dataset with dimensions: 
+  "created_at" => "2023-12-23T22:54:01.721"
posterior_predictive
Dataset with dimensions: 
   Dim{:draw},
   Dim{:chain},
   Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered
@@ -293,7 +293,7 @@
   :y_hat Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)
 
 with metadata Dict{String, Any} with 1 entry:
-  "created_at" => "2023-12-22T04:15:37.515"
log_likelihood
Dataset with dimensions: 
+  "created_at" => "2023-12-23T22:54:01.026"
log_likelihood
Dataset with dimensions: 
   Dim{:draw},
   Dim{:chain},
   Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered
@@ -301,7 +301,7 @@
   :log_lik Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)
 
 with metadata Dict{String, Any} with 1 entry:
-  "created_at" => "2023-12-22T04:15:38.057"
sample_stats
Dataset with dimensions: Dim{:draw}, Dim{:chain}
+  "created_at" => "2023-12-23T22:54:01.559"
sample_stats
Dataset with dimensions: Dim{:draw}, Dim{:chain}
 and 7 layers:
   :tree_depth      Int64 dims: Dim{:draw}, Dim{:chain} (1000×4)
   :energy          Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)
@@ -312,13 +312,13 @@
   :step_size       Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)
 
 with metadata Dict{String, Any} with 1 entry:
-  "created_at" => "2023-12-22T04:15:37.708"
observed_data
Dataset with dimensions: 
+  "created_at" => "2023-12-23T22:54:01.259"
observed_data
Dataset with dimensions: 
   Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered
 and 1 layer:
   :y Float64 dims: Dim{:school} (8)
 
 with metadata Dict{String, Any} with 1 entry:
-  "created_at" => "2023-12-22T04:15:38.341"
begin
+  "created_at" => "2023-12-23T22:54:01.857"
begin
     plot_density(idata_stan; var_names=(:mu, :tau))
     gcf()
 end

Here is a plot showing where the Hamiltonian sampler had divergences:

begin
@@ -330,7 +330,7 @@
     gcf()
 end

Environment

using PlutoUI
using Pkg, InteractiveUtils
with_terminal(Pkg.status; color=false)
Status `~/work/ArviZ.jl/ArviZ.jl/docs/Project.toml`
   [cbdf2221] AlgebraOfGraphics v0.6.17
-  [131c737c] ArviZ v0.10.3 `~/work/ArviZ.jl/ArviZ.jl`
+  [131c737c] ArviZ v0.10.4 `~/work/ArviZ.jl/ArviZ.jl`
   [2f96bb34] ArviZExampleData v0.1.8
   [4a6e88f0] ArviZPythonPlots v0.1.3
   [13f3f980] CairoMakie v0.11.4
@@ -339,14 +339,14 @@
   [31c24e10] Distributions v0.25.104
   [e30172f5] Documenter v1.2.1
   [f6006082] EvoTrees v0.16.5
-  [b5cf5a8d] InferenceObjects v0.3.14
+  [b5cf5a8d] InferenceObjects v0.3.15
   [be115224] MCMCDiagnosticTools v0.3.8
   [a7f614a8] MLJBase v1.0.1
   [614be32b] MLJIteration v0.6.0
   [ce719bf2] PSIS v0.9.4
   [359b1769] PlutoStaticHTML v6.0.18
   [7f904dfe] PlutoUI v0.7.54
-  [7f36be82] PosteriorStats v0.1.4
+  [7f36be82] PosteriorStats v0.2.0
   [c1514b29] StanSample v7.6.0
   [a19d573c] StatisticalMeasures v0.1.3
   [2913bbd2] StatsBase v0.34.2
@@ -375,4 +375,4 @@
   JULIA_CMDSTAN_HOME = /home/runner/work/ArviZ.jl/ArviZ.jl/.cmdstan//cmdstan-2.33.1/
   JULIA_REVISE_WORKER_ONLY = 1
   JULIA_PYTHONCALL_EXE = /home/runner/work/ArviZ.jl/ArviZ.jl/docs/.CondaPkg/env/bin/python
-
\ No newline at end of file + \ No newline at end of file diff --git a/ArviZ/dev/search_index.js b/ArviZ/dev/search_index.js index 85817ed23..3fbad561f 100644 --- a/ArviZ/dev/search_index.js +++ b/ArviZ/dev/search_index.js @@ -1,3 +1,3 @@ var documenterSearchIndex = {"docs": -[{"location":"api/inference_data/#inferencedata-api","page":"InferenceData","title":"InferenceData","text":"","category":"section"},{"location":"api/inference_data/","page":"InferenceData","title":"InferenceData","text":"Pages = [\"inference_data.md\"]","category":"page"},{"location":"api/inference_data/#Type-definition","page":"InferenceData","title":"Type definition","text":"","category":"section"},{"location":"api/inference_data/","page":"InferenceData","title":"InferenceData","text":"InferenceData","category":"page"},{"location":"api/inference_data/#InferenceObjects.InferenceData","page":"InferenceData","title":"InferenceObjects.InferenceData","text":"InferenceData{group_names,group_types}\n\nContainer for inference data storage using DimensionalData.\n\nThis object implements the InferenceData schema.\n\nInternally, groups are stored in a NamedTuple, which can be accessed using parent(::InferenceData).\n\nConstructors\n\nInferenceData(groups::NamedTuple)\nInferenceData(; groups...)\n\nConstruct an inference data from either a NamedTuple or keyword arguments of groups.\n\nGroups must be Dataset objects.\n\nInstead of directly creating an InferenceData, use the exported from_xyz functions or convert_to_inference_data.\n\n\n\n\n\n","category":"type"},{"location":"api/inference_data/#Property-interface","page":"InferenceData","title":"Property interface","text":"","category":"section"},{"location":"api/inference_data/","page":"InferenceData","title":"InferenceData","text":"getproperty\npropertynames","category":"page"},{"location":"api/inference_data/#Base.getproperty","page":"InferenceData","title":"Base.getproperty","text":"getproperty(data::InferenceData, name::Symbol) -> Dataset\n\nGet group with the specified name.\n\n\n\n\n\n","category":"function"},{"location":"api/inference_data/#Base.propertynames","page":"InferenceData","title":"Base.propertynames","text":"propertynames(data::InferenceData) -> Tuple{Symbol}\n\nGet names of groups\n\n\n\n\n\n","category":"function"},{"location":"api/inference_data/#Indexing-interface","page":"InferenceData","title":"Indexing interface","text":"","category":"section"},{"location":"api/inference_data/","page":"InferenceData","title":"InferenceData","text":"getindex\nBase.setindex","category":"page"},{"location":"api/inference_data/#Base.getindex","page":"InferenceData","title":"Base.getindex","text":"Base.getindex(data::InferenceData, groups::Symbol; coords...) -> Dataset\nBase.getindex(data::InferenceData, groups; coords...) -> InferenceData\n\nReturn a new InferenceData containing the specified groups sliced to the specified coords.\n\ncoords specifies a dimension name mapping to an index, a DimensionalData.Selector, or an IntervalSets.AbstractInterval.\n\nIf one or more groups lack the specified dimension, a warning is raised but can be ignored. All groups that contain the dimension must also contain the specified indices, or an exception will be raised.\n\nExamples\n\nSelect data from all groups for just the specified id values.\n\njulia> using InferenceObjects, DimensionalData\n\njulia> idata = from_namedtuple(\n (θ=randn(4, 100, 4), τ=randn(4, 100));\n prior=(θ=randn(4, 100, 4), τ=randn(4, 100)),\n observed_data=(y=randn(4),),\n dims=(θ=[:id], y=[:id]),\n coords=(id=[\"a\", \"b\", \"c\", \"d\"],),\n )\nInferenceData with groups:\n > posterior\n > prior\n > observed_data\n\njulia> idata.posterior\nDataset with dimensions:\n Dim{:chain} Sampled 1:4 ForwardOrdered Regular Points,\n Dim{:draw} Sampled 1:100 ForwardOrdered Regular Points,\n Dim{:id} Categorical String[a, b, c, d] ForwardOrdered\nand 2 layers:\n :θ Float64 dims: Dim{:chain}, Dim{:draw}, Dim{:id} (4×100×4)\n :τ Float64 dims: Dim{:chain}, Dim{:draw} (4×100)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2022-08-11T11:15:21.4\"\n\njulia> idata_sel = idata[id=At([\"a\", \"b\"])]\nInferenceData with groups:\n > posterior\n > prior\n > observed_data\n\njulia> idata_sel.posterior\nDataset with dimensions:\n Dim{:chain} Sampled 1:4 ForwardOrdered Regular Points,\n Dim{:draw} Sampled 1:100 ForwardOrdered Regular Points,\n Dim{:id} Categorical String[a, b] ForwardOrdered\nand 2 layers:\n :θ Float64 dims: Dim{:chain}, Dim{:draw}, Dim{:id} (4×100×2)\n :τ Float64 dims: Dim{:chain}, Dim{:draw} (4×100)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2022-08-11T11:15:21.4\"\n\nSelect data from just the posterior, returning a Dataset if the indices index more than one element from any of the variables:\n\njulia> idata[:observed_data, id=At([\"a\"])]\nDataset with dimensions:\n Dim{:id} Categorical String[a] ForwardOrdered\nand 1 layer:\n :y Float64 dims: Dim{:id} (1)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2022-08-11T11:19:25.982\"\n\nNote that if a single index is provided, the behavior is still to slice so that the dimension is preserved.\n\n\n\n\n\n","category":"function"},{"location":"api/inference_data/#Base.setindex","page":"InferenceData","title":"Base.setindex","text":"Base.setindex(data::InferenceData, group::Dataset, name::Symbol) -> InferenceData\n\nCreate a new InferenceData containing the group with the specified name.\n\nIf a group with name is already in data, it is replaced.\n\n\n\n\n\n","category":"function"},{"location":"api/inference_data/#Iteration-interface","page":"InferenceData","title":"Iteration interface","text":"","category":"section"},{"location":"api/inference_data/","page":"InferenceData","title":"InferenceData","text":"InferenceData also implements the same iteration interface as its underlying NamedTuple. That is, iterating over an InferenceData iterates over its groups.","category":"page"},{"location":"api/inference_data/#General-conversion","page":"InferenceData","title":"General conversion","text":"","category":"section"},{"location":"api/inference_data/","page":"InferenceData","title":"InferenceData","text":"convert_to_inference_data\nfrom_dict\nfrom_namedtuple","category":"page"},{"location":"api/inference_data/#InferenceObjects.convert_to_inference_data","page":"InferenceData","title":"InferenceObjects.convert_to_inference_data","text":"convert_to_inference_data(obj; group, kwargs...) -> InferenceData\n\nConvert a supported object to an InferenceData object.\n\nIf obj converts to a single dataset, group specifies which dataset in the resulting InferenceData that is.\n\nSee convert_to_dataset\n\nArguments\n\nobj can be many objects. Basic supported types are:\nInferenceData: return unchanged\nDataset/DimensionalData.AbstractDimStack: add to InferenceData as the only group\nNamedTuple/AbstractDict: create a Dataset as the only group\nAbstractArray{<:Real}: create a Dataset as the only group, given an arbitrary name, if the name is not set\n\nMore specific types may be documented separately.\n\nKeywords\n\ngroup::Symbol = :posterior: If obj converts to a single dataset, assign the resulting dataset to this group.\ndims: a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are:\nSymbol: dimension name\nType{<:DimensionsionalData.Dimension}: dimension type\nDimensionsionalData.Dimension: dimension, potentially with indices\nNothing: no dimension name provided, dimension name is automatically generated\ncoords: a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated.\nkwargs: remaining keywords forwarded to converter functions\n\n\n\n\n\n","category":"function"},{"location":"api/inference_data/#InferenceObjects.from_dict","page":"InferenceData","title":"InferenceObjects.from_dict","text":"from_dict(posterior::AbstractDict; kwargs...) -> InferenceData\n\nConvert a Dict to an InferenceData.\n\nArguments\n\nposterior: The data to be converted. Its strings must be Symbol or AbstractString, and its values must be arrays.\n\nKeywords\n\nposterior_predictive::Any=nothing: Draws from the posterior predictive distribution\nsample_stats::Any=nothing: Statistics of the posterior sampling process\npredictions::Any=nothing: Out-of-sample predictions for the posterior.\nprior::Dict=nothing: Draws from the prior\nprior_predictive::Any=nothing: Draws from the prior predictive distribution\nsample_stats_prior::Any=nothing: Statistics of the prior sampling process\nobserved_data::NamedTuple: Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values.\nconstant_data::NamedTuple: Model constants, data included in the model which is not modeled as a random variable. Keys are parameter names and values.\npredictions_constant_data::NamedTuple: Constants relevant to the model predictions (i.e. new x values in a linear regression).\nlog_likelihood: Pointwise log-likelihood for the data. 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It may be of the following types:\n::NamedTuple: The keys are the variable names and the values are arrays with dimensions (ndraws, nchains[, sizes...]).\n::Vector{Vector{<:NamedTuple}}: A vector of length nchains whose elements have length ndraws.\n\nKeywords\n\nposterior_predictive::Any=nothing: Draws from the posterior predictive distribution\nsample_stats::Any=nothing: Statistics of the posterior sampling process\npredictions::Any=nothing: Out-of-sample predictions for the posterior.\nprior=nothing: Draws from the prior. Accepts the same types as posterior.\nprior_predictive::Any=nothing: Draws from the prior predictive distribution\nsample_stats_prior::Any=nothing: Statistics of the prior sampling process\nobserved_data::NamedTuple: Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values.\nconstant_data::NamedTuple: Model constants, data included in the model which is not modeled as a random variable. Keys are parameter names and values.\npredictions_constant_data::NamedTuple: Constants relevant to the model predictions (i.e. new x values in a linear regression).\nlog_likelihood: Pointwise log-likelihood for the data. It is recommended to use this argument as a NamedTuple whose keys are observed variable names and whose values are log likelihood arrays.\nlibrary: Name of library that generated the draws\ncoords: Map from named dimension to named indices\ndims: Map from variable name to names of its dimensions\n\nReturns\n\nInferenceData: The data with groups corresponding to the provided data\n\nnote: Note\nIf a NamedTuple is provided for observed_data, constant_data, or predictionsconstantdata`, any non-array values (e.g. integers) are converted to 0-dimensional arrays.\n\nExamples\n\nusing InferenceObjects\nnchains = 2\nndraws = 100\n\ndata1 = (\n x=rand(ndraws, nchains), y=randn(ndraws, nchains, 2), z=randn(ndraws, nchains, 3, 2)\n)\nidata1 = from_namedtuple(data1)\n\ndata2 = [[(x=rand(), y=randn(2), z=randn(3, 2)) for _ in 1:ndraws] for _ in 1:nchains];\nidata2 = from_namedtuple(data2)\n\n\n\n\n\n","category":"function"},{"location":"api/inference_data/#General-functions","page":"InferenceData","title":"General functions","text":"","category":"section"},{"location":"api/inference_data/","page":"InferenceData","title":"InferenceData","text":"cat\nmerge","category":"page"},{"location":"api/inference_data/#Base.cat","page":"InferenceData","title":"Base.cat","text":"cat(data::InferenceData...; [groups=keys(data[1]),] dims) -> InferenceData\n\nConcatenate InferenceData objects along the specified dimension dims.\n\nOnly the groups in groups are concatenated. Remaining groups are merged into the new InferenceData object.\n\nExamples\n\nHere is how we can concatenate all groups of two InferenceData objects along the existing chain dimension:\n\njulia> coords = (; a_dim=[\"x\", \"y\", \"z\"]);\n\njulia> dims = dims=(; a=[:a_dim]);\n\njulia> data = Dict(:a => randn(100, 4, 3), :b => randn(100, 4));\n\njulia> idata = from_dict(data; coords=coords, dims=dims)\nInferenceData with groups:\n > posterior\n\njulia> idata_cat1 = cat(idata, idata; dims=:chain)\nInferenceData with groups:\n > posterior\n\njulia> idata_cat1.posterior\nDataset with dimensions:\n Dim{:draw},\n Dim{:chain},\n Dim{:a_dim} Categorical{String} String[\"x\", \"y\", \"z\"] ForwardOrdered\nand 2 layers:\n :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim} (100×8×3)\n :b Float64 dims: Dim{:draw}, Dim{:chain} (100×8)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-04-03T18:41:35.779\"\n\nAlternatively, we can concatenate along a new run dimension, which will be created.\n\njulia> idata_cat2 = cat(idata, idata; dims=:run)\nInferenceData with groups:\n > posterior\n\njulia> idata_cat2.posterior\nDataset with dimensions:\n Dim{:draw},\n Dim{:chain},\n Dim{:a_dim} Categorical{String} String[\"x\", \"y\", \"z\"] ForwardOrdered,\n Dim{:run}\nand 2 layers:\n :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim}, Dim{:run} (100×4×3×2)\n :b Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:run} (100×4×2)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-04-03T18:41:35.779\"\n\nWe can also concatenate only a subset of groups and merge the rest, which is useful when some groups are present only in some of the InferenceData objects or will be identical in all of them:\n\njulia> observed_data = Dict(:y => randn(10));\n\njulia> idata2 = from_dict(data; observed_data=observed_data, coords=coords, dims=dims)\nInferenceData with groups:\n > posterior\n > observed_data\n\njulia> idata_cat3 = cat(idata, idata2; groups=(:posterior,), dims=:run)\nInferenceData with groups:\n > posterior\n > observed_data\n\njulia> idata_cat3.posterior\nDataset with dimensions:\n Dim{:draw},\n Dim{:chain},\n Dim{:a_dim} Categorical{String} String[\"x\", \"y\", \"z\"] ForwardOrdered,\n Dim{:run}\nand 2 layers:\n :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim}, Dim{:run} (100×4×3×2)\n :b Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:run} (100×4×2)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-04-03T18:41:35.779\"\n\njulia> idata_cat3.observed_data\nDataset with dimensions: Dim{:y_dim_1}\nand 1 layer:\n :y Float64 dims: Dim{:y_dim_1} (10)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-02-17T15:11:00.59\"\n\n\n\n\n\n","category":"function"},{"location":"api/inference_data/#Base.merge","page":"InferenceData","title":"Base.merge","text":"merge(data::InferenceData...) -> InferenceData\n\nMerge InferenceData objects.\n\nThe result contains all groups in data and others. If a group appears more than once, the one that occurs last is kept.\n\nSee also: cat\n\nExamples\n\nHere we merge an InferenceData containing only a posterior group with one containing only a prior group to create a new one containing both groups.\n\njulia> idata1 = from_dict(Dict(:a => randn(100, 4, 3), :b => randn(100, 4)))\nInferenceData with groups:\n > posterior\n\njulia> idata2 = from_dict(; prior=Dict(:a => randn(100, 1, 3), :c => randn(100, 1)))\nInferenceData with groups:\n > prior\n\njulia> idata_merged = merge(idata1, idata2)\nInferenceData with groups:\n > posterior\n > prior\n\n\n\n\n\n","category":"function"},{"location":"quickstart/","page":"Quickstart","title":"Quickstart","text":"\n\n\n

ArviZ Quickstart

Note

This tutorial is adapted from ArviZ's quickstart.

\n\n\n

Setup

Here we add the necessary packages for this notebook and load a few we will use throughout.

\n\n\n\n\n
using ArviZ, ArviZPythonPlots, Distributions, LinearAlgebra, Random, StanSample, Turing
\n\n\n
# ArviZPythonPlots ships with style sheets!\nuse_style(\"arviz-darkgrid\")
\n\n\n\n

Get started with plotting

To plot with ArviZ, we need to load the ArviZPythonPlots package. ArviZ is designed to be used with libraries like Stan, Turing.jl, and Soss.jl but works fine with raw arrays.

\n\n
rng1 = Random.MersenneTwister(37772);
\n\n\n
begin\n    plot_posterior(randn(rng1, 100_000))\n    gcf()\nend
\n\n\n\n

Plotting a dictionary of arrays, ArviZ will interpret each key as the name of a different random variable. Each row of an array is treated as an independent series of draws from the variable, called a chain. Below, we have 10 chains of 50 draws each for four different distributions.

\n\n
let\n    s = (50, 10)\n    plot_forest((\n        normal=randn(rng1, s),\n        gumbel=rand(rng1, Gumbel(), s),\n        student_t=rand(rng1, TDist(6), s),\n        exponential=rand(rng1, Exponential(), s),\n    ),)\n    gcf()\nend
\n\n\n\n

Plotting with MCMCChains.jl's Chains objects produced by Turing.jl

ArviZ is designed to work well with high dimensional, labelled data. Consider the eight schools model, which roughly tries to measure the effectiveness of SAT classes at eight different schools. To show off ArviZ's labelling, I give the schools the names of a different eight schools.

This model is small enough to write down, is hierarchical, and uses labelling. Additionally, a centered parameterization causes divergences (which are interesting for illustration).

First we create our data and set some sampling parameters.

\n\n
begin\n    J = 8\n    y = [28.0, 8.0, -3.0, 7.0, -1.0, 1.0, 18.0, 12.0]\n    σ = [15.0, 10.0, 16.0, 11.0, 9.0, 11.0, 10.0, 18.0]\n    schools = [\n        \"Choate\",\n        \"Deerfield\",\n        \"Phillips Andover\",\n        \"Phillips Exeter\",\n        \"Hotchkiss\",\n        \"Lawrenceville\",\n        \"St. Paul's\",\n        \"Mt. Hermon\",\n    ]\n    ndraws = 1_000\n    ndraws_warmup = 1_000\n    nchains = 4\nend;
\n\n\n\n

Now we write and run the model using Turing:

\n\n
Turing.@model function model_turing(y, σ, J=length(y))\n    μ ~ Normal(0, 5)\n    τ ~ truncated(Cauchy(0, 5), 0, Inf)\n    θ ~ filldist(Normal(μ, τ), J)\n    for i in 1:J\n        y[i] ~ Normal(θ[i], σ[i])\n    end\nend
\n
model_turing (generic function with 4 methods)
\n\n
rng2 = Random.MersenneTwister(16653);
\n\n\n
begin\n    param_mod_turing = model_turing(y, σ)\n    sampler = NUTS(ndraws_warmup, 0.8)\n\n    turing_chns = Turing.sample(\n        rng2, model_turing(y, σ), sampler, MCMCThreads(), ndraws, nchains\n    )\nend;
\n\n\n\n

Most ArviZ functions work fine with Chains objects from Turing:

\n\n
begin\n    plot_autocorr(turing_chns; var_names=(:μ, :τ))\n    gcf()\nend
\n\n\n\n

Convert to InferenceData

For much more powerful querying, analysis and plotting, we can use built-in ArviZ utilities to convert Chains objects to multidimensional data structures with named dimensions and indices. Note that for such dimensions, the information is not contained in Chains, so we need to provide it.

ArviZ is built to work with InferenceData, and the more groups it has access to, the more powerful analyses it can perform.

\n\n
idata_turing_post = from_mcmcchains(\n    turing_chns;\n    coords=(; school=schools),\n    dims=NamedTuple(k => (:school,) for k in (:y, :σ, :θ)),\n    library=\"Turing\",\n)
\n
InferenceData
posterior
Dataset with dimensions: \n  Dim{:draw},\n  Dim{:chain},\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n  :μ Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :τ Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :θ Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)\n\nwith metadata Dict{String, Any} with 2 entries:\n  \"created_at\" => \"2023-12-22T04:14:27.911\"\n  \"inference_library\" => \"Turing\"
sample_stats
Dataset with dimensions: Dim{:draw}, Dim{:chain}\nand 12 layers:\n  :energy           Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :n_steps          Int64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :diverging        Bool dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :max_energy_error Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :energy_error     Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :is_accept        Bool dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :log_density      Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :tree_depth       Int64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :step_size        Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :acceptance_rate  Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :lp               Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :step_size_nom    Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n\nwith metadata Dict{String, Any} with 2 entries:\n  \"created_at\" => \"2023-12-22T04:14:27.823\"\n  \"inference_library\" => \"Turing\"
\n\n\n

Each group is an ArviZ.Dataset, a DimensionalData.AbstractDimStack that can be used identically to a DimensionalData.Dimstack. We can view a summary of the dataset.

\n\n
idata_turing_post.posterior
\n
Dataset with dimensions: \n  Dim{:draw},\n  Dim{:chain},\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n  :μ Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :τ Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :θ Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)\n\nwith metadata Dict{String, Any} with 2 entries:\n  \"created_at\"        => \"2023-12-22T04:14:27.911\"\n  \"inference_library\" => \"Turing\"
\n\n\n

Here is a plot of the trace. Note the intelligent labels.

\n\n
begin\n    plot_trace(idata_turing_post)\n    gcf()\nend
\n\n\n\n

We can also generate summary stats...

\n\n
summarystats(idata_turing_post)
\n
parametermeanstdhdi_3%hdi_97%mcse_meanmcse_stdess_tailess_bulkrhat
1\"μ\"4.263363.32219-1.8079110.51890.1149250.06222581191.94845.3211.00722
2\"τ\"4.36183.305250.67284310.42530.2023870.11768108.703115.1631.04819
3\"θ[Choate]\"6.605916.1128-4.0124617.99780.2079080.1929711626.68749.9241.00779
4\"θ[Deerfield]\"5.049345.0379-4.8064514.17990.1352670.1387131951.991277.111.00555
5\"θ[Phillips Andover]\"3.662795.65126-7.0725514.63860.1412230.1569931979.181429.091.00626
6\"θ[Phillips Exeter]\"4.761025.08264-4.601514.4410.1416990.1365662064.01178.231.00229
7\"θ[Hotchkiss]\"3.32714.92716-6.0833712.63570.1455870.1098251804.291097.651.00571
8\"θ[Lawrenceville]\"3.828345.16045-6.1173513.30490.1349910.1393971964.791331.421.00486
9\"θ[St. Paul's]\"6.644895.3885-2.6812917.35930.1800310.1443071841.62853.4921.0055
10\"θ[Mt. Hermon]\"4.943715.57785-5.7056514.83970.139630.1870221793.721392.591.00363
\n\n\n

...and examine the energy distribution of the Hamiltonian sampler.

\n\n
begin\n    plot_energy(idata_turing_post)\n    gcf()\nend
\n\n\n\n

Additional information in Turing.jl

With a few more steps, we can use Turing to compute additional useful groups to add to the InferenceData.

To sample from the prior, one simply calls sample but with the Prior sampler:

\n\n
prior = Turing.sample(rng2, param_mod_turing, Prior(), ndraws);
\n\n\n\n

To draw from the prior and posterior predictive distributions we can instantiate a \"predictive model\", i.e. a Turing model but with the observations set to missing, and then calling predict on the predictive model and the previously drawn samples:

\n\n
begin\n    # Instantiate the predictive model\n    param_mod_predict = model_turing(similar(y, Missing), σ)\n    # and then sample!\n    prior_predictive = Turing.predict(rng2, param_mod_predict, prior)\n    posterior_predictive = Turing.predict(rng2, param_mod_predict, turing_chns)\nend;
\n\n\n\n

And to extract the pointwise log-likelihoods, which is useful if you want to compute metrics such as loo,

\n\n
log_likelihood = let\n    log_likelihood = Turing.pointwise_loglikelihoods(\n        param_mod_turing, MCMCChains.get_sections(turing_chns, :parameters)\n    )\n    # Ensure the ordering of the loglikelihoods matches the ordering of `posterior_predictive`\n    ynames = string.(keys(posterior_predictive))\n    log_likelihood_y = getindex.(Ref(log_likelihood), ynames)\n    (; y=cat(log_likelihood_y...; dims=3))\nend;
\n\n\n\n

This can then be included in the from_mcmcchains call from above:

\n\n
idata_turing = from_mcmcchains(\n    turing_chns;\n    posterior_predictive,\n    log_likelihood,\n    prior,\n    prior_predictive,\n    observed_data=(; y),\n    coords=(; school=schools),\n    dims=NamedTuple(k => (:school,) for k in (:y, :σ, :θ)),\n    library=Turing,\n)
\n
InferenceData
posterior
Dataset with dimensions: \n  Dim{:draw},\n  Dim{:chain},\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n  :μ Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :τ Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :θ Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)\n\nwith metadata Dict{String, Any} with 3 entries:\n  \"created_at\" => \"2023-12-22T04:14:57.998\"\n  \"inference_library_version\" => \"0.30.0\"\n  \"inference_library\" => \"Turing\"
posterior_predictive
Dataset with dimensions: \n  Dim{:draw},\n  Dim{:chain},\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n  :y Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)\n\nwith metadata Dict{String, Any} with 3 entries:\n  \"created_at\" => \"2023-12-22T04:14:57.366\"\n  \"inference_library_version\" => \"0.30.0\"\n  \"inference_library\" => \"Turing\"
log_likelihood
Dataset with dimensions: \n  Dim{:draw},\n  Dim{:chain},\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n  :y Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)\n\nwith metadata Dict{String, Any} with 3 entries:\n  \"created_at\" => \"2023-12-22T04:14:57.833\"\n  \"inference_library_version\" => \"0.30.0\"\n  \"inference_library\" => \"Turing\"
sample_stats
Dataset with dimensions: Dim{:draw}, Dim{:chain}\nand 12 layers:\n  :energy           Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :n_steps          Int64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :diverging        Bool dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :max_energy_error Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :energy_error     Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :is_accept        Bool dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :log_density      Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :tree_depth       Int64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :step_size        Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :acceptance_rate  Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :lp               Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :step_size_nom    Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n\nwith metadata Dict{String, Any} with 3 entries:\n  \"created_at\" => \"2023-12-22T04:14:57.997\"\n  \"inference_library_version\" => \"0.30.0\"\n  \"inference_library\" => \"Turing\"
prior
Dataset with dimensions: \n  Dim{:draw},\n  Dim{:chain},\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n  :μ Float64 dims: Dim{:draw}, Dim{:chain} (1000×1)\n  :τ Float64 dims: Dim{:draw}, Dim{:chain} (1000×1)\n  :θ Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×1×8)\n\nwith metadata Dict{String, Any} with 3 entries:\n  \"created_at\" => \"2023-12-22T04:14:58.695\"\n  \"inference_library_version\" => \"0.30.0\"\n  \"inference_library\" => \"Turing\"
prior_predictive
Dataset with dimensions: \n  Dim{:draw},\n  Dim{:chain},\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n  :y Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×1×8)\n\nwith metadata Dict{String, Any} with 3 entries:\n  \"created_at\" => \"2023-12-22T04:14:58.479\"\n  \"inference_library_version\" => \"0.30.0\"\n  \"inference_library\" => \"Turing\"
sample_stats_prior
Dataset with dimensions: Dim{:draw}, Dim{:chain}\nand 1 layer:\n  :lp Float64 dims: Dim{:draw}, Dim{:chain} (1000×1)\n\nwith metadata Dict{String, Any} with 3 entries:\n  \"created_at\" => \"2023-12-22T04:14:58.587\"\n  \"inference_library_version\" => \"0.30.0\"\n  \"inference_library\" => \"Turing\"
observed_data
Dataset with dimensions: \n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n  :y Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 3 entries:\n  \"created_at\" => \"2023-12-22T04:14:58.986\"\n  \"inference_library_version\" => \"0.30.0\"\n  \"inference_library\" => \"Turing\"
\n\n\n

Then we can for example compute the expected leave-one-out (LOO) predictive density, which is an estimate of the out-of-distribution predictive fit of the model:

\n\n
loo(idata_turing) # higher ELPD is better
\n
PSISLOOResult with estimates\n elpd  elpd_mcse    p  p_mcse\n  -31        1.4  1.0    0.33\n\nand PSISResult with 1000 draws, 4 chains, and 8 parameters\nPareto shape (k) diagnostic values:\n                    Count      Min. ESS\n (-Inf, 0.5]  good  5 (62.5%)  404\n  (0.5, 0.7]  okay  3 (37.5%)  788
\n\n\n

If the model is well-calibrated, i.e. it replicates the true generative process well, the CDF of the pointwise LOO values should be similarly distributed to a uniform distribution. This can be inspected visually:

\n\n
begin\n    plot_loo_pit(idata_turing; y=:y, ecdf=true)\n    gcf()\nend
\n\n\n\n

Plotting with Stan.jl outputs

StanSample.jl comes with built-in support for producing InferenceData outputs.

Here is the same centered eight schools model in Stan:

\n\n
begin\n    schools_code = \"\"\"\n    data {\n      int<lower=0> J;\n      array[J] real y;\n      array[J] real<lower=0> sigma;\n    }\n\n    parameters {\n      real mu;\n      real<lower=0> tau;\n      array[J] real theta;\n    }\n\n    model {\n      mu ~ normal(0, 5);\n      tau ~ cauchy(0, 5);\n      theta ~ normal(mu, tau);\n      y ~ normal(theta, sigma);\n    }\n\n    generated quantities {\n        vector[J] log_lik;\n        vector[J] y_hat;\n        for (j in 1:J) {\n            log_lik[j] = normal_lpdf(y[j] | theta[j], sigma[j]);\n            y_hat[j] = normal_rng(theta[j], sigma[j]);\n        }\n    }\n    \"\"\"\n\n    schools_data = Dict(\"J\" => J, \"y\" => y, \"sigma\" => σ)\n    idata_stan = mktempdir() do path\n        stan_model = SampleModel(\"schools\", schools_code, path)\n        _ = stan_sample(\n            stan_model;\n            data=schools_data,\n            num_chains=nchains,\n            num_warmups=ndraws_warmup,\n            num_samples=ndraws,\n            seed=28983,\n            summary=false,\n        )\n        return StanSample.inferencedata(\n            stan_model;\n            posterior_predictive_var=:y_hat,\n            observed_data=(; y),\n            log_likelihood_var=:log_lik,\n            coords=(; school=schools),\n            dims=NamedTuple(\n                k => (:school,) for k in (:y, :sigma, :theta, :log_lik, :y_hat)\n            ),\n        )\n    end\nend
\n
InferenceData
posterior
Dataset with dimensions: \n  Dim{:draw},\n  Dim{:chain},\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n  :mu    Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :tau   Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :theta Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)\n\nwith metadata Dict{String, Any} with 1 entry:\n  \"created_at\" => \"2023-12-22T04:15:38.213\"
posterior_predictive
Dataset with dimensions: \n  Dim{:draw},\n  Dim{:chain},\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n  :y_hat Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)\n\nwith metadata Dict{String, Any} with 1 entry:\n  \"created_at\" => \"2023-12-22T04:15:37.515\"
log_likelihood
Dataset with dimensions: \n  Dim{:draw},\n  Dim{:chain},\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n  :log_lik Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)\n\nwith metadata Dict{String, Any} with 1 entry:\n  \"created_at\" => \"2023-12-22T04:15:38.057\"
sample_stats
Dataset with dimensions: Dim{:draw}, Dim{:chain}\nand 7 layers:\n  :tree_depth      Int64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :energy          Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :diverging       Bool dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :acceptance_rate Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :n_steps         Int64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :lp              Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :step_size       Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n\nwith metadata Dict{String, Any} with 1 entry:\n  \"created_at\" => \"2023-12-22T04:15:37.708\"
observed_data
Dataset with dimensions: \n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n  :y Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 1 entry:\n  \"created_at\" => \"2023-12-22T04:15:38.341\"
\n\n
begin\n    plot_density(idata_stan; var_names=(:mu, :tau))\n    gcf()\nend
\n\n\n\n

Here is a plot showing where the Hamiltonian sampler had divergences:

\n\n
begin\n    plot_pair(\n        idata_stan;\n        coords=Dict(:school => [\"Choate\", \"Deerfield\", \"Phillips Andover\"]),\n        divergences=true,\n    )\n    gcf()\nend
\n\n\n\n

Environment

\n\n
using PlutoUI
\n\n\n
using Pkg, InteractiveUtils
\n\n\n
with_terminal(Pkg.status; color=false)
\n
Status `~/work/ArviZ.jl/ArviZ.jl/docs/Project.toml`\n  [cbdf2221] AlgebraOfGraphics v0.6.17\n  [131c737c] ArviZ v0.10.3 `~/work/ArviZ.jl/ArviZ.jl`\n  [2f96bb34] ArviZExampleData v0.1.8\n  [4a6e88f0] ArviZPythonPlots v0.1.3\n  [13f3f980] CairoMakie v0.11.4\n  [a93c6f00] DataFrames v1.6.1\n⌃ [0703355e] DimensionalData v0.24.13\n  [31c24e10] Distributions v0.25.104\n  [e30172f5] Documenter v1.2.1\n  [f6006082] EvoTrees v0.16.5\n  [b5cf5a8d] InferenceObjects v0.3.14\n  [be115224] MCMCDiagnosticTools v0.3.8\n  [a7f614a8] MLJBase v1.0.1\n  [614be32b] MLJIteration v0.6.0\n  [ce719bf2] PSIS v0.9.4\n  [359b1769] PlutoStaticHTML v6.0.18\n  [7f904dfe] PlutoUI v0.7.54\n  [7f36be82] PosteriorStats v0.1.4\n  [c1514b29] StanSample v7.6.0\n  [a19d573c] StatisticalMeasures v0.1.3\n  [2913bbd2] StatsBase v0.34.2\n  [fce5fe82] Turing v0.30.0\n  [f43a241f] Downloads v1.6.0\n  [37e2e46d] LinearAlgebra\n  [10745b16] Statistics v1.9.0\nInfo Packages marked with ⌃ have new versions available and may be upgradable.\n
\n\n
with_terminal(versioninfo)
\n
Julia Version 1.9.4\nCommit 8e5136fa297 (2023-11-14 08:46 UTC)\nBuild Info:\n  Official https://julialang.org/ release\nPlatform Info:\n  OS: Linux (x86_64-linux-gnu)\n  CPU: 4 × AMD EPYC 7763 64-Core Processor\n  WORD_SIZE: 64\n  LIBM: libopenlibm\n  LLVM: libLLVM-14.0.6 (ORCJIT, znver3)\n  Threads: 2 on 4 virtual cores\nEnvironment:\n  JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager\n  JULIA_PROJECT = /home/runner/work/ArviZ.jl/ArviZ.jl/docs/\n  JULIA_DEPOT_PATH = /home/runner/.julia:/opt/hostedtoolcache/julia/1.9.4/x64/local/share/julia:/opt/hostedtoolcache/julia/1.9.4/x64/share/julia\n  JULIA_NUM_THREADS = 2\n  JULIA_LOAD_PATH = @:@v#.#:@stdlib\n  JULIA_CMDSTAN_HOME = /home/runner/work/ArviZ.jl/ArviZ.jl/.cmdstan//cmdstan-2.33.1/\n  JULIA_REVISE_WORKER_ONLY = 1\n  JULIA_PYTHONCALL_EXE = /home/runner/work/ArviZ.jl/ArviZ.jl/docs/.CondaPkg/env/bin/python\n
\n\n","category":"page"},{"location":"quickstart/","page":"Quickstart","title":"Quickstart","text":"EditURL = \"https://github.com/arviz-devs/ArviZ.jl/blob/main/docs/src/quickstart.jl\"","category":"page"},{"location":"api/data/#data-api","page":"Data","title":"Data","text":"","category":"section"},{"location":"api/data/","page":"Data","title":"Data","text":"Pages = [\"data.md\"]","category":"page"},{"location":"api/data/#Inference-library-converters","page":"Data","title":"Inference library converters","text":"","category":"section"},{"location":"api/data/","page":"Data","title":"Data","text":"from_mcmcchains\nfrom_samplechains","category":"page"},{"location":"api/data/#ArviZ.from_mcmcchains","page":"Data","title":"ArviZ.from_mcmcchains","text":"from_mcmcchains(posterior::MCMCChains.Chains; kwargs...) -> InferenceData\nfrom_mcmcchains(; kwargs...) -> InferenceData\nfrom_mcmcchains(\n posterior::MCMCChains.Chains,\n posterior_predictive,\n predictions,\n log_likelihood;\n kwargs...\n) -> InferenceData\n\nConvert data in an MCMCChains.Chains format into an InferenceData.\n\nAny keyword argument below without an an explicitly annotated type above is allowed, so long as it can be passed to convert_to_inference_data.\n\nArguments\n\nposterior::MCMCChains.Chains: Draws from the posterior\n\nKeywords\n\nposterior_predictive::Any=nothing: Draws from the posterior predictive distribution or name(s) of predictive variables in posterior\npredictions: Out-of-sample predictions for the posterior.\nprior: Draws from the prior\nprior_predictive: Draws from the prior predictive distribution or name(s) of predictive variables in prior\nobserved_data: Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values.\nconstant_data: Model constants, data included in the model that are not modeled as random variables. Keys are parameter names.\npredictions_constant_data: Constants relevant to the model predictions (i.e. new x values in a linear regression).\nlog_likelihood: Pointwise log-likelihood for the data. It is recommended to use this argument as a named tuple whose keys are observed variable names and whose values are log likelihood arrays. Alternatively, provide the name of variable in posterior containing log likelihoods.\nlibrary=MCMCChains: Name of library that generated the chains\ncoords: Map from named dimension to named indices\ndims: Map from variable name to names of its dimensions\neltypes: Map from variable names to eltypes. This is primarily used to assign discrete eltypes to discrete variables that were stored in Chains as floats.\n\nReturns\n\nInferenceData: The data with groups corresponding to the provided data\n\n\n\n\n\n","category":"function"},{"location":"api/data/#ArviZ.from_samplechains","page":"Data","title":"ArviZ.from_samplechains","text":"from_samplechains(\n posterior=nothing;\n prior=nothing,\n library=SampleChains,\n kwargs...,\n) -> InferenceData\n\nConvert SampleChains samples to an InferenceData.\n\nEither posterior or prior may be a SampleChains.AbstractChain or SampleChains.MultiChain object.\n\nFor descriptions of remaining kwargs, see from_namedtuple.\n\n\n\n\n\n","category":"function"},{"location":"api/data/#IO-/-Conversion","page":"Data","title":"IO / Conversion","text":"","category":"section"},{"location":"api/data/","page":"Data","title":"Data","text":"from_netcdf\nto_netcdf","category":"page"},{"location":"api/data/#InferenceObjects.from_netcdf","page":"Data","title":"InferenceObjects.from_netcdf","text":"from_netcdf(path::AbstractString; kwargs...) -> InferenceData\n\nLoad an InferenceData from an unopened NetCDF file.\n\nRemaining kwargs are passed to NCDatasets.NCDataset. This method loads data eagerly. To instead load data lazily, pass an opened NCDataset to from_netcdf.\n\nnote: Note\nThis method requires that NCDatasets is loaded before it can be used.\n\nExamples\n\njulia> using InferenceObjects, NCDatasets\n\njulia> idata = from_netcdf(\"centered_eight.nc\")\nInferenceData with groups:\n > posterior\n > posterior_predictive\n > sample_stats\n > prior\n > observed_data\n\nfrom_netcdf(ds::NCDatasets.NCDataset; load_mode) -> InferenceData\n\nLoad an InferenceData from an opened NetCDF file.\n\nload_mode defaults to :lazy, which avoids reading variables into memory. Operations on these arrays will be slow. load_mode can also be :eager, which copies all variables into memory. It is then safe to close ds. If load_mode is :lazy and ds is closed after constructing InferenceData, using the variable arrays will have undefined behavior.\n\nExamples\n\nHere is how we might load an InferenceData from an InferenceData lazily from a web-hosted NetCDF file.\n\njulia> using HTTP, InferenceObjects, NCDatasets\n\njulia> resp = HTTP.get(\"https://github.com/arviz-devs/arviz_example_data/blob/main/data/centered_eight.nc?raw=true\");\n\njulia> ds = NCDataset(\"centered_eight\", \"r\"; memory = resp.body);\n\njulia> idata = from_netcdf(ds)\nInferenceData with groups:\n > posterior\n > posterior_predictive\n > sample_stats\n > prior\n > observed_data\n\njulia> idata_copy = copy(idata); # disconnect from the loaded dataset\n\njulia> close(ds);\n\n\n\n\n\n","category":"function"},{"location":"api/data/#InferenceObjects.to_netcdf","page":"Data","title":"InferenceObjects.to_netcdf","text":"to_netcdf(data, dest::AbstractString; group::Symbol=:posterior, kwargs...)\nto_netcdf(data, dest::NCDatasets.NCDataset; group::Symbol=:posterior)\n\nWrite data to a NetCDF file.\n\ndata is any type that can be converted to an InferenceData using convert_to_inference_data. If not an InferenceData, then group specifies which group the data represents.\n\ndest specifies either the path to the NetCDF file or an opened NetCDF file. If dest is a path, remaining kwargs are passed to NCDatasets.NCDataset.\n\nnote: Note\nThis method requires that NCDatasets is loaded before it can be used.\n\nExamples\n\njulia> using InferenceObjects, NCDatasets\n\njulia> idata = from_namedtuple((; x = randn(4, 100, 3), z = randn(4, 100)))\nInferenceData with groups:\n > posterior\n\njulia> to_netcdf(idata, \"data.nc\")\n\"data.nc\"\n\n\n\n\n\n","category":"function"},{"location":"api/diagnostics/#diagnostics-api","page":"Diagnostics","title":"Diagnostics","text":"","category":"section"},{"location":"api/diagnostics/","page":"Diagnostics","title":"Diagnostics","text":"Pages = [\"diagnostics.md\"]","category":"page"},{"location":"api/diagnostics/#bfmi","page":"Diagnostics","title":"Bayesian fraction of missing information","text":"","category":"section"},{"location":"api/diagnostics/","page":"Diagnostics","title":"Diagnostics","text":"MCMCDiagnosticTools.bfmi","category":"page"},{"location":"api/diagnostics/#MCMCDiagnosticTools.bfmi","page":"Diagnostics","title":"MCMCDiagnosticTools.bfmi","text":"bfmi(energy::AbstractVector{<:Real}) -> Real\nbfmi(energy::AbstractMatrix{<:Real}; dims::Int=1) -> AbstractVector{<:Real}\n\nCalculate the estimated Bayesian fraction of missing information (BFMI).\n\nWhen sampling with Hamiltonian Monte Carlo (HMC), BFMI quantifies how well momentum resampling matches the marginal energy distribution.\n\nThe current advice is that values smaller than 0.3 indicate poor sampling. However, this threshold is provisional and may change. A BFMI value below the threshold often indicates poor adaptation of sampling parameters or that the target distribution has heavy tails that were not well explored by the Markov chain.\n\nFor more information, see Section 6.1 of [Betancourt2018] or [Betancourt2016] for a complete account.\n\nenergy is either a vector of Hamiltonian energies of draws or a matrix of energies of draws for multiple chains. dims indicates the dimension in energy that contains the draws. The default dims=1 assumes energy has the shape draws or (draws, chains). If a different shape is provided, dims must be set accordingly.\n\nIf energy is a vector, a single BFMI value is returned. Otherwise, a vector of BFMI values for each chain is returned.\n\n[Betancourt2018]: Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]\n\n[Betancourt2016]: Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]\n\n\n\n\n\n","category":"function"},{"location":"api/diagnostics/#ess_rhat","page":"Diagnostics","title":"Effective sample size and widehatR diagnostic","text":"","category":"section"},{"location":"api/diagnostics/","page":"Diagnostics","title":"Diagnostics","text":"MCMCDiagnosticTools.ess\nMCMCDiagnosticTools.rhat\nMCMCDiagnosticTools.ess_rhat","category":"page"},{"location":"api/diagnostics/#MCMCDiagnosticTools.ess","page":"Diagnostics","title":"MCMCDiagnosticTools.ess","text":"ess(data::InferenceData; kwargs...) -> Dataset\ness(data::Dataset; kwargs...) -> Dataset\n\nCalculate the effective sample size (ESS) for each parameter in the data.\n\n\n\n\n\ness(\n samples::AbstractArray{<:Union{Missing,Real}};\n kind=:bulk,\n relative::Bool=false,\n autocov_method=AutocovMethod(),\n split_chains::Int=2,\n maxlag::Int=250,\n kwargs...\n)\n\nEstimate the effective sample size (ESS) of the samples of shape (draws, [chains[, parameters...]]) with the autocov_method.\n\nOptionally, the kind of ESS estimate to be computed can be specified (see below). Some kinds accept additional kwargs.\n\nIf relative is true, the relative ESS is returned, i.e. ess / (draws * chains).\n\nsplit_chains indicates the number of chains each chain is split into. When split_chains > 1, then the diagnostics check for within-chain convergence. When d = mod(draws, split_chains) > 0, i.e. the chains cannot be evenly split, then 1 draw is discarded after each of the first d splits within each chain. There must be at least 3 draws in each chain after splitting.\n\nmaxlag indicates the maximum lag for which autocovariance is computed and must be greater than 0.\n\nFor a given estimand, it is recommended that the ESS is at least 100 * chains and that widehatR 101.[VehtariGelman2021]\n\nSee also: AutocovMethod, FFTAutocovMethod, BDAAutocovMethod, rhat, ess_rhat, mcse\n\nKinds of ESS estimates\n\nIf kind isa a Symbol, it may take one of the following values:\n\n:bulk: basic ESS computed on rank-normalized draws. This kind diagnoses poor convergence in the bulk of the distribution due to trends or different locations of the chains.\n:tail: minimum of the quantile-ESS for the symmetric quantiles where tail_prob=0.1 is the probability in the tails. This kind diagnoses poor convergence in the tails of the distribution. If this kind is chosen, kwargs may contain a tail_prob keyword.\n:basic: basic ESS, equivalent to specifying kind=Statistics.mean.\n\nnote: Note\nWhile Bulk-ESS is conceptually related to basic ESS, it is well-defined even if the chains do not have finite variance.[VehtariGelman2021] For each parameter, rank-normalization proceeds by first ranking the inputs using \"tied ranking\" and then transforming the ranks to normal quantiles so that the result is standard normally distributed. This transform is monotonic.\n\nOtherwise, kind specifies one of the following estimators, whose ESS is to be estimated:\n\nStatistics.mean\nStatistics.median\nStatistics.std\nStatsBase.mad\nBase.Fix2(Statistics.quantile, p::Real)\n\n[VehtariGelman2021]: Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved widehat R for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008\n\n\n\n\n\n","category":"function"},{"location":"api/diagnostics/#MCMCDiagnosticTools.rhat","page":"Diagnostics","title":"MCMCDiagnosticTools.rhat","text":"rhat(data::InferenceData; kwargs...) -> Dataset\nrhat(data::Dataset; kwargs...) -> Dataset\n\nCalculate the widehatR diagnostic for each parameter in the data.\n\n\n\n\n\nrhat(samples::AbstractArray{Union{Real,Missing}}; kind::Symbol=:rank, split_chains=2)\n\nCompute the widehatR diagnostics for each parameter in samples of shape (draws, [chains[, parameters...]]).[VehtariGelman2021]\n\nkind indicates the kind of widehatR to compute (see below).\n\nsplit_chains indicates the number of chains each chain is split into. When split_chains > 1, then the diagnostics check for within-chain convergence. When d = mod(draws, split_chains) > 0, i.e. the chains cannot be evenly split, then 1 draw is discarded after each of the first d splits within each chain.\n\nSee also ess, ess_rhat, rstar\n\nKinds of widehatR\n\nThe following kinds are supported:\n\n:rank: maximum of widehatR with kind=:bulk and kind=:tail.\n:bulk: basic widehatR computed on rank-normalized draws. This kind diagnoses poor convergence in the bulk of the distribution due to trends or different locations of the chains.\n:tail: widehatR computed on draws folded around the median and then rank-normalized. This kind diagnoses poor convergence in the tails of the distribution due to different scales of the chains.\n:basic: Classic widehatR.\n\n[VehtariGelman2021]: Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved widehat R for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008\n\n\n\n\n\n","category":"function"},{"location":"api/diagnostics/#MCMCDiagnosticTools.ess_rhat","page":"Diagnostics","title":"MCMCDiagnosticTools.ess_rhat","text":"ess_rhat(data::InferenceData; kwargs...) -> Dataset\ness_rhat(data::Dataset; kwargs...) -> Dataset\n\nCalculate the effective sample size (ESS) and widehatR diagnostic for each parameter in the data.\n\n\n\n\n\ness_rhat(\n samples::AbstractArray{<:Union{Missing,Real}};\n kind::Symbol=:rank,\n kwargs...,\n) -> NamedTuple{(:ess, :rhat)}\n\nEstimate the effective sample size and widehatR of the samples of shape (draws, [chains[, parameters...]]).\n\nWhen both ESS and widehatR are needed, this method is often more efficient than calling ess and rhat separately.\n\nSee rhat for a description of supported kinds and ess for a description of kwargs.\n\n\n\n\n\n","category":"function"},{"location":"api/diagnostics/","page":"Diagnostics","title":"Diagnostics","text":"The following autocovariance methods are supported:","category":"page"},{"location":"api/diagnostics/","page":"Diagnostics","title":"Diagnostics","text":"MCMCDiagnosticTools.AutocovMethod\nMCMCDiagnosticTools.FFTAutocovMethod\nMCMCDiagnosticTools.BDAAutocovMethod","category":"page"},{"location":"api/diagnostics/#MCMCDiagnosticTools.AutocovMethod","page":"Diagnostics","title":"MCMCDiagnosticTools.AutocovMethod","text":"AutocovMethod <: AbstractAutocovMethod\n\nThe AutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains.\n\nIt is is based on the discussion by [VehtariGelman2021] and uses the biased estimator of the autocovariance, as discussed by [Geyer1992].\n\n[VehtariGelman2021]: Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved widehat R for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008\n\n[Geyer1992]: Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.\n\n\n\n\n\n","category":"type"},{"location":"api/diagnostics/#MCMCDiagnosticTools.FFTAutocovMethod","page":"Diagnostics","title":"MCMCDiagnosticTools.FFTAutocovMethod","text":"FFTAutocovMethod <: AbstractAutocovMethod\n\nThe FFTAutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains.\n\nThe algorithm is the same as the one of AutocovMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation.\n\ninfo: Info\nTo be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl.\n\n\n\n\n\n","category":"type"},{"location":"api/diagnostics/#MCMCDiagnosticTools.BDAAutocovMethod","page":"Diagnostics","title":"MCMCDiagnosticTools.BDAAutocovMethod","text":"BDAAutocovMethod <: AbstractAutocovMethod\n\nThe BDAAutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains.\n\nIt is is based on the discussion by [VehtariGelman2021]. and uses the variogram estimator of the autocorrelation function discussed by [BDA3].\n\n[VehtariGelman2021]: Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved widehat R for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008\n\n[BDA3]: Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.\n\n\n\n\n\n","category":"type"},{"location":"api/diagnostics/#mcse","page":"Diagnostics","title":"Monte Carlo standard error","text":"","category":"section"},{"location":"api/diagnostics/","page":"Diagnostics","title":"Diagnostics","text":"MCMCDiagnosticTools.mcse","category":"page"},{"location":"api/diagnostics/#MCMCDiagnosticTools.mcse","page":"Diagnostics","title":"MCMCDiagnosticTools.mcse","text":"mcse(data::InferenceData; kwargs...) -> Dataset\nmcse(data::Dataset; kwargs...) -> Dataset\n\nCalculate the Monte Carlo standard error (MCSE) for each parameter in the data.\n\n\n\n\n\nmcse(samples::AbstractArray{<:Union{Missing,Real}}; kind=Statistics.mean, kwargs...)\n\nEstimate the Monte Carlo standard errors (MCSE) of the estimator kind applied to samples of shape (draws, [chains[, parameters...]]).\n\nSee also: ess\n\nKinds of MCSE estimates\n\nThe estimator whose MCSE should be estimated is specified with kind. kind must accept a vector of the same eltype as samples and return a real estimate.\n\nFor the following estimators, the effective sample size ess and an estimate of the asymptotic variance are used to compute the MCSE, and kwargs are forwarded to ess:\n\nStatistics.mean\nStatistics.median\nStatistics.std\nBase.Fix2(Statistics.quantile, p::Real)\n\nFor other estimators, the subsampling bootstrap method (SBM)[FlegalJones2011][Flegal2012] is used as a fallback, and the only accepted kwargs are batch_size, which indicates the size of the overlapping batches used to estimate the MCSE, defaulting to floor(Int, sqrt(draws * chains)). Note that SBM tends to underestimate the MCSE, especially for highly autocorrelated chains. One should verify that autocorrelation is low by checking the bulk- and tail-ESS values.\n\n[FlegalJones2011]: Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf\n\n[Flegal2012]: Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18\n\n\n\n\n\n","category":"function"},{"location":"api/diagnostics/#rstar","page":"Diagnostics","title":"R^* diagnostic","text":"","category":"section"},{"location":"api/diagnostics/","page":"Diagnostics","title":"Diagnostics","text":"MCMCDiagnosticTools.rstar","category":"page"},{"location":"api/diagnostics/#MCMCDiagnosticTools.rstar","page":"Diagnostics","title":"MCMCDiagnosticTools.rstar","text":"rstar(\n rng::Random.AbstractRNG=Random.default_rng(),\n classifier,\n data::Union{InferenceData,Dataset};\n kwargs...,\n)\n\nCalculate the R^* diagnostic for the data.\n\n\n\n\n\nrstar(\n rng::Random.AbstractRNG=Random.default_rng(),\n classifier,\n samples,\n chain_indices::AbstractVector{Int};\n subset::Real=0.7,\n split_chains::Int=2,\n verbosity::Int=0,\n)\n\nCompute the R^* convergence statistic of the table samples with the classifier.\n\nsamples must be either an AbstractMatrix, an AbstractVector, or a table (i.e. implements the Tables.jl interface) whose rows are draws and whose columns are parameters.\n\nchain_indices indicates the chain ids of each row of samples.\n\nThis method supports ragged chains, i.e. chains of nonequal lengths.\n\n\n\n\n\nrstar(\n rng::Random.AbstractRNG=Random.default_rng(),\n classifier,\n samples::AbstractArray{<:Real};\n subset::Real=0.7,\n split_chains::Int=2,\n verbosity::Int=0,\n)\n\nCompute the R^* convergence statistic of the samples with the classifier.\n\nsamples is an array of draws with the shape (draws, [chains[, parameters...]]).`\n\nThis implementation is an adaption of algorithms 1 and 2 described by Lambert and Vehtari.\n\nThe classifier has to be a supervised classifier of the MLJ framework (see the MLJ documentation for a list of supported models). It is trained with a subset of the samples from each chain. Each chain is split into split_chains separate chains to additionally check for within-chain convergence. The training of the classifier can be inspected by adjusting the verbosity level.\n\nIf the classifier is deterministic, i.e., if it predicts a class, the value of the R^* statistic is returned (algorithm 1). If the classifier is probabilistic, i.e., if it outputs probabilities of classes, the scaled Poisson-binomial distribution of the R^* statistic is returned (algorithm 2).\n\nnote: Note\nThe correctness of the statistic depends on the convergence of the classifier used internally in the statistic.\n\nExamples\n\njulia> using MLJBase, MLJIteration, EvoTrees, Statistics, StatisticalMeasures\n\njulia> samples = fill(4.0, 100, 3, 2);\n\nOne can compute the distribution of the R^* statistic (algorithm 2) with a probabilistic classifier. For instance, we can use a gradient-boosted trees model with nrounds = 100 sequentially stacked trees and learning rate eta = 0.05:\n\njulia> model = EvoTreeClassifier(; nrounds=100, eta=0.05);\n\njulia> distribution = rstar(model, samples);\n\njulia> round(mean(distribution); digits=2)\n1.0f0\n\nNote, however, that it is recommended to determine nrounds based on early-stopping. With the MLJ framework, this can be achieved in the following way (see the MLJ documentation for additional explanations):\n\njulia> model = IteratedModel(;\n model=EvoTreeClassifier(; eta=0.05),\n iteration_parameter=:nrounds,\n resampling=Holdout(),\n measures=log_loss,\n controls=[Step(5), Patience(2), NumberLimit(100)],\n retrain=true,\n );\n\njulia> distribution = rstar(model, samples);\n\njulia> round(mean(distribution); digits=2)\n1.0f0\n\nFor deterministic classifiers, a single R^* statistic (algorithm 1) is returned. Deterministic classifiers can also be derived from probabilistic classifiers by e.g. predicting the mode. In MLJ this corresponds to a pipeline of models.\n\njulia> evotree_deterministic = Pipeline(model; operation=predict_mode);\n\njulia> value = rstar(evotree_deterministic, samples);\n\njulia> round(value; digits=2)\n1.0\n\nReferences\n\nLambert, B., & Vehtari, A. (2020). R^*: A robust MCMC convergence diagnostic with uncertainty using decision tree classifiers.\n\n\n\n\n\n","category":"function"},{"location":"api/#api","page":"API Overview","title":"API Overview","text":"","category":"section"},{"location":"api/","page":"API Overview","title":"API Overview","text":"Pages = [\"data.md\", \"dataset.md\", \"diagnostics.md\", \"inference_data.md\", \"stats.md\"]\nDepth = 1","category":"page"},{"location":"creating_custom_plots/","page":"Creating custom plots","title":"Creating custom plots","text":"\n\n\n

Creating custom plots

\n\n\n\n\n\n

While ArviZ includes many plotting functions for visualizing the data stored in InferenceData objects, you will often need to construct custom plots, or you may want to tweak some of our plots in your favorite plotting package.

In this tutorial, we will show you a few useful techniques you can use to construct these plots using Julia's plotting packages. For demonstration purposes, we'll use Makie.jl and AlgebraOfGraphics.jl, which can consume Dataset objects since they implement the Tables interface. However, we could just as easily have used StatsPlots.jl.

\n\n
begin\n    using ArviZ, ArviZExampleData, DimensionalData, DataFrames, Statistics\n    using AlgebraOfGraphics, CairoMakie\n    using AlgebraOfGraphics: density\n    set_aog_theme!()\nend;
\n\n\n\n

We'll start by loading some draws from an implementation of the non-centered parameterization of the 8 schools model. In this parameterization, the model has some sampling issues.

\n\n
idata = load_example_data(\"centered_eight\")
\n
InferenceData
posterior
Dataset with dimensions: \n  Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n  Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n  :mu    Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n  :tau   Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n  \"created_at\" => \"2022-10-13T14:37:37.315398\"\n  \"inference_library_version\" => \"4.2.2\"\n  \"sampling_time\" => 7.48011\n  \"tuning_steps\" => 1000\n  \"arviz_version\" => \"0.13.0.dev0\"\n  \"inference_library\" => \"pymc\"
posterior_predictive
Dataset with dimensions: \n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n  Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n  Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n  :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n  \"created_at\" => \"2022-10-13T14:37:41.460544\"\n  \"inference_library_version\" => \"4.2.2\"\n  \"arviz_version\" => \"0.13.0.dev0\"\n  \"inference_library\" => \"pymc\"
log_likelihood
Dataset with dimensions: \n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n  Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n  Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n  :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n  \"created_at\" => \"2022-10-13T14:37:37.487399\"\n  \"inference_library_version\" => \"4.2.2\"\n  \"arviz_version\" => \"0.13.0.dev0\"\n  \"inference_library\" => \"pymc\"
sample_stats
Dataset with dimensions: \n  Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n  Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 16 layers:\n  :max_energy_error    Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :energy_error        Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :lp                  Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :index_in_trajectory Int64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :acceptance_rate     Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :diverging           Bool dims: Dim{:draw}, Dim{:chain} (500×4)\n  :process_time_diff   Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :n_steps             Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :perf_counter_start  Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :largest_eigval      Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (500×4)\n  :smallest_eigval     Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (500×4)\n  :step_size_bar       Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :step_size           Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :energy              Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :tree_depth          Int64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :perf_counter_diff   Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n  \"created_at\" => \"2022-10-13T14:37:37.324929\"\n  \"inference_library_version\" => \"4.2.2\"\n  \"sampling_time\" => 7.48011\n  \"tuning_steps\" => 1000\n  \"arviz_version\" => \"0.13.0.dev0\"\n  \"inference_library\" => \"pymc\"
prior
Dataset with dimensions: \n  Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n  Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points,\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n  :tau   Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n  :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n  :mu    Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n  \"created_at\" => \"2022-10-13T14:37:26.602116\"\n  \"inference_library_version\" => \"4.2.2\"\n  \"arviz_version\" => \"0.13.0.dev0\"\n  \"inference_library\" => \"pymc\"
prior_predictive
Dataset with dimensions: \n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n  Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n  Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points\nand 1 layer:\n  :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n  \"created_at\" => \"2022-10-13T14:37:26.604969\"\n  \"inference_library_version\" => \"4.2.2\"\n  \"arviz_version\" => \"0.13.0.dev0\"\n  \"inference_library\" => \"pymc\"
observed_data
Dataset with dimensions: \n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n  :obs Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n  \"created_at\" => \"2022-10-13T14:37:26.606375\"\n  \"inference_library_version\" => \"4.2.2\"\n  \"arviz_version\" => \"0.13.0.dev0\"\n  \"inference_library\" => \"pymc\"
constant_data
Dataset with dimensions: \n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n  :scores Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n  \"created_at\" => \"2022-10-13T14:37:26.607471\"\n  \"inference_library_version\" => \"4.2.2\"\n  \"arviz_version\" => \"0.13.0.dev0\"\n  \"inference_library\" => \"pymc\"
\n\n
idata.posterior
\n
Dataset with dimensions: \n  Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n  Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n  :mu    Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n  :tau   Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n  \"created_at\"                => \"2022-10-13T14:37:37.315398\"\n  \"inference_library_version\" => \"4.2.2\"\n  \"sampling_time\"             => 7.48011\n  \"tuning_steps\"              => 1000\n  \"arviz_version\"             => \"0.13.0.dev0\"\n  \"inference_library\"         => \"pymc\"
\n\n\n

The plotting functions we'll be using interact with a tabular view of a Dataset. Let's see what that view looks like for a Dataset:

\n\n
df = DataFrame(idata.posterior)
\n
drawchainschoolmuthetatau
100\"Choate\"7.871812.32074.72574
210\"Choate\"3.3845511.28563.90899
320\"Choate\"9.100485.708514.84403
430\"Choate\"7.3042910.03731.8567
540\"Choate\"9.879689.149154.74841
650\"Choate\"7.0420314.73593.51387
760\"Choate\"10.378514.3044.20898
870\"Choate\"10.0613.32982.6834
980\"Choate\"10.425310.44981.16889
1090\"Choate\"10.810811.47311.21052
...
160004993\"Mt. Hermon\"3.404461.295054.46125
\n\n\n

The tabular view includes dimensions and variables as columns.

When variables with different dimensions are flattened into a tabular form, there's always some duplication of values. As a simple case, note that chain, draw, and school all have repeated values in the above table.

In this case, theta has the school dimension, but tau doesn't, so the values of tau will be repeated in the table for each value of school.

\n\n
df[df.school .== Ref(\"Choate\"), :].tau == df[df.school .== Ref(\"Deerfield\"), :].tau
\n
true
\n\n\n

In our first example, this will be important.

Here, let's construct a trace plot. Besides idata, all functions and types in the following cell are defined in AlgebraOfGraphics or Makie:

\n\n
draw(\n    data(idata.posterior.mu) *\n    mapping(:draw, :mu; color=:chain => nonnumeric) *\n    visual(Lines; alpha=0.8),\n)
\n\n\n\n

Note the line idata.posterior.mu. If we had just used idata.posterior, the plot would have looked more-or-less the same, but there would be artifacts due to mu being copied many times. By selecting mu directly, all other dimensions are discarded, so each value of mu appears in the plot exactly once.

When examining an MCMC trace plot, we want to see a \"fuzzy caterpillar\". Instead we see a few places where the Markov chains froze. We can do the same for theta as well, but it's more useful here to separate these draws by school.

\n\n
draw(\n    data(idata.posterior) *\n    mapping(:draw, :theta; layout=:school, color=:chain => nonnumeric) *\n    visual(Lines; alpha=0.8),\n)
\n\n\n\n

Suppose we want to compare tau with theta for two different schools. To do so, we use InferenceDatas indexing syntax to subset the data.

\n\n
draw(\n    data(idata[:posterior, school=At([\"Choate\", \"Deerfield\"])]) *\n    mapping(:theta, :tau; color=:school) *\n    density() *\n    visual(Contour; levels=10),\n)
\n\n\n\n

We can also compare the density plots constructed from each chain for different schools.

\n\n
draw(\n    data(idata.posterior) *\n    mapping(:theta; layout=:school, color=:chain => nonnumeric) *\n    density(),\n)
\n\n\n\n

If we want to compare many schools in a single plot, an ECDF plot is more convenient.

\n\n
draw(\n    data(idata.posterior) * mapping(:theta; color=:school => nonnumeric) * visual(ECDFPlot);\n    axis=(; ylabel=\"probability\"),\n)
\n\n\n\n

So far we've just plotted data from one group, but we often want to combine data from multiple groups in one plot. The simplest way to do this is to create the plot out of multiple layers. Here we use this approach to plot the observations over the posterior predictive distribution.

\n\n
draw(\n    (data(idata.posterior_predictive) * mapping(:obs; layout=:school) * density()) +\n    (data(idata.observed_data) * mapping(:obs, :obs => zero => \"\"; layout=:school)),\n)
\n\n\n\n

Another option is to combine the groups into a single dataset.

Here we compare the prior and posterior. Since the prior has 1 chain and the posterior has 4 chains, if we were to combine them into a table, the structure would need to be ragged. This is not currently supported.

We can then either plot the two distributions separately as we did before, or we can compare a single chain from each group. This is what we'll do here. To concatenate the two groups, we introduce a new named dimension using DimensionalData.Dim.

\n\n
draw(\n    data(\n        cat(\n            idata.posterior[chain=[1]], idata.prior; dims=Dim{:group}([:posterior, :prior])\n        )[:mu],\n    ) *\n    mapping(:mu; color=:group) *\n    histogram(; bins=20) *\n    visual(; alpha=0.8);\n    axis=(; ylabel=\"probability\"),\n)
\n\n\n\n

From the trace plots, we suspected the geometry of this posterior was bad. Let's highlight divergent transitions. To do so, we merge posterior and samplestats, which can do with merge since they share no common variable names.

\n\n
draw(\n    data(merge(idata.posterior, idata.sample_stats)) * mapping(\n        :theta,\n        :tau;\n        layout=:school,\n        color=:diverging,\n        markersize=:diverging => (d -> d ? 5 : 2),\n    ),\n)
\n\n\n\n

When we try building more complex plots, we may need to build new Datasets from our existing ones.

One example of this is the corner plot. To build this plot, we need to make a copy of theta with a copy of the school dimension.

\n\n
let\n    theta = idata.posterior.theta[school=1:4]\n    theta2 = rebuild(set(theta; school=:school2); name=:theta2)\n    plot_data = Dataset(theta, theta2, idata.sample_stats.diverging)\n    draw(\n        data(plot_data) * mapping(\n            :theta,\n            :theta2 => \"theta\";\n            col=:school,\n            row=:school2,\n            color=:diverging,\n            markersize=:diverging => (d -> d ? 3 : 1),\n        );\n        figure=(; figsize=(5, 5)),\n        axis=(; aspect=1),\n    )\nend
\n\n\n","category":"page"},{"location":"creating_custom_plots/#Environment","page":"Creating custom plots","title":"Environment","text":"","category":"section"},{"location":"creating_custom_plots/","page":"Creating custom plots","title":"Creating custom plots","text":"
\n
\n\n
using Pkg, InteractiveUtils
\n\n\n
using PlutoUI
\n\n\n
with_terminal(Pkg.status; color=false)
\n
Status `~/work/ArviZ.jl/ArviZ.jl/docs/Project.toml`\n  [cbdf2221] AlgebraOfGraphics v0.6.17\n  [131c737c] ArviZ v0.10.3 `~/work/ArviZ.jl/ArviZ.jl`\n  [2f96bb34] ArviZExampleData v0.1.8\n  [4a6e88f0] ArviZPythonPlots v0.1.3\n  [13f3f980] CairoMakie v0.11.4\n  [a93c6f00] DataFrames v1.6.1\n⌃ [0703355e] DimensionalData v0.24.13\n  [31c24e10] Distributions v0.25.104\n  [e30172f5] Documenter v1.2.1\n  [f6006082] EvoTrees v0.16.5\n  [b5cf5a8d] InferenceObjects v0.3.14\n  [be115224] MCMCDiagnosticTools v0.3.8\n  [a7f614a8] MLJBase v1.0.1\n  [614be32b] MLJIteration v0.6.0\n  [ce719bf2] PSIS v0.9.4\n  [359b1769] PlutoStaticHTML v6.0.18\n  [7f904dfe] PlutoUI v0.7.54\n  [7f36be82] PosteriorStats v0.1.4\n  [c1514b29] StanSample v7.6.0\n  [a19d573c] StatisticalMeasures v0.1.3\n  [2913bbd2] StatsBase v0.34.2\n  [fce5fe82] Turing v0.30.0\n  [f43a241f] Downloads v1.6.0\n  [37e2e46d] LinearAlgebra\n  [10745b16] Statistics v1.9.0\nInfo Packages marked with ⌃ have new versions available and may be upgradable.\n
\n\n
with_terminal(versioninfo)
\n
Julia Version 1.9.4\nCommit 8e5136fa297 (2023-11-14 08:46 UTC)\nBuild Info:\n  Official https://julialang.org/ release\nPlatform Info:\n  OS: Linux (x86_64-linux-gnu)\n  CPU: 4 × AMD EPYC 7763 64-Core Processor\n  WORD_SIZE: 64\n  LIBM: libopenlibm\n  LLVM: libLLVM-14.0.6 (ORCJIT, znver3)\n  Threads: 2 on 4 virtual cores\nEnvironment:\n  JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager\n  JULIA_PROJECT = /home/runner/work/ArviZ.jl/ArviZ.jl/docs/\n  JULIA_DEPOT_PATH = /home/runner/.julia:/opt/hostedtoolcache/julia/1.9.4/x64/local/share/julia:/opt/hostedtoolcache/julia/1.9.4/x64/share/julia\n  JULIA_NUM_THREADS = 2\n  JULIA_LOAD_PATH = @:@v#.#:@stdlib\n  JULIA_CMDSTAN_HOME = /home/runner/work/ArviZ.jl/ArviZ.jl/.cmdstan//cmdstan-2.33.1/\n  JULIA_REVISE_WORKER_ONLY = 1\n
\n\n","category":"page"},{"location":"creating_custom_plots/","page":"Creating custom plots","title":"Creating custom plots","text":"EditURL = \"https://github.com/arviz-devs/ArviZ.jl/blob/main/docs/src/creating_custom_plots.jl\"","category":"page"},{"location":"api/stats/#stats-api","page":"Stats","title":"Stats","text":"","category":"section"},{"location":"api/stats/","page":"Stats","title":"Stats","text":"Pages = [\"stats.md\"]","category":"page"},{"location":"api/stats/#Summary-statistics","page":"Stats","title":"Summary statistics","text":"","category":"section"},{"location":"api/stats/","page":"Stats","title":"Stats","text":"SummaryStats\ndefault_summary_stats\ndefault_stats\ndefault_diagnostics\nsummarize\nsummarystats","category":"page"},{"location":"api/stats/#PosteriorStats.SummaryStats","page":"Stats","title":"PosteriorStats.SummaryStats","text":"A container for a column table of values computed by summarize.\n\nThis object implements the Tables and TableTraits interfaces and has a custom show method.\n\nname: The name of the collection of summary statistics, used as the table title in display.\ndata: The summary statistics for each parameter, with an optional first column parameter containing the parameter names.\n\n\n\n\n\n","category":"type"},{"location":"api/stats/#PosteriorStats.default_summary_stats","page":"Stats","title":"PosteriorStats.default_summary_stats","text":"default_summary_stats(focus=Statistics.mean; kwargs...)\n\nCombinatiton of default_stats and default_diagnostics to be used with summarize.\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PosteriorStats.default_stats","page":"Stats","title":"PosteriorStats.default_stats","text":"default_stats(focus=Statistics.mean; prob_interval=0.94, kwargs...)\n\nDefault statistics to be computed with summarize.\n\nThe value of focus determines the statistics to be returned:\n\nStatistics.mean: mean, std, hdi_3%, hdi_97%\nStatistics.median: median, mad, eti_3%, eti_97%\n\nIf prob_interval is set to a different value than the default, then different HDI and ETI statistics are computed accordingly. hdi refers to the highest-density interval, while eti refers to the equal-tailed interval (i.e. the credible interval computed from symmetric quantiles).\n\nSee also: hdi\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PosteriorStats.default_diagnostics","page":"Stats","title":"PosteriorStats.default_diagnostics","text":"default_diagnostics(focus=Statistics.mean; kwargs...)\n\nDefault diagnostics to be computed with summarize.\n\nThe value of focus determines the diagnostics to be returned:\n\nStatistics.mean: mcse_mean, mcse_std, ess_tail, ess_bulk, rhat\nStatistics.median: mcse_median, ess_tail, ess_bulk, rhat\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PosteriorStats.summarize","page":"Stats","title":"PosteriorStats.summarize","text":"summarize(data, stats_funs...; name=\"SummaryStats\", [var_names]) -> SummaryStats\n\nCompute the summary statistics in stats_funs on each param in data.\n\nstats_funs is a collection of functions that reduces a matrix with shape (draws, chains) to a scalar or a collection of scalars. Alternatively, an item in stats_funs may be a Pair of the form name => fun specifying the name to be used for the statistic or of the form (name1, ...) => fun when the function returns a collection. When the function returns a collection, the names in this latter format must be provided.\n\nIf no stats functions are provided, then those specified in default_summary_stats are computed.\n\nvar_names specifies the names of the parameters in data. If not provided, the names are inferred from data.\n\nTo support computing summary statistics from a custom object, overload this method specifying the type of data.\n\nSee also SummaryStats, default_summary_stats, default_stats, default_diagnostics.\n\nExamples\n\nCompute mean, std and the Monte Carlo standard error (MCSE) of the mean estimate:\n\njulia> using Statistics, StatsBase\n\njulia> x = randn(1000, 4, 3) .+ reshape(0:10:20, 1, 1, :);\n\njulia> summarize(x, mean, std, :mcse_mean => sem; name=\"Mean/Std\")\nMean/Std\n mean std mcse_mean\n 1 0.0003 0.990 0.016\n 2 10.02 0.988 0.016\n 3 19.98 0.988 0.016\n\nAvoid recomputing the mean by using mean_and_std, and provide parameter names:\n\njulia> summarize(x, (:mean, :std) => mean_and_std, mad; var_names=[:a, :b, :c])\nSummaryStats\n mean std mad\n a 0.000305 0.990 0.978\n b 10.0 0.988 0.995\n c 20.0 0.988 0.979\n\nNote that when an estimator and its MCSE are both computed, the MCSE is used to determine the number of significant digits that will be displayed.\n\njulia> summarize(x; var_names=[:a, :b, :c])\nSummaryStats\n mean std hdi_3% hdi_97% mcse_mean mcse_std ess_tail ess_bulk r ⋯\n a 0.0003 0.99 -1.92 1.78 0.016 0.012 3567 3663 1 ⋯\n b 10.02 0.99 8.17 11.9 0.016 0.011 3841 3906 1 ⋯\n c 19.98 0.99 18.1 21.9 0.016 0.012 3892 3749 1 ⋯\n 1 column omitted\n\nCompute just the statistics with an 89% HDI on all parameters, and provide the parameter names:\n\njulia> summarize(x, default_stats(; prob_interval=0.89)...; var_names=[:a, :b, :c])\nSummaryStats\n mean std hdi_5.5% hdi_94.5%\n a 0.000305 0.990 -1.63 1.52\n b 10.0 0.988 8.53 11.6\n c 20.0 0.988 18.5 21.6\n\nCompute the summary stats focusing on Statistics.median:\n\njulia> summarize(x, default_summary_stats(median)...; var_names=[:a, :b, :c])\nSummaryStats\n median mad eti_3% eti_97% mcse_median ess_tail ess_median rhat\n a 0.004 0.978 -1.83 1.89 0.020 3567 3336 1.00\n b 10.02 0.995 8.17 11.9 0.023 3841 3787 1.00\n c 19.99 0.979 18.1 21.9 0.020 3892 3829 1.00\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#StatsBase.summarystats","page":"Stats","title":"StatsBase.summarystats","text":"summarystats(data::InferenceData; group=:posterior, kwargs...) -> SummaryStats\nsummarystats(data::Dataset; kwargs...) -> SummaryStats\n\nCompute default summary statistics for the data using summarize.\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#General-statistics","page":"Stats","title":"General statistics","text":"","category":"section"},{"location":"api/stats/","page":"Stats","title":"Stats","text":"hdi\nhdi!\nr2_score","category":"page"},{"location":"api/stats/#PosteriorStats.hdi","page":"Stats","title":"PosteriorStats.hdi","text":"hdi(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper)\n\nEstimate the unimodal highest density interval (HDI) of samples for the probability prob.\n\nThe HDI is the minimum width Bayesian credible interval (BCI). That is, it is the smallest possible interval containing (100*prob)% of the probability mass.[Hyndman1996]\n\nsamples is an array of shape (draws[, chains[, params...]]). If multiple parameters are present, then lower and upper are arrays with the shape (params...,), computed separately for each marginal.\n\nThis implementation uses the algorithm of [ChenShao1999].\n\nnote: Note\nAny default value of prob is arbitrary. The default value of prob=0.94 instead of a more common default like prob=0.95 is chosen to reminder the user of this arbitrariness.\n\n[Hyndman1996]: Rob J. Hyndman (1996) Computing and Graphing Highest Density Regions, Amer. Stat., 50(2): 120-6. DOI: 10.1080/00031305.1996.10474359 jstor.\n\n[ChenShao1999]: Ming-Hui Chen & Qi-Man Shao (1999) Monte Carlo Estimation of Bayesian Credible and HPD Intervals, J Comput. Graph. Stat., 8:1, 69-92. DOI: 10.1080/10618600.1999.10474802 jstor.\n\nExamples\n\nHere we calculate the 83% HDI for a normal random variable:\n\njulia> x = randn(2_000);\n\njulia> hdi(x; prob=0.83) |> pairs\npairs(::NamedTuple) with 2 entries:\n :lower => -1.38266\n :upper => 1.25982\n\nWe can also calculate the HDI for a 3-dimensional array of samples:\n\njulia> x = randn(1_000, 1, 1) .+ reshape(0:5:10, 1, 1, :);\n\njulia> hdi(x) |> pairs\npairs(::NamedTuple) with 2 entries:\n :lower => [-1.9674, 3.0326, 8.0326]\n :upper => [1.90028, 6.90028, 11.9003]\n\n\n\n\n\nhdi(data::InferenceData; kwargs...) -> Dataset\nhdi(data::Dataset; kwargs...) -> Dataset\n\nCalculate the highest density interval (HDI) for each parameter in the data.\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PosteriorStats.hdi!","page":"Stats","title":"PosteriorStats.hdi!","text":"hdi!(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper)\n\nA version of hdi that sorts samples in-place while computing the HDI.\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PosteriorStats.r2_score","page":"Stats","title":"PosteriorStats.r2_score","text":"r2_score(y_true::AbstractVector, y_pred::AbstractVecOrMat) -> (; r2, r2_std)\n\nR² for linear Bayesian regression models.[GelmanGoodrich2019]\n\nArguments\n\ny_true: Observed data of length noutputs\ny_pred: Predicted data with size (ndraws[, nchains], noutputs)\n\n[GelmanGoodrich2019]: Andrew Gelman, Ben Goodrich, Jonah Gabry & Aki Vehtari (2019) R-squared for Bayesian Regression Models, The American Statistician, 73:3, 307-9, DOI: 10.1080/00031305.2018.1549100.\n\nExamples\n\njulia> using ArviZExampleData\n\njulia> idata = load_example_data(\"regression1d\");\n\njulia> y_true = idata.observed_data.y;\n\njulia> y_pred = PermutedDimsArray(idata.posterior_predictive.y, (:draw, :chain, :y_dim_0));\n\njulia> r2_score(y_true, y_pred) |> pairs\npairs(::NamedTuple) with 2 entries:\n :r2 => 0.683197\n :r2_std => 0.0368838\n\n\n\n\n\nr2_score(idata::InferenceData; y_name, y_pred_name) -> (; r2, r2_std)\n\nCompute R² from idata, automatically formatting the predictions to the correct shape.\n\nKeywords\n\ny_name: Name of observed data variable in idata.observed_data. If not provided, then the only observed data variable is used.\ny_pred_name: Name of posterior predictive variable in idata.posterior_predictive. If not provided, then y_name is used.\n\nExamples\n\njulia> using ArviZExampleData, PosteriorStats\n\njulia> idata = load_example_data(\"regression10d\");\n\njulia> r2_score(idata) |> pairs\npairs(::NamedTuple) with 2 entries:\n :r2 => 0.998385\n :r2_std => 0.000100621\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#Pareto-smoothed-importance-sampling","page":"Stats","title":"Pareto-smoothed importance sampling","text":"","category":"section"},{"location":"api/stats/","page":"Stats","title":"Stats","text":"PSISResult\ness_is\nPSISPlots.paretoshapeplot\npsis\npsis!","category":"page"},{"location":"api/stats/#PSIS.PSISResult","page":"Stats","title":"PSIS.PSISResult","text":"PSISResult\n\nResult of Pareto-smoothed importance sampling (PSIS) using psis.\n\nProperties\n\nlog_weights: un-normalized Pareto-smoothed log weights\nweights: normalized Pareto-smoothed weights (allocates a copy)\npareto_shape: Pareto k=ξ shape parameter\nnparams: number of parameters in log_weights\nndraws: number of draws in log_weights\nnchains: number of chains in log_weights\nreff: the ratio of the effective sample size of the unsmoothed importance ratios and the actual sample size.\ness: estimated effective sample size of estimate of mean using smoothed importance samples (see ess_is)\ntail_length: length of the upper tail of log_weights that was smoothed\ntail_dist: the generalized Pareto distribution that was fit to the tail of log_weights. Note that the tail weights are scaled to have a maximum of 1, so tail_dist * exp(maximum(log_ratios)) is the corresponding fit directly to the tail of log_ratios.\nnormalized::Bool:indicates whether log_weights are log-normalized along the sample dimensions.\n\nDiagnostic\n\nThe pareto_shape parameter k=ξ of the generalized Pareto distribution tail_dist can be used to diagnose reliability and convergence of estimates using the importance weights [VehtariSimpson2021].\n\nif k frac13, importance sampling is stable, and importance sampling (IS) and PSIS both are reliable.\nif k frac12, then the importance ratio distributon has finite variance, and the central limit theorem holds. As k approaches the upper bound, IS becomes less reliable, while PSIS still works well but with a higher RMSE.\nif frac12 k 07, then the variance is infinite, and IS can behave quite poorly. However, PSIS works well in this regime.\nif 07 k 1, then it quickly becomes impractical to collect enough importance weights to reliably compute estimates, and importance sampling is not recommended.\nif k 1, then neither the variance nor the mean of the raw importance ratios exists. The convergence rate is close to zero, and bias can be large with practical sample sizes.\n\nSee PSISPlots.paretoshapeplot for a diagnostic plot.\n\n[VehtariSimpson2021]: Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO]\n\n\n\n\n\n","category":"type"},{"location":"api/stats/#PSIS.ess_is","page":"Stats","title":"PSIS.ess_is","text":"ess_is(weights; reff=1)\n\nEstimate effective sample size (ESS) for importance sampling over the sample dimensions.\n\nGiven normalized weights w_1n, the ESS is estimated using the L2-norm of the weights:\n\nmathrmESS(w_1n) = fracr_mathrmeffsum_i=1^n w_i^2\n\nwhere r_mathrmeff is the relative efficiency of the log_weights.\n\ness_is(result::PSISResult; bad_shape_nan=true)\n\nEstimate ESS for Pareto-smoothed importance sampling.\n\nnote: Note\nESS estimates for Pareto shape values k 07, which are unreliable and misleadingly high, are set to NaN. To avoid this, set bad_shape_nan=false.\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PSIS.PSISPlots.paretoshapeplot","page":"Stats","title":"PSIS.PSISPlots.paretoshapeplot","text":"paretoshapeplot(values; showlines=false, ...)\nparetoshapeplot!(values; showlines=false, kwargs...)\n\nPlot shape parameters of fitted Pareto tail distributions for diagnosing convergence.\n\nvalues may be either a vector of Pareto shape parameters or a PSIS.PSISResult.\n\nIf showlines==true, horizontal lines indicating relevant Pareto shape thresholds are drawn. See PSIS.PSISResult for an explanation of the thresholds.\n\nAll remaining kwargs are forwarded to the plotting function.\n\nSee psis, PSISResult.\n\nExamples\n\nusing PSIS, Distributions, Plots\nproposal = Normal()\ntarget = TDist(7)\nx = rand(proposal, 1_000, 100)\nlog_ratios = logpdf.(target, x) .- logpdf.(proposal, x)\nresult = psis(log_ratios)\nparetoshapeplot(result)\n\nWe can also plot the Pareto shape parameters directly:\n\nparetoshapeplot(result.pareto_shape)\n\nWe can also use plot directly:\n\nplot(result.pareto_shape; showlines=true)\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PSIS.psis","page":"Stats","title":"PSIS.psis","text":"psis(log_ratios, reff = 1.0; kwargs...) -> PSISResult\npsis!(log_ratios, reff = 1.0; kwargs...) -> PSISResult\n\nCompute Pareto smoothed importance sampling (PSIS) log weights [VehtariSimpson2021].\n\nWhile psis computes smoothed log weights out-of-place, psis! smooths them in-place.\n\nArguments\n\nlog_ratios: an array of logarithms of importance ratios, with size (draws, [chains, [parameters...]]), where chains>1 would be used when chains are generated using Markov chain Monte Carlo.\nreff::Union{Real,AbstractArray}: the ratio(s) of effective sample size of log_ratios and the actual sample size reff = ess/(draws * chains), used to account for autocorrelation, e.g. due to Markov chain Monte Carlo. If an array, it must have the size (parameters...,) to match log_ratios.\n\nKeywords\n\nwarn=true: If true, warning messages are delivered\nnormalize=true: If true, the log-weights will be log-normalized so that exp.(log_weights) sums to 1 along the sample dimensions.\n\nReturns\n\nresult: a PSISResult object containing the results of the Pareto-smoothing.\n\nA warning is raised if the Pareto shape parameter k 07. See PSISResult for details and PSISPlots.paretoshapeplot for a diagnostic plot.\n\n[VehtariSimpson2021]: Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO]\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PSIS.psis!","page":"Stats","title":"PSIS.psis!","text":"psis(log_ratios, reff = 1.0; kwargs...) -> PSISResult\npsis!(log_ratios, reff = 1.0; kwargs...) -> PSISResult\n\nCompute Pareto smoothed importance sampling (PSIS) log weights [VehtariSimpson2021].\n\nWhile psis computes smoothed log weights out-of-place, psis! smooths them in-place.\n\nArguments\n\nlog_ratios: an array of logarithms of importance ratios, with size (draws, [chains, [parameters...]]), where chains>1 would be used when chains are generated using Markov chain Monte Carlo.\nreff::Union{Real,AbstractArray}: the ratio(s) of effective sample size of log_ratios and the actual sample size reff = ess/(draws * chains), used to account for autocorrelation, e.g. due to Markov chain Monte Carlo. If an array, it must have the size (parameters...,) to match log_ratios.\n\nKeywords\n\nwarn=true: If true, warning messages are delivered\nnormalize=true: If true, the log-weights will be log-normalized so that exp.(log_weights) sums to 1 along the sample dimensions.\n\nReturns\n\nresult: a PSISResult object containing the results of the Pareto-smoothing.\n\nA warning is raised if the Pareto shape parameter k 07. See PSISResult for details and PSISPlots.paretoshapeplot for a diagnostic plot.\n\n[VehtariSimpson2021]: Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO]\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#LOO-and-WAIC","page":"Stats","title":"LOO and WAIC","text":"","category":"section"},{"location":"api/stats/","page":"Stats","title":"Stats","text":"AbstractELPDResult\nPSISLOOResult\nWAICResult\nelpd_estimates\ninformation_criterion\nloo\nwaic","category":"page"},{"location":"api/stats/#PosteriorStats.AbstractELPDResult","page":"Stats","title":"PosteriorStats.AbstractELPDResult","text":"abstract type AbstractELPDResult\n\nAn abstract type representing the result of an ELPD computation.\n\nEvery subtype stores estimates of both the expected log predictive density (elpd) and the effective number of parameters p, as well as standard errors and pointwise estimates of each, from which other relevant estimates can be computed.\n\nSubtypes implement the following functions:\n\nelpd_estimates\ninformation_criterion\n\n\n\n\n\n","category":"type"},{"location":"api/stats/#PosteriorStats.PSISLOOResult","page":"Stats","title":"PosteriorStats.PSISLOOResult","text":"Results of Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO).\n\nSee also: loo, AbstractELPDResult\n\nestimates: Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p)\npointwise: Pointwise estimates\npsis_result: Pareto-smoothed importance sampling (PSIS) results\n\n\n\n\n\n","category":"type"},{"location":"api/stats/#PosteriorStats.WAICResult","page":"Stats","title":"PosteriorStats.WAICResult","text":"Results of computing the widely applicable information criterion (WAIC).\n\nSee also: waic, AbstractELPDResult\n\nestimates: Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p)\npointwise: Pointwise estimates\n\n\n\n\n\n","category":"type"},{"location":"api/stats/#PosteriorStats.elpd_estimates","page":"Stats","title":"PosteriorStats.elpd_estimates","text":"elpd_estimates(result::AbstractELPDResult; pointwise=false) -> (; elpd, elpd_mcse, lpd)\n\nReturn the (E)LPD estimates from the result.\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PosteriorStats.information_criterion","page":"Stats","title":"PosteriorStats.information_criterion","text":"information_criterion(elpd, scale::Symbol)\n\nCompute the information criterion for the given scale from the elpd estimate.\n\nscale must be one of (:deviance, :log, :negative_log).\n\nSee also: loo, waic\n\n\n\n\n\ninformation_criterion(result::AbstractELPDResult, scale::Symbol; pointwise=false)\n\nCompute information criterion for the given scale from the existing ELPD result.\n\nscale must be one of (:deviance, :log, :negative_log).\n\nIf pointwise=true, then pointwise estimates are returned.\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PosteriorStats.loo","page":"Stats","title":"PosteriorStats.loo","text":"loo(log_likelihood; reff=nothing, kwargs...) -> PSISLOOResult{<:NamedTuple,<:NamedTuple}\n\nCompute the Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO). [Vehtari2017][LOOFAQ]\n\nlog_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]).\n\nKeywords\n\nreff::Union{Real,AbstractArray{<:Real}}: The relative effective sample size(s) of the likelihood values. If an array, it must have the same data dimensions as the corresponding log-likelihood variable. If not provided, then this is estimated using MCMCDiagnosticTools.ess.\nkwargs: Remaining keywords are forwarded to [PSIS.psis].\n\nSee also: PSISLOOResult, waic\n\n[Vehtari2017]: Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544\n\n[LOOFAQ]: Aki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html\n\nExamples\n\nManually compute R_mathrmeff and calculate PSIS-LOO of a model:\n\njulia> using ArviZExampleData, MCMCDiagnosticTools\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> reff = ess(log_like; kind=:basic, split_chains=1, relative=true);\n\njulia> loo(log_like; reff)\nPSISLOOResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.34\n\nand PSISResult with 500 draws, 4 chains, and 8 parameters\nPareto shape (k) diagnostic values:\n Count Min. ESS\n (-Inf, 0.5] good 7 (87.5%) 151\n (0.5, 0.7] okay 1 (12.5%) 446\n\n\n\n\n\nloo(data::Dataset; [var_name::Symbol,] kwargs...) -> PSISLOOResult{<:NamedTuple,<:Dataset}\nloo(data::InferenceData; [var_name::Symbol,] kwargs...) -> PSISLOOResult{<:NamedTuple,<:Dataset}\n\nCompute PSIS-LOO from log-likelihood values in data.\n\nIf more than one log-likelihood variable is present, then var_name must be provided.\n\nExamples\n\nCalculate PSIS-LOO of a model:\n\njulia> using ArviZExampleData, PosteriorStats\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> loo(idata)\nPSISLOOResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.34\n\nand PSISResult with 500 draws, 4 chains, and 8 parameters\nPareto shape (k) diagnostic values:\n Count Min. ESS\n (-Inf, 0.5] good 6 (75.0%) 135\n (0.5, 0.7] okay 2 (25.0%) 421\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PosteriorStats.waic","page":"Stats","title":"PosteriorStats.waic","text":"waic(log_likelihood::AbstractArray) -> WAICResult{<:NamedTuple,<:NamedTuple}\n\nCompute the widely applicable information criterion (WAIC).[Watanabe2010][Vehtari2017][LOOFAQ]\n\nlog_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]).\n\nSee also: WAICResult, loo\n\n[Watanabe2010]: Watanabe, S. Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory. 11(116):3571−3594, 2010. https://jmlr.csail.mit.edu/papers/v11/watanabe10a.html\n\n[Vehtari2017]: Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544\n\n[LOOFAQ]: Aki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html\n\nExamples\n\nCalculate WAIC of a model:\n\njulia> using ArviZExampleData\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> waic(log_like)\nWAICResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.33\n\n\n\n\n\nwaic(data::Dataset; [var_name::Symbol]) -> WAICResult{<:NamedTuple,<:Dataset}\nwaic(data::InferenceData; [var_name::Symbol]) -> WAICResult{<:NamedTuple,<:Dataset}\n\nCompute WAIC from log-likelihood values in data.\n\nIf more than one log-likelihood variable is present, then var_name must be provided.\n\nExamples\n\nCalculate WAIC of a model:\n\njulia> using ArviZExampleData, PosteriorStats\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> waic(idata)\nWAICResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.33\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#Model-comparison","page":"Stats","title":"Model comparison","text":"","category":"section"},{"location":"api/stats/","page":"Stats","title":"Stats","text":"ModelComparisonResult\ncompare\nmodel_weights","category":"page"},{"location":"api/stats/#PosteriorStats.ModelComparisonResult","page":"Stats","title":"PosteriorStats.ModelComparisonResult","text":"ModelComparisonResult\n\nResult of model comparison using ELPD.\n\nThis struct implements the Tables and TableTraits interfaces.\n\nEach field returns a collection of the corresponding entry for each model:\n\nname: Names of the models, if provided.\nrank: Ranks of the models (ordered by decreasing ELPD)\nelpd_diff: ELPD of a model subtracted from the largest ELPD of any model\nelpd_diff_mcse: Monte Carlo standard error of the ELPD difference\nweight: Model weights computed with weights_method\nelpd_result: AbstactELPDResults for each model, which can be used to access useful stats like ELPD estimates, pointwise estimates, and Pareto shape values for PSIS-LOO\nweights_method: Method used to compute model weights with model_weights\n\n\n\n\n\n","category":"type"},{"location":"api/stats/#PosteriorStats.compare","page":"Stats","title":"PosteriorStats.compare","text":"compare(models; kwargs...) -> ModelComparisonResult\n\nCompare models based on their expected log pointwise predictive density (ELPD).\n\nThe ELPD is estimated either by Pareto smoothed importance sampling leave-one-out cross-validation (LOO) or using the widely applicable information criterion (WAIC). We recommend loo. Read more theory here - in a paper by some of the leading authorities on model comparison dx.doi.org/10.1111/1467-9868.00353\n\nArguments\n\nmodels: a Tuple, NamedTuple, or AbstractVector whose values are either AbstractELPDResult entries or any argument to elpd_method.\n\nKeywords\n\nweights_method::AbstractModelWeightsMethod=Stacking(): the method to be used to weight the models. See model_weights for details\nelpd_method=loo: a method that computes an AbstractELPDResult from an argument in models.\nsort::Bool=true: Whether to sort models by decreasing ELPD.\n\nReturns\n\nModelComparisonResult: A container for the model comparison results. The fields contain a similar collection to models.\n\nExamples\n\nCompare the centered and non centered models of the eight school problem using the defaults: loo and Stacking weights. A custom myloo method formates the inputs as expected by loo.\n\njulia> using ArviZExampleData\n\njulia> models = (\n centered=load_example_data(\"centered_eight\"),\n non_centered=load_example_data(\"non_centered_eight\"),\n );\n\njulia> function myloo(idata)\n log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1))\n return loo(log_like)\n end;\n\njulia> mc = compare(models; elpd_method=myloo)\n┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.\n└ @ PSIS ~/.julia/packages/PSIS/...\nModelComparisonResult with Stacking weights\n rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯\n non_centered 1 -31 1.4 0 0.0 1.0 0.9 ⋯\n centered 2 -31 1.4 0.06 0.067 0.0 0.9 ⋯\n 1 column omitted\njulia> mc.weight |> pairs\npairs(::NamedTuple) with 2 entries:\n :non_centered => 1.0\n :centered => 5.34175e-19\n\nCompare the same models from pre-computed PSIS-LOO results and computing BootstrappedPseudoBMA weights:\n\njulia> elpd_results = mc.elpd_result;\n\njulia> compare(elpd_results; weights_method=BootstrappedPseudoBMA())\nModelComparisonResult with BootstrappedPseudoBMA weights\n rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯\n non_centered 1 -31 1.4 0 0.0 0.52 0.9 ⋯\n centered 2 -31 1.4 0.06 0.067 0.48 0.9 ⋯\n 1 column omitted\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PosteriorStats.model_weights","page":"Stats","title":"PosteriorStats.model_weights","text":"model_weights(elpd_results; method=Stacking())\nmodel_weights(method::AbstractModelWeightsMethod, elpd_results)\n\nCompute weights for each model in elpd_results using method.\n\nelpd_results is a Tuple, NamedTuple, or AbstractVector with AbstractELPDResult entries. The weights are returned in the same type of collection.\n\nStacking is the recommended approach, as it performs well even when the true data generating process is not included among the candidate models. See [YaoVehtari2018] for details.\n\nSee also: AbstractModelWeightsMethod, compare\n\n[YaoVehtari2018]: Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030\n\nExamples\n\nCompute Stacking weights for two models:\n\njulia> using ArviZExampleData\n\njulia> models = (\n centered=load_example_data(\"centered_eight\"),\n non_centered=load_example_data(\"non_centered_eight\"),\n );\n\njulia> elpd_results = map(models) do idata\n log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1))\n return loo(log_like)\n end;\n┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.\n└ @ PSIS ~/.julia/packages/PSIS/...\n\njulia> model_weights(elpd_results; method=Stacking()) |> pairs\npairs(::NamedTuple) with 2 entries:\n :centered => 5.34175e-19\n :non_centered => 1.0\n\nNow we compute BootstrappedPseudoBMA weights for the same models:\n\njulia> model_weights(elpd_results; method=BootstrappedPseudoBMA()) |> pairs\npairs(::NamedTuple) with 2 entries:\n :centered => 0.483723\n :non_centered => 0.516277\n\n\n\n\n\n","category":"function"},{"location":"api/stats/","page":"Stats","title":"Stats","text":"The following model weighting methods are available","category":"page"},{"location":"api/stats/","page":"Stats","title":"Stats","text":"AbstractModelWeightsMethod\nBootstrappedPseudoBMA\nPseudoBMA\nStacking","category":"page"},{"location":"api/stats/#PosteriorStats.AbstractModelWeightsMethod","page":"Stats","title":"PosteriorStats.AbstractModelWeightsMethod","text":"abstract type AbstractModelWeightsMethod\n\nAn abstract type representing methods for computing model weights.\n\nSubtypes implement model_weights(method, elpd_results).\n\n\n\n\n\n","category":"type"},{"location":"api/stats/#PosteriorStats.BootstrappedPseudoBMA","page":"Stats","title":"PosteriorStats.BootstrappedPseudoBMA","text":"struct BootstrappedPseudoBMA{R<:Random.AbstractRNG, T<:Real} <: AbstractModelWeightsMethod\n\nModel weighting method using pseudo Bayesian Model Averaging using Akaike-type weighting with the Bayesian bootstrap (pseudo-BMA+)[YaoVehtari2018].\n\nThe Bayesian bootstrap stabilizes the model weights.\n\nBootstrappedPseudoBMA(; rng=Random.default_rng(), samples=1_000, alpha=1)\nBootstrappedPseudoBMA(rng, samples, alpha)\n\nConstruct the method.\n\nrng::Random.AbstractRNG: The random number generator to use for the Bayesian bootstrap\nsamples::Int64: The number of samples to draw for bootstrapping\nalpha::Real: The shape parameter in the Dirichlet distribution used for the Bayesian bootstrap. The default (1) corresponds to a uniform distribution on the simplex.\n\nSee also: Stacking\n\n[YaoVehtari2018]: Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030\n\n\n\n\n\n","category":"type"},{"location":"api/stats/#PosteriorStats.PseudoBMA","page":"Stats","title":"PosteriorStats.PseudoBMA","text":"struct PseudoBMA <: AbstractModelWeightsMethod\n\nModel weighting method using pseudo Bayesian Model Averaging (pseudo-BMA) and Akaike-type weighting.\n\nPseudoBMA(; regularize=false)\nPseudoBMA(regularize)\n\nConstruct the method with optional regularization of the weights using the standard error of the ELPD estimate.\n\nnote: Note\nThis approach is not recommended, as it produces unstable weight estimates. It is recommended to instead use BootstrappedPseudoBMA to stabilize the weights or Stacking. For details, see [YaoVehtari2018].\n\n[YaoVehtari2018]: Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030\n\nSee also: Stacking\n\n\n\n\n\n","category":"type"},{"location":"api/stats/#PosteriorStats.Stacking","page":"Stats","title":"PosteriorStats.Stacking","text":"struct Stacking{O<:Optim.AbstractOptimizer} <: AbstractModelWeightsMethod\n\nModel weighting using stacking of predictive distributions[YaoVehtari2018].\n\nStacking(; optimizer=Optim.LBFGS(), options=Optim.Options()\nStacking(optimizer[, options])\n\nConstruct the method, optionally customizing the optimization.\n\noptimizer::Optim.AbstractOptimizer: The optimizer to use for the optimization of the weights. The optimizer must support projected gradient optimization via a manifold field.\noptions::Optim.Options: The Optim options to use for the optimization of the weights.\n\nSee also: BootstrappedPseudoBMA\n\n[YaoVehtari2018]: Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030\n\n\n\n\n\n","category":"type"},{"location":"api/stats/#Predictive-checks","page":"Stats","title":"Predictive checks","text":"","category":"section"},{"location":"api/stats/","page":"Stats","title":"Stats","text":"loo_pit","category":"page"},{"location":"api/stats/#PosteriorStats.loo_pit","page":"Stats","title":"PosteriorStats.loo_pit","text":"loo_pit(y, y_pred, log_weights; kwargs...) -> Union{Real,AbstractArray}\n\nCompute leave-one-out probability integral transform (LOO-PIT) checks.\n\nArguments\n\ny: array of observations with shape (params...,)\ny_pred: array of posterior predictive samples with shape (draws, chains, params...).\nlog_weights: array of normalized log LOO importance weights with shape (draws, chains, params...).\n\nKeywords\n\nis_discrete: If not provided, then it is set to true iff elements of y and y_pred are all integer-valued. If true, then data are smoothed using smooth_data to make them non-discrete before estimating LOO-PIT values.\nkwargs: Remaining keywords are forwarded to smooth_data if data is discrete.\n\nReturns\n\npitvals: LOO-PIT values with same size as y. If y is a scalar, then pitvals is a scalar.\n\nLOO-PIT is a marginal posterior predictive check. If y_-i is the array y of observations with the ith observation left out, and y_i^* is a posterior prediction of the ith observation, then the LOO-PIT value for the ith observation is defined as\n\nP(y_i^* le y_i mid y_-i) = int_-infty^y_i p(y_i^* mid y_-i) mathrmd y_i^*\n\nThe LOO posterior predictions and the corresponding observations should have similar distributions, so if conditional predictive distributions are well-calibrated, then all LOO-PIT values should be approximately uniformly distributed on 0 1.[Gabry2019]\n\n[Gabry2019]: Gabry, J., Simpson, D., Vehtari, A., Betancourt, M. & Gelman, A. Visualization in Bayesian Workflow. J. R. Stat. Soc. Ser. A Stat. Soc. 182, 389–402 (2019). doi: 10.1111/rssa.12378 arXiv: 1709.01449\n\nExamples\n\nCalculate LOO-PIT values using as test quantity the observed values themselves.\n\njulia> using ArviZExampleData\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> y = idata.observed_data.obs;\n\njulia> y_pred = PermutedDimsArray(idata.posterior_predictive.obs, (:draw, :chain, :school));\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> log_weights = loo(log_like).psis_result.log_weights;\n\njulia> loo_pit(y, y_pred, log_weights)\n8-element DimArray{Float64,1} with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.943511\n \"Deerfield\" 0.63797\n \"Phillips Andover\" 0.316697\n \"Phillips Exeter\" 0.582252\n \"Hotchkiss\" 0.295321\n \"Lawrenceville\" 0.403318\n \"St. Paul's\" 0.902508\n \"Mt. Hermon\" 0.655275\n\nCalculate LOO-PIT values using as test quantity the square of the difference between each observation and mu.\n\njulia> using Statistics\n\njulia> mu = idata.posterior.mu;\n\njulia> T = y .- median(mu);\n\njulia> T_pred = y_pred .- mu;\n\njulia> loo_pit(T .^ 2, T_pred .^ 2, log_weights)\n8-element DimArray{Float64,1} with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.873577\n \"Deerfield\" 0.243686\n \"Phillips Andover\" 0.357563\n \"Phillips Exeter\" 0.149908\n \"Hotchkiss\" 0.435094\n \"Lawrenceville\" 0.220627\n \"St. Paul's\" 0.775086\n \"Mt. Hermon\" 0.296706\n\n\n\n\n\nloo_pit(idata::InferenceData, log_weights; kwargs...) -> DimArray\n\nCompute LOO-PIT values using existing normalized log LOO importance weights.\n\nKeywords\n\ny_name: Name of observed data variable in idata.observed_data. If not provided, then the only observed data variable is used.\ny_pred_name: Name of posterior predictive variable in idata.posterior_predictive. If not provided, then y_name is used.\nkwargs: Remaining keywords are forwarded to the base method of loo_pit.\n\nExamples\n\nCalculate LOO-PIT values using already computed log weights.\n\njulia> using ArviZExampleData, PosteriorStats\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> loo_result = loo(idata; var_name=:obs);\n\njulia> loo_pit(idata, loo_result.psis_result.log_weights; y_name=:obs)\n8-element DimArray{Float64,1} loo_pit_obs with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.943511\n \"Deerfield\" 0.63797\n \"Phillips Andover\" 0.316697\n \"Phillips Exeter\" 0.582252\n \"Hotchkiss\" 0.295321\n \"Lawrenceville\" 0.403318\n \"St. Paul's\" 0.902508\n \"Mt. Hermon\" 0.655275\n\n\n\n\n\nloo_pit(idata::InferenceData; kwargs...) -> DimArray\n\nCompute LOO-PIT from groups in idata using PSIS-LOO.\n\nKeywords\n\ny_name: Name of observed data variable in idata.observed_data. If not provided, then the only observed data variable is used.\ny_pred_name: Name of posterior predictive variable in idata.posterior_predictive. If not provided, then y_name is used.\nlog_likelihood_name: Name of log-likelihood variable in idata.log_likelihood. If not provided, then y_name is used if idata has a log_likelihood group, otherwise the only variable is used.\nreff::Union{Real,AbstractArray{<:Real}}: The relative effective sample size(s) of the likelihood values. If an array, it must have the same data dimensions as the corresponding log-likelihood variable. If not provided, then this is estimated using ess.\nkwargs: Remaining keywords are forwarded to the base method of loo_pit.\n\nExamples\n\nCalculate LOO-PIT values using as test quantity the observed values themselves.\n\njulia> using ArviZExampleData, PosteriorStats\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> loo_pit(idata; y_name=:obs)\n8-element DimArray{Float64,1} loo_pit_obs with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.943511\n \"Deerfield\" 0.63797\n \"Phillips Andover\" 0.316697\n \"Phillips Exeter\" 0.582252\n \"Hotchkiss\" 0.295321\n \"Lawrenceville\" 0.403318\n \"St. Paul's\" 0.902508\n \"Mt. Hermon\" 0.655275\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#Utilities","page":"Stats","title":"Utilities","text":"","category":"section"},{"location":"api/stats/","page":"Stats","title":"Stats","text":"PosteriorStats.smooth_data","category":"page"},{"location":"api/stats/#PosteriorStats.smooth_data","page":"Stats","title":"PosteriorStats.smooth_data","text":"smooth_data(y; dims=:, interp_method=CubicSpline, offset_frac=0.01)\n\nSmooth y along dims using interp_method.\n\ninterp_method is a 2-argument callabale that takes the arguments y and x and returns a DataInterpolations.jl interpolation method, defaulting to a cubic spline interpolator.\n\noffset_frac is the fraction of the length of y to use as an offset when interpolating.\n\n\n\n\n\n","category":"function"},{"location":"api/dataset/#dataset-api","page":"Dataset","title":"Dataset","text":"","category":"section"},{"location":"api/dataset/","page":"Dataset","title":"Dataset","text":"Pages = [\"dataset.md\"]","category":"page"},{"location":"api/dataset/#Type-definition","page":"Dataset","title":"Type definition","text":"","category":"section"},{"location":"api/dataset/","page":"Dataset","title":"Dataset","text":"Dataset","category":"page"},{"location":"api/dataset/#InferenceObjects.Dataset","page":"Dataset","title":"InferenceObjects.Dataset","text":"Dataset{L} <: DimensionalData.AbstractDimStack{L}\n\nContainer of dimensional arrays sharing some dimensions.\n\nThis type is an DimensionalData.AbstractDimStack that implements the same interface as DimensionalData.DimStack and has identical usage.\n\nWhen a Dataset is passed to Python, it is converted to an xarray.Dataset without copying the data. That is, the Python object shares the same memory as the Julia object. However, if an xarray.Dataset is passed to Julia, its data must be copied.\n\nConstructors\n\nDataset(data::DimensionalData.AbstractDimArray...)\nDataset(data::Tuple{Vararg{<:DimensionalData.AbstractDimArray}})\nDataset(data::NamedTuple{Keys,Vararg{<:DimensionalData.AbstractDimArray}})\nDataset(\n data::NamedTuple,\n dims::Tuple{Vararg{DimensionalData.Dimension}};\n metadata=DimensionalData.NoMetadata(),\n)\n\nIn most cases, use convert_to_dataset to create a Dataset instead of directly using a constructor.\n\n\n\n\n\n","category":"type"},{"location":"api/dataset/#General-conversion","page":"Dataset","title":"General conversion","text":"","category":"section"},{"location":"api/dataset/","page":"Dataset","title":"Dataset","text":"convert_to_dataset\nnamedtuple_to_dataset","category":"page"},{"location":"api/dataset/#InferenceObjects.convert_to_dataset","page":"Dataset","title":"InferenceObjects.convert_to_dataset","text":"convert_to_dataset(obj; group = :posterior, kwargs...) -> Dataset\n\nConvert a supported object to a Dataset.\n\nIn most cases, this function calls convert_to_inference_data and returns the corresponding group.\n\n\n\n\n\n","category":"function"},{"location":"api/dataset/#InferenceObjects.namedtuple_to_dataset","page":"Dataset","title":"InferenceObjects.namedtuple_to_dataset","text":"namedtuple_to_dataset(data; kwargs...) -> Dataset\n\nConvert NamedTuple mapping variable names to arrays to a Dataset.\n\nAny non-array values will be converted to a 0-dimensional array.\n\nKeywords\n\nattrs::AbstractDict{<:AbstractString}: a collection of metadata to attach to the dataset, in addition to defaults. Values should be JSON serializable.\nlibrary::Union{String,Module}: library used for performing inference. Will be attached to the attrs metadata.\ndims: a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are:\nSymbol: dimension name\nType{<:DimensionsionalData.Dimension}: dimension type\nDimensionsionalData.Dimension: dimension, potentially with indices\nNothing: no dimension name provided, dimension name is automatically generated\ncoords: a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated.\n\n\n\n\n\n","category":"function"},{"location":"api/dataset/#DimensionalData","page":"Dataset","title":"DimensionalData","text":"","category":"section"},{"location":"api/dataset/","page":"Dataset","title":"Dataset","text":"As a DimensionalData.AbstractDimStack, Dataset also implements the AbstractDimStack API and can be used like a DimStack. See DimensionalData's documentation for example usage.","category":"page"},{"location":"api/dataset/#Tables-inteface","page":"Dataset","title":"Tables inteface","text":"","category":"section"},{"location":"api/dataset/","page":"Dataset","title":"Dataset","text":"Dataset implements the Tables interface. This allows Datasets to be used as sources for any function that can accept a table. For example, it's straightforward to:","category":"page"},{"location":"api/dataset/","page":"Dataset","title":"Dataset","text":"write to CSV with CSV.jl\nflatten to a DataFrame with DataFrames.jl\nplot with StatsPlots.jl\nplot with AlgebraOfGraphics.jl","category":"page"},{"location":"#arvizjl","page":"Home","title":"ArviZ.jl: Exploratory analysis of Bayesian models in Julia","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"ArviZ.jl is a Julia meta-package for exploratory analysis of Bayesian models. It is part of the ArviZ project, which also includes a related Python package.","category":"page"},{"location":"","page":"Home","title":"Home","text":"ArviZ consists of and re-exports the following subpackages, along with extensions integrating them with InferenceObjects:","category":"page"},{"location":"","page":"Home","title":"Home","text":"InferenceObjects.jl: a base package implementing the InferenceData type with utilities for building, saving, and working with it\nMCMCDiagnosticTools.jl: diagnostics for Markov Chain Monte Carlo methods\nPSIS.jl: Pareto-smoothed importance sampling\nPosteriorStats.jl: common statistical analyses for the Bayesian workflow","category":"page"},{"location":"","page":"Home","title":"Home","text":"Additional functionality can be loaded with the following packages:","category":"page"},{"location":"","page":"Home","title":"Home","text":"ArviZExampleData.jl: example InferenceData objects, useful for demonstration and testing\nArviZPythonPlots.jl: Python ArviZ's library of plotting functions for Julia types","category":"page"},{"location":"","page":"Home","title":"Home","text":"See the navigation bar for more useful packages.","category":"page"},{"location":"#installation","page":"Home","title":"Installation","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"From the Julia REPL, type ] to enter the Pkg REPL mode and run","category":"page"},{"location":"","page":"Home","title":"Home","text":"pkg> add ArviZ","category":"page"},{"location":"#usage","page":"Home","title":"Usage","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"See the Quickstart for example usage and the API Overview for description of functions.","category":"page"},{"location":"#extendingarviz","page":"Home","title":"Extending ArviZ.jl","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"To use a custom data type with ArviZ.jl, simply overload InferenceObjects.convert_to_inference_data to convert your input(s) to an InferenceObjects.InferenceData.","category":"page"},{"location":"working_with_inference_data/#working-with-inference-data","page":"Working with InferenceData","title":"Working with InferenceData","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"using ArviZ, ArviZExampleData, DimensionalData, Statistics","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Here we present a collection of common manipulations you can use while working with InferenceData.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Let's load one of ArviZ's example datasets. posterior, posterior_predictive, etc are the groups stored in idata, and they are stored as Datasets. In this HTML view, you can click a group name to expand a summary of the group.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"idata = load_example_data(\"centered_eight\")","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"info: Info\nDatasets are DimensionalData.AbstractDimStacks and can be used identically. The variables a Dataset contains are called \"layers\", and dimensions of the same name that appear in more than one layer within a Dataset must have the same indices.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"InferenceData behaves like a NamedTuple and can be used similarly. Note that unlike a NamedTuple, the groups always appear in a specific order.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"length(idata) # number of groups","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"keys(idata) # group names","category":"page"},{"location":"working_with_inference_data/#Get-the-dataset-corresponding-to-a-single-group","page":"Working with InferenceData","title":"Get the dataset corresponding to a single group","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Group datasets can be accessed both as properties or as indexed items.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"post = idata.posterior","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"post is the dataset itself, so this is a non-allocating operation.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"idata[:posterior] === post","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"InferenceData supports a more advanced indexing syntax, which we'll see later.","category":"page"},{"location":"working_with_inference_data/#Getting-a-new-InferenceData-with-a-subset-of-groups","page":"Working with InferenceData","title":"Getting a new InferenceData with a subset of groups","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"We can index by a collection of group names to get a new InferenceData with just those groups. This is also non-allocating.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"idata_sub = idata[(:posterior, :posterior_predictive)]","category":"page"},{"location":"working_with_inference_data/#Adding-groups-to-an-InferenceData","page":"Working with InferenceData","title":"Adding groups to an InferenceData","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"InferenceData is immutable, so to add or replace groups we use merge to create a new object.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"merge(idata_sub, idata[(:observed_data, :prior)])","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"We can also use Base.setindex to out-of-place add or replace a single group.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Base.setindex(idata_sub, idata.prior, :prior)","category":"page"},{"location":"working_with_inference_data/#Add-a-new-variable","page":"Working with InferenceData","title":"Add a new variable","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Dataset is also immutable. So while the values within the underlying data arrays can be mutated, layers cannot be added or removed from Datasets, and groups cannot be added/removed from InferenceData.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Instead, we do this out-of-place also using merge.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"merge(post, (log_tau=log.(post[:tau]),))","category":"page"},{"location":"working_with_inference_data/#Obtain-an-array-for-a-given-parameter","page":"Working with InferenceData","title":"Obtain an array for a given parameter","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Let’s say we want to get the values for mu as an array. Parameters can be accessed with either property or index syntax.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"post.tau","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"post[:tau] === post.tau","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"To remove the dimensions, just use parent to retrieve the underlying array.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"parent(post.tau)","category":"page"},{"location":"working_with_inference_data/#Get-the-dimension-lengths","page":"Working with InferenceData","title":"Get the dimension lengths","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Let’s check how many groups are in our hierarchical model.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"size(idata.observed_data, :school)","category":"page"},{"location":"working_with_inference_data/#Get-coordinate/index-values","page":"Working with InferenceData","title":"Get coordinate/index values","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"What are the names of the groups in our hierarchical model? You can access them from the coordinate name school in this case.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"DimensionalData.index(idata.observed_data, :school)","category":"page"},{"location":"working_with_inference_data/#Get-a-subset-of-chains","page":"Working with InferenceData","title":"Get a subset of chains","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Let’s keep only chain 0 here. For the subset to take effect on all relevant InferenceData groups – posterior, sample_stats, log_likelihood, and posterior_predictive – we will index InferenceData instead of Dataset.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Here we use DimensionalData's At selector. Its other selectors are also supported.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"idata[chain=At(0)]","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Note that in this case, prior only has a chain of 0. If it also had the other chains, we could have passed chain=At([0, 2]) to subset by chains 0 and 2.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"warning: Warning\nIf we used idata[chain=[0, 2]] without the At selector, this is equivalent to idata[chain=DimensionalData.index(idata.posterior, :chain)[0, 2]], that is, [0, 2] indexes an array of dimension indices, which here would error. But if we had requested idata[chain=[1, 2]] we would not hit an error, but we would index the wrong chains. So it's important to always use a selector to index by values of dimension indices.","category":"page"},{"location":"working_with_inference_data/#Remove-the-first-n-draws-(burn-in)","page":"Working with InferenceData","title":"Remove the first n draws (burn-in)","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Let’s say we want to remove the first 100 draws from all the chains and all InferenceData groups with draws. To do this we use the .. syntax from IntervalSets.jl, which is exported by DimensionalData.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"idata[draw=100 .. Inf]","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"If you check the object you will see that the groups posterior, posterior_predictive, prior, and sample_stats have 400 draws compared to idata, which has 500. The group observed_data has not been affected because it does not have the draw dimension.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Alternatively, you can change a subset of groups by combining indexing styles with merge. Here we use this to build a new InferenceData where we have discarded the first 100 draws only from posterior.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"merge(idata, idata[(:posterior,), draw=100 .. Inf])","category":"page"},{"location":"working_with_inference_data/#Compute-posterior-mean-values-along-draw-and-chain-dimensions","page":"Working with InferenceData","title":"Compute posterior mean values along draw and chain dimensions","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"To compute the mean value of the posterior samples, do the following:","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"mean(post)","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"This computes the mean along all dimensions, discarding all dimensions and returning the result as a NamedTuple. This may be what you wanted for mu and tau, which have only two dimensions (chain and draw), but maybe not what you expected for theta, which has one more dimension school.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"You can specify along which dimension you want to compute the mean (or other functions), which instead returns a Dataset.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"mean(post; dims=(:chain, :draw))","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"The singleton dimensions of chain and draw now contain meaningless indices, so you may want to discard them, which you can do with dropdims.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"dropdims(mean(post; dims=(:chain, :draw)); dims=(:chain, :draw))","category":"page"},{"location":"working_with_inference_data/#Renaming-a-dimension","page":"Working with InferenceData","title":"Renaming a dimension","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"We can rename a dimension in a Dataset using DimensionalData's set method:","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"theta_bis = set(post.theta; school=:school_bis)","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"We can use this, for example, to broadcast functions across multiple arrays, automatically matching up shared dimensions, using DimensionalData.broadcast_dims.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"theta_school_diff = broadcast_dims(-, post.theta, theta_bis)","category":"page"},{"location":"working_with_inference_data/#Compute-and-store-posterior-pushforward-quantities","page":"Working with InferenceData","title":"Compute and store posterior pushforward quantities","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"We use “posterior pushfoward quantities” to refer to quantities that are not variables in the posterior but deterministic computations using posterior variables.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"You can compute these pushforward operations and store them as a new variable in a copy of the posterior group.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Here we'll create a new InferenceData with theta_school_diff in the posterior:","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"idata_new = Base.setindex(idata, merge(post, (; theta_school_diff)), :posterior)","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Once you have these pushforward quantities in an InferenceData, you’ll then be able to plot them with ArviZ functions, calculate stats and diagnostics on them, or save and share the InferenceData object with the pushforward quantities included.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Here we compute the mcse of theta_school_diff:","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"mcse(idata_new.posterior).theta_school_diff","category":"page"},{"location":"working_with_inference_data/#Advanced-subsetting","page":"Working with InferenceData","title":"Advanced subsetting","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"To select the value corresponding to the difference between the Choate and Deerfield schools do:","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"school_idx = [\"Choate\", \"Hotchkiss\", \"Mt. Hermon\"]\nschool_bis_idx = [\"Deerfield\", \"Choate\", \"Lawrenceville\"]\ntheta_school_diff[school=At(school_idx), school_bis=At(school_bis_idx)]","category":"page"},{"location":"working_with_inference_data/#Add-new-chains-using-cat","page":"Working with InferenceData","title":"Add new chains using cat","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Suppose after checking the mcse and realizing you need more samples, you rerun the model with two chains and obtain an idata_rerun object.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"idata_rerun = InferenceData(; posterior=set(post[chain=At([0, 1])]; chain=[4, 5]))","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"You can combine the two using cat.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"cat(idata[[:posterior]], idata_rerun; dims=:chain)","category":"page"}] +[{"location":"api/inference_data/#inferencedata-api","page":"InferenceData","title":"InferenceData","text":"","category":"section"},{"location":"api/inference_data/","page":"InferenceData","title":"InferenceData","text":"Pages = [\"inference_data.md\"]","category":"page"},{"location":"api/inference_data/#Type-definition","page":"InferenceData","title":"Type definition","text":"","category":"section"},{"location":"api/inference_data/","page":"InferenceData","title":"InferenceData","text":"InferenceData","category":"page"},{"location":"api/inference_data/#InferenceObjects.InferenceData","page":"InferenceData","title":"InferenceObjects.InferenceData","text":"InferenceData{group_names,group_types}\n\nContainer for inference data storage using DimensionalData.\n\nThis object implements the InferenceData schema.\n\nInternally, groups are stored in a NamedTuple, which can be accessed using parent(::InferenceData).\n\nConstructors\n\nInferenceData(groups::NamedTuple)\nInferenceData(; groups...)\n\nConstruct an inference data from either a NamedTuple or keyword arguments of groups.\n\nGroups must be Dataset objects.\n\nInstead of directly creating an InferenceData, use the exported from_xyz functions or convert_to_inference_data.\n\n\n\n\n\n","category":"type"},{"location":"api/inference_data/#Property-interface","page":"InferenceData","title":"Property interface","text":"","category":"section"},{"location":"api/inference_data/","page":"InferenceData","title":"InferenceData","text":"getproperty\npropertynames","category":"page"},{"location":"api/inference_data/#Base.getproperty","page":"InferenceData","title":"Base.getproperty","text":"getproperty(data::InferenceData, name::Symbol) -> Dataset\n\nGet group with the specified name.\n\n\n\n\n\n","category":"function"},{"location":"api/inference_data/#Base.propertynames","page":"InferenceData","title":"Base.propertynames","text":"propertynames(data::InferenceData) -> Tuple{Symbol}\n\nGet names of groups\n\n\n\n\n\n","category":"function"},{"location":"api/inference_data/#Indexing-interface","page":"InferenceData","title":"Indexing interface","text":"","category":"section"},{"location":"api/inference_data/","page":"InferenceData","title":"InferenceData","text":"getindex\nBase.setindex","category":"page"},{"location":"api/inference_data/#Base.getindex","page":"InferenceData","title":"Base.getindex","text":"Base.getindex(data::InferenceData, groups::Symbol; coords...) -> Dataset\nBase.getindex(data::InferenceData, groups; coords...) -> InferenceData\n\nReturn a new InferenceData containing the specified groups sliced to the specified coords.\n\ncoords specifies a dimension name mapping to an index, a DimensionalData.Selector, or an IntervalSets.AbstractInterval.\n\nIf one or more groups lack the specified dimension, a warning is raised but can be ignored. All groups that contain the dimension must also contain the specified indices, or an exception will be raised.\n\nExamples\n\nSelect data from all groups for just the specified id values.\n\njulia> using InferenceObjects, DimensionalData\n\njulia> idata = from_namedtuple(\n (θ=randn(4, 100, 4), τ=randn(4, 100));\n prior=(θ=randn(4, 100, 4), τ=randn(4, 100)),\n observed_data=(y=randn(4),),\n dims=(θ=[:id], y=[:id]),\n coords=(id=[\"a\", \"b\", \"c\", \"d\"],),\n )\nInferenceData with groups:\n > posterior\n > prior\n > observed_data\n\njulia> idata.posterior\nDataset with dimensions:\n Dim{:chain} Sampled 1:4 ForwardOrdered Regular Points,\n Dim{:draw} Sampled 1:100 ForwardOrdered Regular Points,\n Dim{:id} Categorical String[a, b, c, d] ForwardOrdered\nand 2 layers:\n :θ Float64 dims: Dim{:chain}, Dim{:draw}, Dim{:id} (4×100×4)\n :τ Float64 dims: Dim{:chain}, Dim{:draw} (4×100)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2022-08-11T11:15:21.4\"\n\njulia> idata_sel = idata[id=At([\"a\", \"b\"])]\nInferenceData with groups:\n > posterior\n > prior\n > observed_data\n\njulia> idata_sel.posterior\nDataset with dimensions:\n Dim{:chain} Sampled 1:4 ForwardOrdered Regular Points,\n Dim{:draw} Sampled 1:100 ForwardOrdered Regular Points,\n Dim{:id} Categorical String[a, b] ForwardOrdered\nand 2 layers:\n :θ Float64 dims: Dim{:chain}, Dim{:draw}, Dim{:id} (4×100×2)\n :τ Float64 dims: Dim{:chain}, Dim{:draw} (4×100)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2022-08-11T11:15:21.4\"\n\nSelect data from just the posterior, returning a Dataset if the indices index more than one element from any of the variables:\n\njulia> idata[:observed_data, id=At([\"a\"])]\nDataset with dimensions:\n Dim{:id} Categorical String[a] ForwardOrdered\nand 1 layer:\n :y Float64 dims: Dim{:id} (1)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2022-08-11T11:19:25.982\"\n\nNote that if a single index is provided, the behavior is still to slice so that the dimension is preserved.\n\n\n\n\n\n","category":"function"},{"location":"api/inference_data/#Base.setindex","page":"InferenceData","title":"Base.setindex","text":"Base.setindex(data::InferenceData, group::Dataset, name::Symbol) -> InferenceData\n\nCreate a new InferenceData containing the group with the specified name.\n\nIf a group with name is already in data, it is replaced.\n\n\n\n\n\n","category":"function"},{"location":"api/inference_data/#Iteration-interface","page":"InferenceData","title":"Iteration interface","text":"","category":"section"},{"location":"api/inference_data/","page":"InferenceData","title":"InferenceData","text":"InferenceData also implements the same iteration interface as its underlying NamedTuple. That is, iterating over an InferenceData iterates over its groups.","category":"page"},{"location":"api/inference_data/#General-conversion","page":"InferenceData","title":"General conversion","text":"","category":"section"},{"location":"api/inference_data/","page":"InferenceData","title":"InferenceData","text":"convert_to_inference_data\nfrom_dict\nfrom_namedtuple","category":"page"},{"location":"api/inference_data/#InferenceObjects.convert_to_inference_data","page":"InferenceData","title":"InferenceObjects.convert_to_inference_data","text":"convert_to_inference_data(obj; group, kwargs...) -> InferenceData\n\nConvert a supported object to an InferenceData object.\n\nIf obj converts to a single dataset, group specifies which dataset in the resulting InferenceData that is.\n\nSee convert_to_dataset\n\nArguments\n\nobj can be many objects. Basic supported types are:\nInferenceData: return unchanged\nDataset/DimensionalData.AbstractDimStack: add to InferenceData as the only group\nNamedTuple/AbstractDict: create a Dataset as the only group\nAbstractArray{<:Real}: create a Dataset as the only group, given an arbitrary name, if the name is not set\n\nMore specific types may be documented separately.\n\nKeywords\n\ngroup::Symbol = :posterior: If obj converts to a single dataset, assign the resulting dataset to this group.\ndims: a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are:\nSymbol: dimension name\nType{<:DimensionsionalData.Dimension}: dimension type\nDimensionsionalData.Dimension: dimension, potentially with indices\nNothing: no dimension name provided, dimension name is automatically generated\ncoords: a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated.\nkwargs: remaining keywords forwarded to converter functions\n\n\n\n\n\n","category":"function"},{"location":"api/inference_data/#InferenceObjects.from_dict","page":"InferenceData","title":"InferenceObjects.from_dict","text":"from_dict(posterior::AbstractDict; kwargs...) -> InferenceData\n\nConvert a Dict to an InferenceData.\n\nArguments\n\nposterior: The data to be converted. Its strings must be Symbol or AbstractString, and its values must be arrays.\n\nKeywords\n\nposterior_predictive::Any=nothing: Draws from the posterior predictive distribution\nsample_stats::Any=nothing: Statistics of the posterior sampling process\npredictions::Any=nothing: Out-of-sample predictions for the posterior.\nprior::Dict=nothing: Draws from the prior\nprior_predictive::Any=nothing: Draws from the prior predictive distribution\nsample_stats_prior::Any=nothing: Statistics of the prior sampling process\nobserved_data::NamedTuple: Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values.\nconstant_data::NamedTuple: Model constants, data included in the model which is not modeled as a random variable. Keys are parameter names and values.\npredictions_constant_data::NamedTuple: Constants relevant to the model predictions (i.e. new x values in a linear regression).\nlog_likelihood: Pointwise log-likelihood for the data. It is recommended to use this argument as a NamedTuple whose keys are observed variable names and whose values are log likelihood arrays.\nlibrary: Name of library that generated the draws\ncoords: Map from named dimension to named indices\ndims: Map from variable name to names of its dimensions\n\nReturns\n\nInferenceData: The data with groups corresponding to the provided data\n\nExamples\n\nusing InferenceObjects\nnchains = 2\nndraws = 100\n\ndata = Dict(\n :x => rand(ndraws, nchains),\n :y => randn(2, ndraws, nchains),\n :z => randn(3, 2, ndraws, nchains),\n)\nidata = from_dict(data)\n\n\n\n\n\n","category":"function"},{"location":"api/inference_data/#InferenceObjects.from_namedtuple","page":"InferenceData","title":"InferenceObjects.from_namedtuple","text":"from_namedtuple(posterior::NamedTuple; kwargs...) -> InferenceData\nfrom_namedtuple(posterior::Vector{Vector{<:NamedTuple}}; kwargs...) -> InferenceData\nfrom_namedtuple(\n posterior::NamedTuple,\n sample_stats::Any,\n posterior_predictive::Any,\n predictions::Any,\n log_likelihood::Any;\n kwargs...\n) -> InferenceData\n\nConvert a NamedTuple or container of NamedTuples to an InferenceData.\n\nIf containers are passed, they are flattened into a single NamedTuple with array elements whose first dimensions correspond to the dimensions of the containers.\n\nArguments\n\nposterior: The data to be converted. It may be of the following types:\n::NamedTuple: The keys are the variable names and the values are arrays with dimensions (ndraws, nchains[, sizes...]).\n::Vector{Vector{<:NamedTuple}}: A vector of length nchains whose elements have length ndraws.\n\nKeywords\n\nposterior_predictive::Any=nothing: Draws from the posterior predictive distribution\nsample_stats::Any=nothing: Statistics of the posterior sampling process\npredictions::Any=nothing: Out-of-sample predictions for the posterior.\nprior=nothing: Draws from the prior. Accepts the same types as posterior.\nprior_predictive::Any=nothing: Draws from the prior predictive distribution\nsample_stats_prior::Any=nothing: Statistics of the prior sampling process\nobserved_data::NamedTuple: Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values.\nconstant_data::NamedTuple: Model constants, data included in the model which is not modeled as a random variable. Keys are parameter names and values.\npredictions_constant_data::NamedTuple: Constants relevant to the model predictions (i.e. new x values in a linear regression).\nlog_likelihood: Pointwise log-likelihood for the data. It is recommended to use this argument as a NamedTuple whose keys are observed variable names and whose values are log likelihood arrays.\nlibrary: Name of library that generated the draws\ncoords: Map from named dimension to named indices\ndims: Map from variable name to names of its dimensions\n\nReturns\n\nInferenceData: The data with groups corresponding to the provided data\n\nnote: Note\nIf a NamedTuple is provided for observed_data, constant_data, or predictionsconstantdata`, any non-array values (e.g. integers) are converted to 0-dimensional arrays.\n\nExamples\n\nusing InferenceObjects\nnchains = 2\nndraws = 100\n\ndata1 = (\n x=rand(ndraws, nchains), y=randn(ndraws, nchains, 2), z=randn(ndraws, nchains, 3, 2)\n)\nidata1 = from_namedtuple(data1)\n\ndata2 = [[(x=rand(), y=randn(2), z=randn(3, 2)) for _ in 1:ndraws] for _ in 1:nchains];\nidata2 = from_namedtuple(data2)\n\n\n\n\n\n","category":"function"},{"location":"api/inference_data/#General-functions","page":"InferenceData","title":"General functions","text":"","category":"section"},{"location":"api/inference_data/","page":"InferenceData","title":"InferenceData","text":"cat\nmerge","category":"page"},{"location":"api/inference_data/#Base.cat","page":"InferenceData","title":"Base.cat","text":"cat(data::InferenceData...; [groups=keys(data[1]),] dims) -> InferenceData\n\nConcatenate InferenceData objects along the specified dimension dims.\n\nOnly the groups in groups are concatenated. Remaining groups are merged into the new InferenceData object.\n\nExamples\n\nHere is how we can concatenate all groups of two InferenceData objects along the existing chain dimension:\n\njulia> coords = (; a_dim=[\"x\", \"y\", \"z\"]);\n\njulia> dims = dims=(; a=[:a_dim]);\n\njulia> data = Dict(:a => randn(100, 4, 3), :b => randn(100, 4));\n\njulia> idata = from_dict(data; coords=coords, dims=dims)\nInferenceData with groups:\n > posterior\n\njulia> idata_cat1 = cat(idata, idata; dims=:chain)\nInferenceData with groups:\n > posterior\n\njulia> idata_cat1.posterior\nDataset with dimensions:\n Dim{:draw},\n Dim{:chain},\n Dim{:a_dim} Categorical{String} String[\"x\", \"y\", \"z\"] ForwardOrdered\nand 2 layers:\n :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim} (100×8×3)\n :b Float64 dims: Dim{:draw}, Dim{:chain} (100×8)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-04-03T18:41:35.779\"\n\nAlternatively, we can concatenate along a new run dimension, which will be created.\n\njulia> idata_cat2 = cat(idata, idata; dims=:run)\nInferenceData with groups:\n > posterior\n\njulia> idata_cat2.posterior\nDataset with dimensions:\n Dim{:draw},\n Dim{:chain},\n Dim{:a_dim} Categorical{String} String[\"x\", \"y\", \"z\"] ForwardOrdered,\n Dim{:run}\nand 2 layers:\n :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim}, Dim{:run} (100×4×3×2)\n :b Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:run} (100×4×2)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-04-03T18:41:35.779\"\n\nWe can also concatenate only a subset of groups and merge the rest, which is useful when some groups are present only in some of the InferenceData objects or will be identical in all of them:\n\njulia> observed_data = Dict(:y => randn(10));\n\njulia> idata2 = from_dict(data; observed_data=observed_data, coords=coords, dims=dims)\nInferenceData with groups:\n > posterior\n > observed_data\n\njulia> idata_cat3 = cat(idata, idata2; groups=(:posterior,), dims=:run)\nInferenceData with groups:\n > posterior\n > observed_data\n\njulia> idata_cat3.posterior\nDataset with dimensions:\n Dim{:draw},\n Dim{:chain},\n Dim{:a_dim} Categorical{String} String[\"x\", \"y\", \"z\"] ForwardOrdered,\n Dim{:run}\nand 2 layers:\n :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim}, Dim{:run} (100×4×3×2)\n :b Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:run} (100×4×2)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-04-03T18:41:35.779\"\n\njulia> idata_cat3.observed_data\nDataset with dimensions: Dim{:y_dim_1}\nand 1 layer:\n :y Float64 dims: Dim{:y_dim_1} (10)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-02-17T15:11:00.59\"\n\n\n\n\n\n","category":"function"},{"location":"api/inference_data/#Base.merge","page":"InferenceData","title":"Base.merge","text":"merge(data::InferenceData...) -> InferenceData\n\nMerge InferenceData objects.\n\nThe result contains all groups in data and others. If a group appears more than once, the one that occurs last is kept.\n\nSee also: cat\n\nExamples\n\nHere we merge an InferenceData containing only a posterior group with one containing only a prior group to create a new one containing both groups.\n\njulia> idata1 = from_dict(Dict(:a => randn(100, 4, 3), :b => randn(100, 4)))\nInferenceData with groups:\n > posterior\n\njulia> idata2 = from_dict(; prior=Dict(:a => randn(100, 1, 3), :c => randn(100, 1)))\nInferenceData with groups:\n > prior\n\njulia> idata_merged = merge(idata1, idata2)\nInferenceData with groups:\n > posterior\n > prior\n\n\n\n\n\n","category":"function"},{"location":"quickstart/","page":"Quickstart","title":"Quickstart","text":"\n\n\n

ArviZ Quickstart

Note

This tutorial is adapted from ArviZ's quickstart.

\n\n\n

Setup

Here we add the necessary packages for this notebook and load a few we will use throughout.

\n\n\n\n\n
using ArviZ, ArviZPythonPlots, Distributions, LinearAlgebra, Random, StanSample, Turing
\n\n\n
# ArviZPythonPlots ships with style sheets!\nuse_style(\"arviz-darkgrid\")
\n\n\n\n

Get started with plotting

To plot with ArviZ, we need to load the ArviZPythonPlots package. ArviZ is designed to be used with libraries like Stan, Turing.jl, and Soss.jl but works fine with raw arrays.

\n\n
rng1 = Random.MersenneTwister(37772);
\n\n\n
begin\n    plot_posterior(randn(rng1, 100_000))\n    gcf()\nend
\n\n\n\n

Plotting a dictionary of arrays, ArviZ will interpret each key as the name of a different random variable. Each row of an array is treated as an independent series of draws from the variable, called a chain. Below, we have 10 chains of 50 draws each for four different distributions.

\n\n
let\n    s = (50, 10)\n    plot_forest((\n        normal=randn(rng1, s),\n        gumbel=rand(rng1, Gumbel(), s),\n        student_t=rand(rng1, TDist(6), s),\n        exponential=rand(rng1, Exponential(), s),\n    ),)\n    gcf()\nend
\n\n\n\n

Plotting with MCMCChains.jl's Chains objects produced by Turing.jl

ArviZ is designed to work well with high dimensional, labelled data. Consider the eight schools model, which roughly tries to measure the effectiveness of SAT classes at eight different schools. To show off ArviZ's labelling, I give the schools the names of a different eight schools.

This model is small enough to write down, is hierarchical, and uses labelling. Additionally, a centered parameterization causes divergences (which are interesting for illustration).

First we create our data and set some sampling parameters.

\n\n
begin\n    J = 8\n    y = [28.0, 8.0, -3.0, 7.0, -1.0, 1.0, 18.0, 12.0]\n    σ = [15.0, 10.0, 16.0, 11.0, 9.0, 11.0, 10.0, 18.0]\n    schools = [\n        \"Choate\",\n        \"Deerfield\",\n        \"Phillips Andover\",\n        \"Phillips Exeter\",\n        \"Hotchkiss\",\n        \"Lawrenceville\",\n        \"St. Paul's\",\n        \"Mt. Hermon\",\n    ]\n    ndraws = 1_000\n    ndraws_warmup = 1_000\n    nchains = 4\nend;
\n\n\n\n

Now we write and run the model using Turing:

\n\n
Turing.@model function model_turing(y, σ, J=length(y))\n    μ ~ Normal(0, 5)\n    τ ~ truncated(Cauchy(0, 5), 0, Inf)\n    θ ~ filldist(Normal(μ, τ), J)\n    for i in 1:J\n        y[i] ~ Normal(θ[i], σ[i])\n    end\nend
\n
model_turing (generic function with 4 methods)
\n\n
rng2 = Random.MersenneTwister(16653);
\n\n\n
begin\n    param_mod_turing = model_turing(y, σ)\n    sampler = NUTS(ndraws_warmup, 0.8)\n\n    turing_chns = Turing.sample(\n        rng2, model_turing(y, σ), sampler, MCMCThreads(), ndraws, nchains\n    )\nend;
\n\n\n\n

Most ArviZ functions work fine with Chains objects from Turing:

\n\n
begin\n    plot_autocorr(turing_chns; var_names=(:μ, :τ))\n    gcf()\nend
\n\n\n\n

Convert to InferenceData

For much more powerful querying, analysis and plotting, we can use built-in ArviZ utilities to convert Chains objects to multidimensional data structures with named dimensions and indices. Note that for such dimensions, the information is not contained in Chains, so we need to provide it.

ArviZ is built to work with InferenceData, and the more groups it has access to, the more powerful analyses it can perform.

\n\n
idata_turing_post = from_mcmcchains(\n    turing_chns;\n    coords=(; school=schools),\n    dims=NamedTuple(k => (:school,) for k in (:y, :σ, :θ)),\n    library=\"Turing\",\n)
\n
InferenceData
posterior
Dataset with dimensions: \n  Dim{:draw},\n  Dim{:chain},\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n  :μ Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :τ Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :θ Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)\n\nwith metadata Dict{String, Any} with 2 entries:\n  \"created_at\" => \"2023-12-23T22:52:52.783\"\n  \"inference_library\" => \"Turing\"
sample_stats
Dataset with dimensions: Dim{:draw}, Dim{:chain}\nand 12 layers:\n  :energy           Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :n_steps          Int64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :diverging        Bool dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :max_energy_error Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :energy_error     Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :is_accept        Bool dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :log_density      Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :tree_depth       Int64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :step_size        Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :acceptance_rate  Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :lp               Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :step_size_nom    Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n\nwith metadata Dict{String, Any} with 2 entries:\n  \"created_at\" => \"2023-12-23T22:52:52.666\"\n  \"inference_library\" => \"Turing\"
\n\n\n

Each group is an ArviZ.Dataset, a DimensionalData.AbstractDimStack that can be used identically to a DimensionalData.Dimstack. We can view a summary of the dataset.

\n\n
idata_turing_post.posterior
\n
Dataset with dimensions: \n  Dim{:draw},\n  Dim{:chain},\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n  :μ Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :τ Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :θ Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)\n\nwith metadata Dict{String, Any} with 2 entries:\n  \"created_at\"        => \"2023-12-23T22:52:52.783\"\n  \"inference_library\" => \"Turing\"
\n\n\n

Here is a plot of the trace. Note the intelligent labels.

\n\n
begin\n    plot_trace(idata_turing_post)\n    gcf()\nend
\n\n\n\n

We can also generate summary stats...

\n\n
summarystats(idata_turing_post)
\n
SummaryStats
meanstdhdi_3%hdi_97%mcse_meanmcse_stdess_tailess_bulkrhat
μ4.33.3-1.8110.50.110.06211928451.01
τ4.43.30.67310.40.200.121091151.05
θ[Choate]6.66.1-4.0118.00.210.1916277501.01
θ[Deerfield]5.05.0-4.8114.20.140.14195212771.01
θ[Phillips Andover]3.75.7-7.0714.60.140.16197914291.01
θ[Phillips Exeter]4.85.1-4.6014.40.140.14206411781.00
θ[Hotchkiss]3.34.9-6.0812.60.150.11180410981.01
θ[Lawrenceville]3.85.2-6.1213.30.130.14196513311.00
θ[St. Paul's]6.65.4-2.6817.40.180.1418428531.01
θ[Mt. Hermon]4.95.6-5.7114.80.140.19179413931.00
\n\n\n

...and examine the energy distribution of the Hamiltonian sampler.

\n\n
begin\n    plot_energy(idata_turing_post)\n    gcf()\nend
\n\n\n\n

Additional information in Turing.jl

With a few more steps, we can use Turing to compute additional useful groups to add to the InferenceData.

To sample from the prior, one simply calls sample but with the Prior sampler:

\n\n
prior = Turing.sample(rng2, param_mod_turing, Prior(), ndraws);
\n\n\n\n

To draw from the prior and posterior predictive distributions we can instantiate a \"predictive model\", i.e. a Turing model but with the observations set to missing, and then calling predict on the predictive model and the previously drawn samples:

\n\n
begin\n    # Instantiate the predictive model\n    param_mod_predict = model_turing(similar(y, Missing), σ)\n    # and then sample!\n    prior_predictive = Turing.predict(rng2, param_mod_predict, prior)\n    posterior_predictive = Turing.predict(rng2, param_mod_predict, turing_chns)\nend;
\n\n\n\n

And to extract the pointwise log-likelihoods, which is useful if you want to compute metrics such as loo,

\n\n
log_likelihood = let\n    log_likelihood = Turing.pointwise_loglikelihoods(\n        param_mod_turing, MCMCChains.get_sections(turing_chns, :parameters)\n    )\n    # Ensure the ordering of the loglikelihoods matches the ordering of `posterior_predictive`\n    ynames = string.(keys(posterior_predictive))\n    log_likelihood_y = getindex.(Ref(log_likelihood), ynames)\n    (; y=cat(log_likelihood_y...; dims=3))\nend;
\n\n\n\n

This can then be included in the from_mcmcchains call from above:

\n\n
idata_turing = from_mcmcchains(\n    turing_chns;\n    posterior_predictive,\n    log_likelihood,\n    prior,\n    prior_predictive,\n    observed_data=(; y),\n    coords=(; school=schools),\n    dims=NamedTuple(k => (:school,) for k in (:y, :σ, :θ)),\n    library=Turing,\n)
\n
InferenceData
posterior
Dataset with dimensions: \n  Dim{:draw},\n  Dim{:chain},\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n  :μ Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :τ Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :θ Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)\n\nwith metadata Dict{String, Any} with 3 entries:\n  \"created_at\" => \"2023-12-23T22:53:24.667\"\n  \"inference_library_version\" => \"0.30.0\"\n  \"inference_library\" => \"Turing\"
posterior_predictive
Dataset with dimensions: \n  Dim{:draw},\n  Dim{:chain},\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n  :y Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)\n\nwith metadata Dict{String, Any} with 3 entries:\n  \"created_at\" => \"2023-12-23T22:53:23.998\"\n  \"inference_library_version\" => \"0.30.0\"\n  \"inference_library\" => \"Turing\"
log_likelihood
Dataset with dimensions: \n  Dim{:draw},\n  Dim{:chain},\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n  :y Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)\n\nwith metadata Dict{String, Any} with 3 entries:\n  \"created_at\" => \"2023-12-23T22:53:24.498\"\n  \"inference_library_version\" => \"0.30.0\"\n  \"inference_library\" => \"Turing\"
sample_stats
Dataset with dimensions: Dim{:draw}, Dim{:chain}\nand 12 layers:\n  :energy           Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :n_steps          Int64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :diverging        Bool dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :max_energy_error Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :energy_error     Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :is_accept        Bool dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :log_density      Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :tree_depth       Int64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :step_size        Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :acceptance_rate  Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :lp               Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :step_size_nom    Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n\nwith metadata Dict{String, Any} with 3 entries:\n  \"created_at\" => \"2023-12-23T22:53:24.666\"\n  \"inference_library_version\" => \"0.30.0\"\n  \"inference_library\" => \"Turing\"
prior
Dataset with dimensions: \n  Dim{:draw},\n  Dim{:chain},\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n  :μ Float64 dims: Dim{:draw}, Dim{:chain} (1000×1)\n  :τ Float64 dims: Dim{:draw}, Dim{:chain} (1000×1)\n  :θ Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×1×8)\n\nwith metadata Dict{String, Any} with 3 entries:\n  \"created_at\" => \"2023-12-23T22:53:25.381\"\n  \"inference_library_version\" => \"0.30.0\"\n  \"inference_library\" => \"Turing\"
prior_predictive
Dataset with dimensions: \n  Dim{:draw},\n  Dim{:chain},\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n  :y Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×1×8)\n\nwith metadata Dict{String, Any} with 3 entries:\n  \"created_at\" => \"2023-12-23T22:53:25.163\"\n  \"inference_library_version\" => \"0.30.0\"\n  \"inference_library\" => \"Turing\"
sample_stats_prior
Dataset with dimensions: Dim{:draw}, Dim{:chain}\nand 1 layer:\n  :lp Float64 dims: Dim{:draw}, Dim{:chain} (1000×1)\n\nwith metadata Dict{String, Any} with 3 entries:\n  \"created_at\" => \"2023-12-23T22:53:25.275\"\n  \"inference_library_version\" => \"0.30.0\"\n  \"inference_library\" => \"Turing\"
observed_data
Dataset with dimensions: \n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n  :y Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 3 entries:\n  \"created_at\" => \"2023-12-23T22:53:25.662\"\n  \"inference_library_version\" => \"0.30.0\"\n  \"inference_library\" => \"Turing\"
\n\n\n

Then we can for example compute the expected leave-one-out (LOO) predictive density, which is an estimate of the out-of-distribution predictive fit of the model:

\n\n
loo(idata_turing) # higher ELPD is better
\n
PSISLOOResult with estimates\n elpd  elpd_mcse    p  p_mcse\n  -31        1.4  1.0    0.33\n\nand PSISResult with 1000 draws, 4 chains, and 8 parameters\nPareto shape (k) diagnostic values:\n                    Count      Min. ESS\n (-Inf, 0.5]  good  5 (62.5%)  404\n  (0.5, 0.7]  okay  3 (37.5%)  788
\n\n\n

If the model is well-calibrated, i.e. it replicates the true generative process well, the CDF of the pointwise LOO values should be similarly distributed to a uniform distribution. This can be inspected visually:

\n\n
begin\n    plot_loo_pit(idata_turing; y=:y, ecdf=true)\n    gcf()\nend
\n\n\n\n

Plotting with Stan.jl outputs

StanSample.jl comes with built-in support for producing InferenceData outputs.

Here is the same centered eight schools model in Stan:

\n\n
begin\n    schools_code = \"\"\"\n    data {\n      int<lower=0> J;\n      array[J] real y;\n      array[J] real<lower=0> sigma;\n    }\n\n    parameters {\n      real mu;\n      real<lower=0> tau;\n      array[J] real theta;\n    }\n\n    model {\n      mu ~ normal(0, 5);\n      tau ~ cauchy(0, 5);\n      theta ~ normal(mu, tau);\n      y ~ normal(theta, sigma);\n    }\n\n    generated quantities {\n        vector[J] log_lik;\n        vector[J] y_hat;\n        for (j in 1:J) {\n            log_lik[j] = normal_lpdf(y[j] | theta[j], sigma[j]);\n            y_hat[j] = normal_rng(theta[j], sigma[j]);\n        }\n    }\n    \"\"\"\n\n    schools_data = Dict(\"J\" => J, \"y\" => y, \"sigma\" => σ)\n    idata_stan = mktempdir() do path\n        stan_model = SampleModel(\"schools\", schools_code, path)\n        _ = stan_sample(\n            stan_model;\n            data=schools_data,\n            num_chains=nchains,\n            num_warmups=ndraws_warmup,\n            num_samples=ndraws,\n            seed=28983,\n            summary=false,\n        )\n        return StanSample.inferencedata(\n            stan_model;\n            posterior_predictive_var=:y_hat,\n            observed_data=(; y),\n            log_likelihood_var=:log_lik,\n            coords=(; school=schools),\n            dims=NamedTuple(\n                k => (:school,) for k in (:y, :sigma, :theta, :log_lik, :y_hat)\n            ),\n        )\n    end\nend
\n
InferenceData
posterior
Dataset with dimensions: \n  Dim{:draw},\n  Dim{:chain},\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n  :mu    Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :tau   Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :theta Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)\n\nwith metadata Dict{String, Any} with 1 entry:\n  \"created_at\" => \"2023-12-23T22:54:01.721\"
posterior_predictive
Dataset with dimensions: \n  Dim{:draw},\n  Dim{:chain},\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n  :y_hat Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)\n\nwith metadata Dict{String, Any} with 1 entry:\n  \"created_at\" => \"2023-12-23T22:54:01.026\"
log_likelihood
Dataset with dimensions: \n  Dim{:draw},\n  Dim{:chain},\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n  :log_lik Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:school} (1000×4×8)\n\nwith metadata Dict{String, Any} with 1 entry:\n  \"created_at\" => \"2023-12-23T22:54:01.559\"
sample_stats
Dataset with dimensions: Dim{:draw}, Dim{:chain}\nand 7 layers:\n  :tree_depth      Int64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :energy          Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :diverging       Bool dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :acceptance_rate Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :n_steps         Int64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :lp              Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n  :step_size       Float64 dims: Dim{:draw}, Dim{:chain} (1000×4)\n\nwith metadata Dict{String, Any} with 1 entry:\n  \"created_at\" => \"2023-12-23T22:54:01.259\"
observed_data
Dataset with dimensions: \n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n  :y Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 1 entry:\n  \"created_at\" => \"2023-12-23T22:54:01.857\"
\n\n
begin\n    plot_density(idata_stan; var_names=(:mu, :tau))\n    gcf()\nend
\n\n\n\n

Here is a plot showing where the Hamiltonian sampler had divergences:

\n\n
begin\n    plot_pair(\n        idata_stan;\n        coords=Dict(:school => [\"Choate\", \"Deerfield\", \"Phillips Andover\"]),\n        divergences=true,\n    )\n    gcf()\nend
\n\n\n\n

Environment

\n\n
using PlutoUI
\n\n\n
using Pkg, InteractiveUtils
\n\n\n
with_terminal(Pkg.status; color=false)
\n
Status `~/work/ArviZ.jl/ArviZ.jl/docs/Project.toml`\n  [cbdf2221] AlgebraOfGraphics v0.6.17\n  [131c737c] ArviZ v0.10.4 `~/work/ArviZ.jl/ArviZ.jl`\n  [2f96bb34] ArviZExampleData v0.1.8\n  [4a6e88f0] ArviZPythonPlots v0.1.3\n  [13f3f980] CairoMakie v0.11.4\n  [a93c6f00] DataFrames v1.6.1\n⌃ [0703355e] DimensionalData v0.24.13\n  [31c24e10] Distributions v0.25.104\n  [e30172f5] Documenter v1.2.1\n  [f6006082] EvoTrees v0.16.5\n  [b5cf5a8d] InferenceObjects v0.3.15\n  [be115224] MCMCDiagnosticTools v0.3.8\n  [a7f614a8] MLJBase v1.0.1\n  [614be32b] MLJIteration v0.6.0\n  [ce719bf2] PSIS v0.9.4\n  [359b1769] PlutoStaticHTML v6.0.18\n  [7f904dfe] PlutoUI v0.7.54\n  [7f36be82] PosteriorStats v0.2.0\n  [c1514b29] StanSample v7.6.0\n  [a19d573c] StatisticalMeasures v0.1.3\n  [2913bbd2] StatsBase v0.34.2\n  [fce5fe82] Turing v0.30.0\n  [f43a241f] Downloads v1.6.0\n  [37e2e46d] LinearAlgebra\n  [10745b16] Statistics v1.9.0\nInfo Packages marked with ⌃ have new versions available and may be upgradable.\n
\n\n
with_terminal(versioninfo)
\n
Julia Version 1.9.4\nCommit 8e5136fa297 (2023-11-14 08:46 UTC)\nBuild Info:\n  Official https://julialang.org/ release\nPlatform Info:\n  OS: Linux (x86_64-linux-gnu)\n  CPU: 4 × AMD EPYC 7763 64-Core Processor\n  WORD_SIZE: 64\n  LIBM: libopenlibm\n  LLVM: libLLVM-14.0.6 (ORCJIT, znver3)\n  Threads: 2 on 4 virtual cores\nEnvironment:\n  JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager\n  JULIA_PROJECT = /home/runner/work/ArviZ.jl/ArviZ.jl/docs/\n  JULIA_DEPOT_PATH = /home/runner/.julia:/opt/hostedtoolcache/julia/1.9.4/x64/local/share/julia:/opt/hostedtoolcache/julia/1.9.4/x64/share/julia\n  JULIA_NUM_THREADS = 2\n  JULIA_LOAD_PATH = @:@v#.#:@stdlib\n  JULIA_CMDSTAN_HOME = /home/runner/work/ArviZ.jl/ArviZ.jl/.cmdstan//cmdstan-2.33.1/\n  JULIA_REVISE_WORKER_ONLY = 1\n  JULIA_PYTHONCALL_EXE = /home/runner/work/ArviZ.jl/ArviZ.jl/docs/.CondaPkg/env/bin/python\n
\n\n","category":"page"},{"location":"quickstart/","page":"Quickstart","title":"Quickstart","text":"EditURL = \"https://github.com/arviz-devs/ArviZ.jl/blob/main/docs/src/quickstart.jl\"","category":"page"},{"location":"api/data/#data-api","page":"Data","title":"Data","text":"","category":"section"},{"location":"api/data/","page":"Data","title":"Data","text":"Pages = [\"data.md\"]","category":"page"},{"location":"api/data/#Inference-library-converters","page":"Data","title":"Inference library converters","text":"","category":"section"},{"location":"api/data/","page":"Data","title":"Data","text":"from_mcmcchains\nfrom_samplechains","category":"page"},{"location":"api/data/#ArviZ.from_mcmcchains","page":"Data","title":"ArviZ.from_mcmcchains","text":"from_mcmcchains(posterior::MCMCChains.Chains; kwargs...) -> InferenceData\nfrom_mcmcchains(; kwargs...) -> InferenceData\nfrom_mcmcchains(\n posterior::MCMCChains.Chains,\n posterior_predictive,\n predictions,\n log_likelihood;\n kwargs...\n) -> InferenceData\n\nConvert data in an MCMCChains.Chains format into an InferenceData.\n\nAny keyword argument below without an an explicitly annotated type above is allowed, so long as it can be passed to convert_to_inference_data.\n\nArguments\n\nposterior::MCMCChains.Chains: Draws from the posterior\n\nKeywords\n\nposterior_predictive::Any=nothing: Draws from the posterior predictive distribution or name(s) of predictive variables in posterior\npredictions: Out-of-sample predictions for the posterior.\nprior: Draws from the prior\nprior_predictive: Draws from the prior predictive distribution or name(s) of predictive variables in prior\nobserved_data: Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values.\nconstant_data: Model constants, data included in the model that are not modeled as random variables. Keys are parameter names.\npredictions_constant_data: Constants relevant to the model predictions (i.e. new x values in a linear regression).\nlog_likelihood: Pointwise log-likelihood for the data. It is recommended to use this argument as a named tuple whose keys are observed variable names and whose values are log likelihood arrays. Alternatively, provide the name of variable in posterior containing log likelihoods.\nlibrary=MCMCChains: Name of library that generated the chains\ncoords: Map from named dimension to named indices\ndims: Map from variable name to names of its dimensions\neltypes: Map from variable names to eltypes. This is primarily used to assign discrete eltypes to discrete variables that were stored in Chains as floats.\n\nReturns\n\nInferenceData: The data with groups corresponding to the provided data\n\n\n\n\n\n","category":"function"},{"location":"api/data/#ArviZ.from_samplechains","page":"Data","title":"ArviZ.from_samplechains","text":"from_samplechains(\n posterior=nothing;\n prior=nothing,\n library=SampleChains,\n kwargs...,\n) -> InferenceData\n\nConvert SampleChains samples to an InferenceData.\n\nEither posterior or prior may be a SampleChains.AbstractChain or SampleChains.MultiChain object.\n\nFor descriptions of remaining kwargs, see from_namedtuple.\n\n\n\n\n\n","category":"function"},{"location":"api/data/#IO-/-Conversion","page":"Data","title":"IO / Conversion","text":"","category":"section"},{"location":"api/data/","page":"Data","title":"Data","text":"from_netcdf\nto_netcdf","category":"page"},{"location":"api/data/#InferenceObjects.from_netcdf","page":"Data","title":"InferenceObjects.from_netcdf","text":"from_netcdf(path::AbstractString; kwargs...) -> InferenceData\n\nLoad an InferenceData from an unopened NetCDF file.\n\nRemaining kwargs are passed to NCDatasets.NCDataset. This method loads data eagerly. To instead load data lazily, pass an opened NCDataset to from_netcdf.\n\nnote: Note\nThis method requires that NCDatasets is loaded before it can be used.\n\nExamples\n\njulia> using InferenceObjects, NCDatasets\n\njulia> idata = from_netcdf(\"centered_eight.nc\")\nInferenceData with groups:\n > posterior\n > posterior_predictive\n > sample_stats\n > prior\n > observed_data\n\nfrom_netcdf(ds::NCDatasets.NCDataset; load_mode) -> InferenceData\n\nLoad an InferenceData from an opened NetCDF file.\n\nload_mode defaults to :lazy, which avoids reading variables into memory. Operations on these arrays will be slow. load_mode can also be :eager, which copies all variables into memory. It is then safe to close ds. If load_mode is :lazy and ds is closed after constructing InferenceData, using the variable arrays will have undefined behavior.\n\nExamples\n\nHere is how we might load an InferenceData from an InferenceData lazily from a web-hosted NetCDF file.\n\njulia> using HTTP, InferenceObjects, NCDatasets\n\njulia> resp = HTTP.get(\"https://github.com/arviz-devs/arviz_example_data/blob/main/data/centered_eight.nc?raw=true\");\n\njulia> ds = NCDataset(\"centered_eight\", \"r\"; memory = resp.body);\n\njulia> idata = from_netcdf(ds)\nInferenceData with groups:\n > posterior\n > posterior_predictive\n > sample_stats\n > prior\n > observed_data\n\njulia> idata_copy = copy(idata); # disconnect from the loaded dataset\n\njulia> close(ds);\n\n\n\n\n\n","category":"function"},{"location":"api/data/#InferenceObjects.to_netcdf","page":"Data","title":"InferenceObjects.to_netcdf","text":"to_netcdf(data, dest::AbstractString; group::Symbol=:posterior, kwargs...)\nto_netcdf(data, dest::NCDatasets.NCDataset; group::Symbol=:posterior)\n\nWrite data to a NetCDF file.\n\ndata is any type that can be converted to an InferenceData using convert_to_inference_data. If not an InferenceData, then group specifies which group the data represents.\n\ndest specifies either the path to the NetCDF file or an opened NetCDF file. If dest is a path, remaining kwargs are passed to NCDatasets.NCDataset.\n\nnote: Note\nThis method requires that NCDatasets is loaded before it can be used.\n\nExamples\n\njulia> using InferenceObjects, NCDatasets\n\njulia> idata = from_namedtuple((; x = randn(4, 100, 3), z = randn(4, 100)))\nInferenceData with groups:\n > posterior\n\njulia> to_netcdf(idata, \"data.nc\")\n\"data.nc\"\n\n\n\n\n\n","category":"function"},{"location":"api/diagnostics/#diagnostics-api","page":"Diagnostics","title":"Diagnostics","text":"","category":"section"},{"location":"api/diagnostics/","page":"Diagnostics","title":"Diagnostics","text":"Pages = [\"diagnostics.md\"]","category":"page"},{"location":"api/diagnostics/#bfmi","page":"Diagnostics","title":"Bayesian fraction of missing information","text":"","category":"section"},{"location":"api/diagnostics/","page":"Diagnostics","title":"Diagnostics","text":"MCMCDiagnosticTools.bfmi","category":"page"},{"location":"api/diagnostics/#MCMCDiagnosticTools.bfmi","page":"Diagnostics","title":"MCMCDiagnosticTools.bfmi","text":"bfmi(energy::AbstractVector{<:Real}) -> Real\nbfmi(energy::AbstractMatrix{<:Real}; dims::Int=1) -> AbstractVector{<:Real}\n\nCalculate the estimated Bayesian fraction of missing information (BFMI).\n\nWhen sampling with Hamiltonian Monte Carlo (HMC), BFMI quantifies how well momentum resampling matches the marginal energy distribution.\n\nThe current advice is that values smaller than 0.3 indicate poor sampling. However, this threshold is provisional and may change. A BFMI value below the threshold often indicates poor adaptation of sampling parameters or that the target distribution has heavy tails that were not well explored by the Markov chain.\n\nFor more information, see Section 6.1 of [Betancourt2018] or [Betancourt2016] for a complete account.\n\nenergy is either a vector of Hamiltonian energies of draws or a matrix of energies of draws for multiple chains. dims indicates the dimension in energy that contains the draws. The default dims=1 assumes energy has the shape draws or (draws, chains). If a different shape is provided, dims must be set accordingly.\n\nIf energy is a vector, a single BFMI value is returned. Otherwise, a vector of BFMI values for each chain is returned.\n\n[Betancourt2018]: Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]\n\n[Betancourt2016]: Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]\n\n\n\n\n\n","category":"function"},{"location":"api/diagnostics/#ess_rhat","page":"Diagnostics","title":"Effective sample size and widehatR diagnostic","text":"","category":"section"},{"location":"api/diagnostics/","page":"Diagnostics","title":"Diagnostics","text":"MCMCDiagnosticTools.ess\nMCMCDiagnosticTools.rhat\nMCMCDiagnosticTools.ess_rhat","category":"page"},{"location":"api/diagnostics/#MCMCDiagnosticTools.ess","page":"Diagnostics","title":"MCMCDiagnosticTools.ess","text":"ess(\n samples::AbstractArray{<:Union{Missing,Real}};\n kind=:bulk,\n relative::Bool=false,\n autocov_method=AutocovMethod(),\n split_chains::Int=2,\n maxlag::Int=250,\n kwargs...\n)\n\nEstimate the effective sample size (ESS) of the samples of shape (draws, [chains[, parameters...]]) with the autocov_method.\n\nOptionally, the kind of ESS estimate to be computed can be specified (see below). Some kinds accept additional kwargs.\n\nIf relative is true, the relative ESS is returned, i.e. ess / (draws * chains).\n\nsplit_chains indicates the number of chains each chain is split into. When split_chains > 1, then the diagnostics check for within-chain convergence. When d = mod(draws, split_chains) > 0, i.e. the chains cannot be evenly split, then 1 draw is discarded after each of the first d splits within each chain. There must be at least 3 draws in each chain after splitting.\n\nmaxlag indicates the maximum lag for which autocovariance is computed and must be greater than 0.\n\nFor a given estimand, it is recommended that the ESS is at least 100 * chains and that widehatR 101.[VehtariGelman2021]\n\nSee also: AutocovMethod, FFTAutocovMethod, BDAAutocovMethod, rhat, ess_rhat, mcse\n\nKinds of ESS estimates\n\nIf kind isa a Symbol, it may take one of the following values:\n\n:bulk: basic ESS computed on rank-normalized draws. This kind diagnoses poor convergence in the bulk of the distribution due to trends or different locations of the chains.\n:tail: minimum of the quantile-ESS for the symmetric quantiles where tail_prob=0.1 is the probability in the tails. This kind diagnoses poor convergence in the tails of the distribution. If this kind is chosen, kwargs may contain a tail_prob keyword.\n:basic: basic ESS, equivalent to specifying kind=Statistics.mean.\n\nnote: Note\nWhile Bulk-ESS is conceptually related to basic ESS, it is well-defined even if the chains do not have finite variance.[VehtariGelman2021] For each parameter, rank-normalization proceeds by first ranking the inputs using \"tied ranking\" and then transforming the ranks to normal quantiles so that the result is standard normally distributed. This transform is monotonic.\n\nOtherwise, kind specifies one of the following estimators, whose ESS is to be estimated:\n\nStatistics.mean\nStatistics.median\nStatistics.std\nStatsBase.mad\nBase.Fix2(Statistics.quantile, p::Real)\n\n[VehtariGelman2021]: Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved widehat R for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008\n\n\n\n\n\ness(data::InferenceData; kwargs...) -> Dataset\ness(data::Dataset; kwargs...) -> Dataset\n\nCalculate the effective sample size (ESS) for each parameter in the data.\n\n\n\n\n\n","category":"function"},{"location":"api/diagnostics/#MCMCDiagnosticTools.rhat","page":"Diagnostics","title":"MCMCDiagnosticTools.rhat","text":"rhat(samples::AbstractArray{Union{Real,Missing}}; kind::Symbol=:rank, split_chains=2)\n\nCompute the widehatR diagnostics for each parameter in samples of shape (draws, [chains[, parameters...]]).[VehtariGelman2021]\n\nkind indicates the kind of widehatR to compute (see below).\n\nsplit_chains indicates the number of chains each chain is split into. When split_chains > 1, then the diagnostics check for within-chain convergence. When d = mod(draws, split_chains) > 0, i.e. the chains cannot be evenly split, then 1 draw is discarded after each of the first d splits within each chain.\n\nSee also ess, ess_rhat, rstar\n\nKinds of widehatR\n\nThe following kinds are supported:\n\n:rank: maximum of widehatR with kind=:bulk and kind=:tail.\n:bulk: basic widehatR computed on rank-normalized draws. This kind diagnoses poor convergence in the bulk of the distribution due to trends or different locations of the chains.\n:tail: widehatR computed on draws folded around the median and then rank-normalized. This kind diagnoses poor convergence in the tails of the distribution due to different scales of the chains.\n:basic: Classic widehatR.\n\n[VehtariGelman2021]: Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved widehat R for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008\n\n\n\n\n\nrhat(data::InferenceData; kwargs...) -> Dataset\nrhat(data::Dataset; kwargs...) -> Dataset\n\nCalculate the widehatR diagnostic for each parameter in the data.\n\n\n\n\n\n","category":"function"},{"location":"api/diagnostics/#MCMCDiagnosticTools.ess_rhat","page":"Diagnostics","title":"MCMCDiagnosticTools.ess_rhat","text":"ess_rhat(\n samples::AbstractArray{<:Union{Missing,Real}};\n kind::Symbol=:rank,\n kwargs...,\n) -> NamedTuple{(:ess, :rhat)}\n\nEstimate the effective sample size and widehatR of the samples of shape (draws, [chains[, parameters...]]).\n\nWhen both ESS and widehatR are needed, this method is often more efficient than calling ess and rhat separately.\n\nSee rhat for a description of supported kinds and ess for a description of kwargs.\n\n\n\n\n\ness_rhat(data::InferenceData; kwargs...) -> Dataset\ness_rhat(data::Dataset; kwargs...) -> Dataset\n\nCalculate the effective sample size (ESS) and widehatR diagnostic for each parameter in the data.\n\n\n\n\n\n","category":"function"},{"location":"api/diagnostics/","page":"Diagnostics","title":"Diagnostics","text":"The following autocovariance methods are supported:","category":"page"},{"location":"api/diagnostics/","page":"Diagnostics","title":"Diagnostics","text":"MCMCDiagnosticTools.AutocovMethod\nMCMCDiagnosticTools.FFTAutocovMethod\nMCMCDiagnosticTools.BDAAutocovMethod","category":"page"},{"location":"api/diagnostics/#MCMCDiagnosticTools.AutocovMethod","page":"Diagnostics","title":"MCMCDiagnosticTools.AutocovMethod","text":"AutocovMethod <: AbstractAutocovMethod\n\nThe AutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains.\n\nIt is is based on the discussion by [VehtariGelman2021] and uses the biased estimator of the autocovariance, as discussed by [Geyer1992].\n\n[VehtariGelman2021]: Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved widehat R for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008\n\n[Geyer1992]: Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.\n\n\n\n\n\n","category":"type"},{"location":"api/diagnostics/#MCMCDiagnosticTools.FFTAutocovMethod","page":"Diagnostics","title":"MCMCDiagnosticTools.FFTAutocovMethod","text":"FFTAutocovMethod <: AbstractAutocovMethod\n\nThe FFTAutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains.\n\nThe algorithm is the same as the one of AutocovMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation.\n\ninfo: Info\nTo be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl.\n\n\n\n\n\n","category":"type"},{"location":"api/diagnostics/#MCMCDiagnosticTools.BDAAutocovMethod","page":"Diagnostics","title":"MCMCDiagnosticTools.BDAAutocovMethod","text":"BDAAutocovMethod <: AbstractAutocovMethod\n\nThe BDAAutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains.\n\nIt is is based on the discussion by [VehtariGelman2021]. and uses the variogram estimator of the autocorrelation function discussed by [BDA3].\n\n[VehtariGelman2021]: Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved widehat R for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008\n\n[BDA3]: Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.\n\n\n\n\n\n","category":"type"},{"location":"api/diagnostics/#mcse","page":"Diagnostics","title":"Monte Carlo standard error","text":"","category":"section"},{"location":"api/diagnostics/","page":"Diagnostics","title":"Diagnostics","text":"MCMCDiagnosticTools.mcse","category":"page"},{"location":"api/diagnostics/#MCMCDiagnosticTools.mcse","page":"Diagnostics","title":"MCMCDiagnosticTools.mcse","text":"mcse(samples::AbstractArray{<:Union{Missing,Real}}; kind=Statistics.mean, kwargs...)\n\nEstimate the Monte Carlo standard errors (MCSE) of the estimator kind applied to samples of shape (draws, [chains[, parameters...]]).\n\nSee also: ess\n\nKinds of MCSE estimates\n\nThe estimator whose MCSE should be estimated is specified with kind. kind must accept a vector of the same eltype as samples and return a real estimate.\n\nFor the following estimators, the effective sample size ess and an estimate of the asymptotic variance are used to compute the MCSE, and kwargs are forwarded to ess:\n\nStatistics.mean\nStatistics.median\nStatistics.std\nBase.Fix2(Statistics.quantile, p::Real)\n\nFor other estimators, the subsampling bootstrap method (SBM)[FlegalJones2011][Flegal2012] is used as a fallback, and the only accepted kwargs are batch_size, which indicates the size of the overlapping batches used to estimate the MCSE, defaulting to floor(Int, sqrt(draws * chains)). Note that SBM tends to underestimate the MCSE, especially for highly autocorrelated chains. One should verify that autocorrelation is low by checking the bulk- and tail-ESS values.\n\n[FlegalJones2011]: Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf\n\n[Flegal2012]: Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18\n\n\n\n\n\nmcse(data::InferenceData; kwargs...) -> Dataset\nmcse(data::Dataset; kwargs...) -> Dataset\n\nCalculate the Monte Carlo standard error (MCSE) for each parameter in the data.\n\n\n\n\n\n","category":"function"},{"location":"api/diagnostics/#rstar","page":"Diagnostics","title":"R^* diagnostic","text":"","category":"section"},{"location":"api/diagnostics/","page":"Diagnostics","title":"Diagnostics","text":"MCMCDiagnosticTools.rstar","category":"page"},{"location":"api/diagnostics/#MCMCDiagnosticTools.rstar","page":"Diagnostics","title":"MCMCDiagnosticTools.rstar","text":"rstar(\n rng::Random.AbstractRNG=Random.default_rng(),\n classifier,\n samples,\n chain_indices::AbstractVector{Int};\n subset::Real=0.7,\n split_chains::Int=2,\n verbosity::Int=0,\n)\n\nCompute the R^* convergence statistic of the table samples with the classifier.\n\nsamples must be either an AbstractMatrix, an AbstractVector, or a table (i.e. implements the Tables.jl interface) whose rows are draws and whose columns are parameters.\n\nchain_indices indicates the chain ids of each row of samples.\n\nThis method supports ragged chains, i.e. chains of nonequal lengths.\n\n\n\n\n\nrstar(\n rng::Random.AbstractRNG=Random.default_rng(),\n classifier,\n samples::AbstractArray{<:Real};\n subset::Real=0.7,\n split_chains::Int=2,\n verbosity::Int=0,\n)\n\nCompute the R^* convergence statistic of the samples with the classifier.\n\nsamples is an array of draws with the shape (draws, [chains[, parameters...]]).`\n\nThis implementation is an adaption of algorithms 1 and 2 described by Lambert and Vehtari.\n\nThe classifier has to be a supervised classifier of the MLJ framework (see the MLJ documentation for a list of supported models). It is trained with a subset of the samples from each chain. Each chain is split into split_chains separate chains to additionally check for within-chain convergence. The training of the classifier can be inspected by adjusting the verbosity level.\n\nIf the classifier is deterministic, i.e., if it predicts a class, the value of the R^* statistic is returned (algorithm 1). If the classifier is probabilistic, i.e., if it outputs probabilities of classes, the scaled Poisson-binomial distribution of the R^* statistic is returned (algorithm 2).\n\nnote: Note\nThe correctness of the statistic depends on the convergence of the classifier used internally in the statistic.\n\nExamples\n\njulia> using MLJBase, MLJIteration, EvoTrees, Statistics, StatisticalMeasures\n\njulia> samples = fill(4.0, 100, 3, 2);\n\nOne can compute the distribution of the R^* statistic (algorithm 2) with a probabilistic classifier. For instance, we can use a gradient-boosted trees model with nrounds = 100 sequentially stacked trees and learning rate eta = 0.05:\n\njulia> model = EvoTreeClassifier(; nrounds=100, eta=0.05);\n\njulia> distribution = rstar(model, samples);\n\njulia> round(mean(distribution); digits=2)\n1.0f0\n\nNote, however, that it is recommended to determine nrounds based on early-stopping. With the MLJ framework, this can be achieved in the following way (see the MLJ documentation for additional explanations):\n\njulia> model = IteratedModel(;\n model=EvoTreeClassifier(; eta=0.05),\n iteration_parameter=:nrounds,\n resampling=Holdout(),\n measures=log_loss,\n controls=[Step(5), Patience(2), NumberLimit(100)],\n retrain=true,\n );\n\njulia> distribution = rstar(model, samples);\n\njulia> round(mean(distribution); digits=2)\n1.0f0\n\nFor deterministic classifiers, a single R^* statistic (algorithm 1) is returned. Deterministic classifiers can also be derived from probabilistic classifiers by e.g. predicting the mode. In MLJ this corresponds to a pipeline of models.\n\njulia> evotree_deterministic = Pipeline(model; operation=predict_mode);\n\njulia> value = rstar(evotree_deterministic, samples);\n\njulia> round(value; digits=2)\n1.0\n\nReferences\n\nLambert, B., & Vehtari, A. (2020). R^*: A robust MCMC convergence diagnostic with uncertainty using decision tree classifiers.\n\n\n\n\n\nrstar(\n rng::Random.AbstractRNG=Random.default_rng(),\n classifier,\n data::Union{InferenceData,Dataset};\n kwargs...,\n)\n\nCalculate the R^* diagnostic for the data.\n\n\n\n\n\n","category":"function"},{"location":"api/#api","page":"API Overview","title":"API Overview","text":"","category":"section"},{"location":"api/","page":"API Overview","title":"API Overview","text":"Pages = [\"data.md\", \"dataset.md\", \"diagnostics.md\", \"inference_data.md\", \"stats.md\"]\nDepth = 1","category":"page"},{"location":"creating_custom_plots/","page":"Creating custom plots","title":"Creating custom plots","text":"\n\n\n

Creating custom plots

\n\n\n\n\n\n

While ArviZ includes many plotting functions for visualizing the data stored in InferenceData objects, you will often need to construct custom plots, or you may want to tweak some of our plots in your favorite plotting package.

In this tutorial, we will show you a few useful techniques you can use to construct these plots using Julia's plotting packages. For demonstration purposes, we'll use Makie.jl and AlgebraOfGraphics.jl, which can consume Dataset objects since they implement the Tables interface. However, we could just as easily have used StatsPlots.jl.

\n\n
begin\n    using ArviZ, ArviZExampleData, DimensionalData, DataFrames, Statistics\n    using AlgebraOfGraphics, CairoMakie\n    using AlgebraOfGraphics: density\n    set_aog_theme!()\nend;
\n\n\n\n

We'll start by loading some draws from an implementation of the non-centered parameterization of the 8 schools model. In this parameterization, the model has some sampling issues.

\n\n
idata = load_example_data(\"centered_eight\")
\n
InferenceData
posterior
Dataset with dimensions: \n  Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n  Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n  :mu    Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n  :tau   Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n  \"created_at\" => \"2022-10-13T14:37:37.315398\"\n  \"inference_library_version\" => \"4.2.2\"\n  \"sampling_time\" => 7.48011\n  \"tuning_steps\" => 1000\n  \"arviz_version\" => \"0.13.0.dev0\"\n  \"inference_library\" => \"pymc\"
posterior_predictive
Dataset with dimensions: \n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n  Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n  Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n  :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n  \"created_at\" => \"2022-10-13T14:37:41.460544\"\n  \"inference_library_version\" => \"4.2.2\"\n  \"arviz_version\" => \"0.13.0.dev0\"\n  \"inference_library\" => \"pymc\"
log_likelihood
Dataset with dimensions: \n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n  Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n  Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n  :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n  \"created_at\" => \"2022-10-13T14:37:37.487399\"\n  \"inference_library_version\" => \"4.2.2\"\n  \"arviz_version\" => \"0.13.0.dev0\"\n  \"inference_library\" => \"pymc\"
sample_stats
Dataset with dimensions: \n  Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n  Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 16 layers:\n  :max_energy_error    Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :energy_error        Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :lp                  Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :index_in_trajectory Int64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :acceptance_rate     Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :diverging           Bool dims: Dim{:draw}, Dim{:chain} (500×4)\n  :process_time_diff   Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :n_steps             Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :perf_counter_start  Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :largest_eigval      Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (500×4)\n  :smallest_eigval     Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (500×4)\n  :step_size_bar       Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :step_size           Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :energy              Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :tree_depth          Int64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :perf_counter_diff   Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n  \"created_at\" => \"2022-10-13T14:37:37.324929\"\n  \"inference_library_version\" => \"4.2.2\"\n  \"sampling_time\" => 7.48011\n  \"tuning_steps\" => 1000\n  \"arviz_version\" => \"0.13.0.dev0\"\n  \"inference_library\" => \"pymc\"
prior
Dataset with dimensions: \n  Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n  Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points,\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n  :tau   Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n  :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n  :mu    Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n  \"created_at\" => \"2022-10-13T14:37:26.602116\"\n  \"inference_library_version\" => \"4.2.2\"\n  \"arviz_version\" => \"0.13.0.dev0\"\n  \"inference_library\" => \"pymc\"
prior_predictive
Dataset with dimensions: \n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n  Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n  Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points\nand 1 layer:\n  :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n  \"created_at\" => \"2022-10-13T14:37:26.604969\"\n  \"inference_library_version\" => \"4.2.2\"\n  \"arviz_version\" => \"0.13.0.dev0\"\n  \"inference_library\" => \"pymc\"
observed_data
Dataset with dimensions: \n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n  :obs Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n  \"created_at\" => \"2022-10-13T14:37:26.606375\"\n  \"inference_library_version\" => \"4.2.2\"\n  \"arviz_version\" => \"0.13.0.dev0\"\n  \"inference_library\" => \"pymc\"
constant_data
Dataset with dimensions: \n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n  :scores Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n  \"created_at\" => \"2022-10-13T14:37:26.607471\"\n  \"inference_library_version\" => \"4.2.2\"\n  \"arviz_version\" => \"0.13.0.dev0\"\n  \"inference_library\" => \"pymc\"
\n\n
idata.posterior
\n
Dataset with dimensions: \n  Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n  Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n  :mu    Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n  :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n  :tau   Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n  \"created_at\"                => \"2022-10-13T14:37:37.315398\"\n  \"inference_library_version\" => \"4.2.2\"\n  \"sampling_time\"             => 7.48011\n  \"tuning_steps\"              => 1000\n  \"arviz_version\"             => \"0.13.0.dev0\"\n  \"inference_library\"         => \"pymc\"
\n\n\n

The plotting functions we'll be using interact with a tabular view of a Dataset. Let's see what that view looks like for a Dataset:

\n\n
df = DataFrame(idata.posterior)
\n
drawchainschoolmuthetatau
100\"Choate\"7.871812.32074.72574
210\"Choate\"3.3845511.28563.90899
320\"Choate\"9.100485.708514.84403
430\"Choate\"7.3042910.03731.8567
540\"Choate\"9.879689.149154.74841
650\"Choate\"7.0420314.73593.51387
760\"Choate\"10.378514.3044.20898
870\"Choate\"10.0613.32982.6834
980\"Choate\"10.425310.44981.16889
1090\"Choate\"10.810811.47311.21052
...
160004993\"Mt. Hermon\"3.404461.295054.46125
\n\n\n

The tabular view includes dimensions and variables as columns.

When variables with different dimensions are flattened into a tabular form, there's always some duplication of values. As a simple case, note that chain, draw, and school all have repeated values in the above table.

In this case, theta has the school dimension, but tau doesn't, so the values of tau will be repeated in the table for each value of school.

\n\n
df[df.school .== Ref(\"Choate\"), :].tau == df[df.school .== Ref(\"Deerfield\"), :].tau
\n
true
\n\n\n

In our first example, this will be important.

Here, let's construct a trace plot. Besides idata, all functions and types in the following cell are defined in AlgebraOfGraphics or Makie:

\n\n
draw(\n    data(idata.posterior.mu) *\n    mapping(:draw, :mu; color=:chain => nonnumeric) *\n    visual(Lines; alpha=0.8),\n)
\n\n\n\n

Note the line idata.posterior.mu. If we had just used idata.posterior, the plot would have looked more-or-less the same, but there would be artifacts due to mu being copied many times. By selecting mu directly, all other dimensions are discarded, so each value of mu appears in the plot exactly once.

When examining an MCMC trace plot, we want to see a \"fuzzy caterpillar\". Instead we see a few places where the Markov chains froze. We can do the same for theta as well, but it's more useful here to separate these draws by school.

\n\n
draw(\n    data(idata.posterior) *\n    mapping(:draw, :theta; layout=:school, color=:chain => nonnumeric) *\n    visual(Lines; alpha=0.8),\n)
\n\n\n\n

Suppose we want to compare tau with theta for two different schools. To do so, we use InferenceDatas indexing syntax to subset the data.

\n\n
draw(\n    data(idata[:posterior, school=At([\"Choate\", \"Deerfield\"])]) *\n    mapping(:theta, :tau; color=:school) *\n    density() *\n    visual(Contour; levels=10),\n)
\n\n\n\n

We can also compare the density plots constructed from each chain for different schools.

\n\n
draw(\n    data(idata.posterior) *\n    mapping(:theta; layout=:school, color=:chain => nonnumeric) *\n    density(),\n)
\n\n\n\n

If we want to compare many schools in a single plot, an ECDF plot is more convenient.

\n\n
draw(\n    data(idata.posterior) * mapping(:theta; color=:school => nonnumeric) * visual(ECDFPlot);\n    axis=(; ylabel=\"probability\"),\n)
\n\n\n\n

So far we've just plotted data from one group, but we often want to combine data from multiple groups in one plot. The simplest way to do this is to create the plot out of multiple layers. Here we use this approach to plot the observations over the posterior predictive distribution.

\n\n
draw(\n    (data(idata.posterior_predictive) * mapping(:obs; layout=:school) * density()) +\n    (data(idata.observed_data) * mapping(:obs, :obs => zero => \"\"; layout=:school)),\n)
\n\n\n\n

Another option is to combine the groups into a single dataset.

Here we compare the prior and posterior. Since the prior has 1 chain and the posterior has 4 chains, if we were to combine them into a table, the structure would need to be ragged. This is not currently supported.

We can then either plot the two distributions separately as we did before, or we can compare a single chain from each group. This is what we'll do here. To concatenate the two groups, we introduce a new named dimension using DimensionalData.Dim.

\n\n
draw(\n    data(\n        cat(\n            idata.posterior[chain=[1]], idata.prior; dims=Dim{:group}([:posterior, :prior])\n        )[:mu],\n    ) *\n    mapping(:mu; color=:group) *\n    histogram(; bins=20) *\n    visual(; alpha=0.8);\n    axis=(; ylabel=\"probability\"),\n)
\n\n\n\n

From the trace plots, we suspected the geometry of this posterior was bad. Let's highlight divergent transitions. To do so, we merge posterior and samplestats, which can do with merge since they share no common variable names.

\n\n
draw(\n    data(merge(idata.posterior, idata.sample_stats)) * mapping(\n        :theta,\n        :tau;\n        layout=:school,\n        color=:diverging,\n        markersize=:diverging => (d -> d ? 5 : 2),\n    ),\n)
\n\n\n\n

When we try building more complex plots, we may need to build new Datasets from our existing ones.

One example of this is the corner plot. To build this plot, we need to make a copy of theta with a copy of the school dimension.

\n\n
let\n    theta = idata.posterior.theta[school=1:4]\n    theta2 = rebuild(set(theta; school=:school2); name=:theta2)\n    plot_data = Dataset(theta, theta2, idata.sample_stats.diverging)\n    draw(\n        data(plot_data) * mapping(\n            :theta,\n            :theta2 => \"theta\";\n            col=:school,\n            row=:school2,\n            color=:diverging,\n            markersize=:diverging => (d -> d ? 3 : 1),\n        );\n        figure=(; figsize=(5, 5)),\n        axis=(; aspect=1),\n    )\nend
\n\n\n","category":"page"},{"location":"creating_custom_plots/#Environment","page":"Creating custom plots","title":"Environment","text":"","category":"section"},{"location":"creating_custom_plots/","page":"Creating custom plots","title":"Creating custom plots","text":"
\n
\n\n
using Pkg, InteractiveUtils
\n\n\n
using PlutoUI
\n\n\n
with_terminal(Pkg.status; color=false)
\n
Status `~/work/ArviZ.jl/ArviZ.jl/docs/Project.toml`\n  [cbdf2221] AlgebraOfGraphics v0.6.17\n  [131c737c] ArviZ v0.10.4 `~/work/ArviZ.jl/ArviZ.jl`\n  [2f96bb34] ArviZExampleData v0.1.8\n  [4a6e88f0] ArviZPythonPlots v0.1.3\n  [13f3f980] CairoMakie v0.11.4\n  [a93c6f00] DataFrames v1.6.1\n⌃ [0703355e] DimensionalData v0.24.13\n  [31c24e10] Distributions v0.25.104\n  [e30172f5] Documenter v1.2.1\n  [f6006082] EvoTrees v0.16.5\n  [b5cf5a8d] InferenceObjects v0.3.15\n  [be115224] MCMCDiagnosticTools v0.3.8\n  [a7f614a8] MLJBase v1.0.1\n  [614be32b] MLJIteration v0.6.0\n  [ce719bf2] PSIS v0.9.4\n  [359b1769] PlutoStaticHTML v6.0.18\n  [7f904dfe] PlutoUI v0.7.54\n  [7f36be82] PosteriorStats v0.2.0\n  [c1514b29] StanSample v7.6.0\n  [a19d573c] StatisticalMeasures v0.1.3\n  [2913bbd2] StatsBase v0.34.2\n  [fce5fe82] Turing v0.30.0\n  [f43a241f] Downloads v1.6.0\n  [37e2e46d] LinearAlgebra\n  [10745b16] Statistics v1.9.0\nInfo Packages marked with ⌃ have new versions available and may be upgradable.\n
\n\n
with_terminal(versioninfo)
\n
Julia Version 1.9.4\nCommit 8e5136fa297 (2023-11-14 08:46 UTC)\nBuild Info:\n  Official https://julialang.org/ release\nPlatform Info:\n  OS: Linux (x86_64-linux-gnu)\n  CPU: 4 × AMD EPYC 7763 64-Core Processor\n  WORD_SIZE: 64\n  LIBM: libopenlibm\n  LLVM: libLLVM-14.0.6 (ORCJIT, znver3)\n  Threads: 2 on 4 virtual cores\nEnvironment:\n  JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager\n  JULIA_PROJECT = /home/runner/work/ArviZ.jl/ArviZ.jl/docs/\n  JULIA_DEPOT_PATH = /home/runner/.julia:/opt/hostedtoolcache/julia/1.9.4/x64/local/share/julia:/opt/hostedtoolcache/julia/1.9.4/x64/share/julia\n  JULIA_NUM_THREADS = 2\n  JULIA_LOAD_PATH = @:@v#.#:@stdlib\n  JULIA_CMDSTAN_HOME = /home/runner/work/ArviZ.jl/ArviZ.jl/.cmdstan//cmdstan-2.33.1/\n  JULIA_REVISE_WORKER_ONLY = 1\n
\n\n","category":"page"},{"location":"creating_custom_plots/","page":"Creating custom plots","title":"Creating custom plots","text":"EditURL = \"https://github.com/arviz-devs/ArviZ.jl/blob/main/docs/src/creating_custom_plots.jl\"","category":"page"},{"location":"api/stats/#stats-api","page":"Stats","title":"Stats","text":"","category":"section"},{"location":"api/stats/","page":"Stats","title":"Stats","text":"Pages = [\"stats.md\"]","category":"page"},{"location":"api/stats/#Summary-statistics","page":"Stats","title":"Summary statistics","text":"","category":"section"},{"location":"api/stats/","page":"Stats","title":"Stats","text":"SummaryStats\ndefault_summary_stats\ndefault_stats\ndefault_diagnostics\nsummarize\nsummarystats","category":"page"},{"location":"api/stats/#PosteriorStats.SummaryStats","page":"Stats","title":"PosteriorStats.SummaryStats","text":"struct SummaryStats{D, V<:(AbstractVector)}\n\nA container for a column table of values computed by summarize.\n\nThis object implements the Tables and TableTraits column table interfaces. It has a custom show method.\n\nSummaryStats behaves like an OrderedDict of columns, where the columns can be accessed using either Symbols or a 1-based integer index.\n\nname::String: The name of the collection of summary statistics, used as the table title in display.\ndata::Any: The summary statistics for each parameter. It must implement the Tables interface.\nparameter_names::AbstractVector: Names of the parameters\n\nSummaryStats([name::String,] data[, parameter_names])\nSummaryStats(data[, parameter_names]; name::String=\"SummaryStats\")\n\nConstruct a SummaryStats from tabular data with optional stats name and param_names.\n\ndata must not contain a column :parameter, as this is reserved for the parameter names, which are always in the first column.\n\n\n\n\n\n","category":"type"},{"location":"api/stats/#PosteriorStats.default_summary_stats","page":"Stats","title":"PosteriorStats.default_summary_stats","text":"default_summary_stats(focus=Statistics.mean; kwargs...)\n\nCombinatiton of default_stats and default_diagnostics to be used with summarize.\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PosteriorStats.default_stats","page":"Stats","title":"PosteriorStats.default_stats","text":"default_stats(focus=Statistics.mean; prob_interval=0.94, kwargs...)\n\nDefault statistics to be computed with summarize.\n\nThe value of focus determines the statistics to be returned:\n\nStatistics.mean: mean, std, hdi_3%, hdi_97%\nStatistics.median: median, mad, eti_3%, eti_97%\n\nIf prob_interval is set to a different value than the default, then different HDI and ETI statistics are computed accordingly. hdi refers to the highest-density interval, while eti refers to the equal-tailed interval (i.e. the credible interval computed from symmetric quantiles).\n\nSee also: hdi\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PosteriorStats.default_diagnostics","page":"Stats","title":"PosteriorStats.default_diagnostics","text":"default_diagnostics(focus=Statistics.mean; kwargs...)\n\nDefault diagnostics to be computed with summarize.\n\nThe value of focus determines the diagnostics to be returned:\n\nStatistics.mean: mcse_mean, mcse_std, ess_tail, ess_bulk, rhat\nStatistics.median: mcse_median, ess_tail, ess_bulk, rhat\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PosteriorStats.summarize","page":"Stats","title":"PosteriorStats.summarize","text":"summarize(data, stats_funs...; name=\"SummaryStats\", [var_names]) -> SummaryStats\n\nCompute the summary statistics in stats_funs on each param in data.\n\nstats_funs is a collection of functions that reduces a matrix with shape (draws, chains) to a scalar or a collection of scalars. Alternatively, an item in stats_funs may be a Pair of the form name => fun specifying the name to be used for the statistic or of the form (name1, ...) => fun when the function returns a collection. When the function returns a collection, the names in this latter format must be provided.\n\nIf no stats functions are provided, then those specified in default_summary_stats are computed.\n\nvar_names specifies the names of the parameters in data. If not provided, the names are inferred from data.\n\nTo support computing summary statistics from a custom object, overload this method specifying the type of data.\n\nSee also SummaryStats, default_summary_stats, default_stats, default_diagnostics.\n\nExamples\n\nCompute mean, std and the Monte Carlo standard error (MCSE) of the mean estimate:\n\njulia> using Statistics, StatsBase\n\njulia> x = randn(1000, 4, 3) .+ reshape(0:10:20, 1, 1, :);\n\njulia> summarize(x, mean, std, :mcse_mean => sem; name=\"Mean/Std\")\nMean/Std\n mean std mcse_mean\n 1 0.0003 0.990 0.016\n 2 10.02 0.988 0.016\n 3 19.98 0.988 0.016\n\nAvoid recomputing the mean by using mean_and_std, and provide parameter names:\n\njulia> summarize(x, (:mean, :std) => mean_and_std, mad; var_names=[:a, :b, :c])\nSummaryStats\n mean std mad\n a 0.000305 0.990 0.978\n b 10.0 0.988 0.995\n c 20.0 0.988 0.979\n\nNote that when an estimator and its MCSE are both computed, the MCSE is used to determine the number of significant digits that will be displayed.\n\njulia> summarize(x; var_names=[:a, :b, :c])\nSummaryStats\n mean std hdi_3% hdi_97% mcse_mean mcse_std ess_tail ess_bulk r ⋯\n a 0.0003 0.99 -1.92 1.78 0.016 0.012 3567 3663 1 ⋯\n b 10.02 0.99 8.17 11.9 0.016 0.011 3841 3906 1 ⋯\n c 19.98 0.99 18.1 21.9 0.016 0.012 3892 3749 1 ⋯\n 1 column omitted\n\nCompute just the statistics with an 89% HDI on all parameters, and provide the parameter names:\n\njulia> summarize(x, default_stats(; prob_interval=0.89)...; var_names=[:a, :b, :c])\nSummaryStats\n mean std hdi_5.5% hdi_94.5%\n a 0.000305 0.990 -1.63 1.52\n b 10.0 0.988 8.53 11.6\n c 20.0 0.988 18.5 21.6\n\nCompute the summary stats focusing on Statistics.median:\n\njulia> summarize(x, default_summary_stats(median)...; var_names=[:a, :b, :c])\nSummaryStats\n median mad eti_3% eti_97% mcse_median ess_tail ess_median rhat\n a 0.004 0.978 -1.83 1.89 0.020 3567 3336 1.00\n b 10.02 0.995 8.17 11.9 0.023 3841 3787 1.00\n c 19.99 0.979 18.1 21.9 0.020 3892 3829 1.00\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#StatsBase.summarystats","page":"Stats","title":"StatsBase.summarystats","text":"summarystats(data::InferenceData; group=:posterior, kwargs...) -> SummaryStats\nsummarystats(data::Dataset; kwargs...) -> SummaryStats\n\nCompute default summary statistics for the data using summarize.\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#General-statistics","page":"Stats","title":"General statistics","text":"","category":"section"},{"location":"api/stats/","page":"Stats","title":"Stats","text":"hdi\nhdi!\nr2_score","category":"page"},{"location":"api/stats/#PosteriorStats.hdi","page":"Stats","title":"PosteriorStats.hdi","text":"hdi(data::InferenceData; kwargs...) -> Dataset\nhdi(data::Dataset; kwargs...) -> Dataset\n\nCalculate the highest density interval (HDI) for each parameter in the data.\n\n\n\n\n\nhdi(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper)\n\nEstimate the unimodal highest density interval (HDI) of samples for the probability prob.\n\nThe HDI is the minimum width Bayesian credible interval (BCI). That is, it is the smallest possible interval containing (100*prob)% of the probability mass.[Hyndman1996]\n\nsamples is an array of shape (draws[, chains[, params...]]). If multiple parameters are present, then lower and upper are arrays with the shape (params...,), computed separately for each marginal.\n\nThis implementation uses the algorithm of [ChenShao1999].\n\nnote: Note\nAny default value of prob is arbitrary. The default value of prob=0.94 instead of a more common default like prob=0.95 is chosen to reminder the user of this arbitrariness.\n\n[Hyndman1996]: Rob J. Hyndman (1996) Computing and Graphing Highest Density Regions, Amer. Stat., 50(2): 120-6. DOI: 10.1080/00031305.1996.10474359 jstor.\n\n[ChenShao1999]: Ming-Hui Chen & Qi-Man Shao (1999) Monte Carlo Estimation of Bayesian Credible and HPD Intervals, J Comput. Graph. Stat., 8:1, 69-92. DOI: 10.1080/10618600.1999.10474802 jstor.\n\nExamples\n\nHere we calculate the 83% HDI for a normal random variable:\n\njulia> x = randn(2_000);\n\njulia> hdi(x; prob=0.83) |> pairs\npairs(::NamedTuple) with 2 entries:\n :lower => -1.38266\n :upper => 1.25982\n\nWe can also calculate the HDI for a 3-dimensional array of samples:\n\njulia> x = randn(1_000, 1, 1) .+ reshape(0:5:10, 1, 1, :);\n\njulia> hdi(x) |> pairs\npairs(::NamedTuple) with 2 entries:\n :lower => [-1.9674, 3.0326, 8.0326]\n :upper => [1.90028, 6.90028, 11.9003]\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PosteriorStats.hdi!","page":"Stats","title":"PosteriorStats.hdi!","text":"hdi!(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper)\n\nA version of hdi that sorts samples in-place while computing the HDI.\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PosteriorStats.r2_score","page":"Stats","title":"PosteriorStats.r2_score","text":"r2_score(idata::InferenceData; y_name, y_pred_name) -> (; r2, r2_std)\n\nCompute R² from idata, automatically formatting the predictions to the correct shape.\n\nKeywords\n\ny_name: Name of observed data variable in idata.observed_data. If not provided, then the only observed data variable is used.\ny_pred_name: Name of posterior predictive variable in idata.posterior_predictive. If not provided, then y_name is used.\n\nExamples\n\njulia> using ArviZExampleData, PosteriorStats\n\njulia> idata = load_example_data(\"regression10d\");\n\njulia> r2_score(idata) |> pairs\npairs(::NamedTuple) with 2 entries:\n :r2 => 0.998385\n :r2_std => 0.000100621\n\n\n\n\n\nr2_score(y_true::AbstractVector, y_pred::AbstractArray) -> (; r2, r2_std)\n\nR² for linear Bayesian regression models.[GelmanGoodrich2019]\n\nArguments\n\ny_true: Observed data of length noutputs\ny_pred: Predicted data with size (ndraws[, nchains], noutputs)\n\n[GelmanGoodrich2019]: Andrew Gelman, Ben Goodrich, Jonah Gabry & Aki Vehtari (2019) R-squared for Bayesian Regression Models, The American Statistician, 73:3, 307-9, DOI: 10.1080/00031305.2018.1549100.\n\nExamples\n\njulia> using ArviZExampleData\n\njulia> idata = load_example_data(\"regression1d\");\n\njulia> y_true = idata.observed_data.y;\n\njulia> y_pred = PermutedDimsArray(idata.posterior_predictive.y, (:draw, :chain, :y_dim_0));\n\njulia> r2_score(y_true, y_pred) |> pairs\npairs(::NamedTuple) with 2 entries:\n :r2 => 0.683197\n :r2_std => 0.0368838\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#Pareto-smoothed-importance-sampling","page":"Stats","title":"Pareto-smoothed importance sampling","text":"","category":"section"},{"location":"api/stats/","page":"Stats","title":"Stats","text":"PSISResult\ness_is\nPSISPlots.paretoshapeplot\npsis\npsis!","category":"page"},{"location":"api/stats/#PSIS.PSISResult","page":"Stats","title":"PSIS.PSISResult","text":"PSISResult\n\nResult of Pareto-smoothed importance sampling (PSIS) using psis.\n\nProperties\n\nlog_weights: un-normalized Pareto-smoothed log weights\nweights: normalized Pareto-smoothed weights (allocates a copy)\npareto_shape: Pareto k=ξ shape parameter\nnparams: number of parameters in log_weights\nndraws: number of draws in log_weights\nnchains: number of chains in log_weights\nreff: the ratio of the effective sample size of the unsmoothed importance ratios and the actual sample size.\ness: estimated effective sample size of estimate of mean using smoothed importance samples (see ess_is)\ntail_length: length of the upper tail of log_weights that was smoothed\ntail_dist: the generalized Pareto distribution that was fit to the tail of log_weights. Note that the tail weights are scaled to have a maximum of 1, so tail_dist * exp(maximum(log_ratios)) is the corresponding fit directly to the tail of log_ratios.\nnormalized::Bool:indicates whether log_weights are log-normalized along the sample dimensions.\n\nDiagnostic\n\nThe pareto_shape parameter k=ξ of the generalized Pareto distribution tail_dist can be used to diagnose reliability and convergence of estimates using the importance weights [VehtariSimpson2021].\n\nif k frac13, importance sampling is stable, and importance sampling (IS) and PSIS both are reliable.\nif k frac12, then the importance ratio distributon has finite variance, and the central limit theorem holds. As k approaches the upper bound, IS becomes less reliable, while PSIS still works well but with a higher RMSE.\nif frac12 k 07, then the variance is infinite, and IS can behave quite poorly. However, PSIS works well in this regime.\nif 07 k 1, then it quickly becomes impractical to collect enough importance weights to reliably compute estimates, and importance sampling is not recommended.\nif k 1, then neither the variance nor the mean of the raw importance ratios exists. The convergence rate is close to zero, and bias can be large with practical sample sizes.\n\nSee PSISPlots.paretoshapeplot for a diagnostic plot.\n\n[VehtariSimpson2021]: Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO]\n\n\n\n\n\n","category":"type"},{"location":"api/stats/#PSIS.ess_is","page":"Stats","title":"PSIS.ess_is","text":"ess_is(weights; reff=1)\n\nEstimate effective sample size (ESS) for importance sampling over the sample dimensions.\n\nGiven normalized weights w_1n, the ESS is estimated using the L2-norm of the weights:\n\nmathrmESS(w_1n) = fracr_mathrmeffsum_i=1^n w_i^2\n\nwhere r_mathrmeff is the relative efficiency of the log_weights.\n\ness_is(result::PSISResult; bad_shape_nan=true)\n\nEstimate ESS for Pareto-smoothed importance sampling.\n\nnote: Note\nESS estimates for Pareto shape values k 07, which are unreliable and misleadingly high, are set to NaN. To avoid this, set bad_shape_nan=false.\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PSIS.PSISPlots.paretoshapeplot","page":"Stats","title":"PSIS.PSISPlots.paretoshapeplot","text":"paretoshapeplot(values; showlines=false, ...)\nparetoshapeplot!(values; showlines=false, kwargs...)\n\nPlot shape parameters of fitted Pareto tail distributions for diagnosing convergence.\n\nvalues may be either a vector of Pareto shape parameters or a PSIS.PSISResult.\n\nIf showlines==true, horizontal lines indicating relevant Pareto shape thresholds are drawn. See PSIS.PSISResult for an explanation of the thresholds.\n\nAll remaining kwargs are forwarded to the plotting function.\n\nSee psis, PSISResult.\n\nExamples\n\nusing PSIS, Distributions, Plots\nproposal = Normal()\ntarget = TDist(7)\nx = rand(proposal, 1_000, 100)\nlog_ratios = logpdf.(target, x) .- logpdf.(proposal, x)\nresult = psis(log_ratios)\nparetoshapeplot(result)\n\nWe can also plot the Pareto shape parameters directly:\n\nparetoshapeplot(result.pareto_shape)\n\nWe can also use plot directly:\n\nplot(result.pareto_shape; showlines=true)\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PSIS.psis","page":"Stats","title":"PSIS.psis","text":"psis(log_ratios, reff = 1.0; kwargs...) -> PSISResult\npsis!(log_ratios, reff = 1.0; kwargs...) -> PSISResult\n\nCompute Pareto smoothed importance sampling (PSIS) log weights [VehtariSimpson2021].\n\nWhile psis computes smoothed log weights out-of-place, psis! smooths them in-place.\n\nArguments\n\nlog_ratios: an array of logarithms of importance ratios, with size (draws, [chains, [parameters...]]), where chains>1 would be used when chains are generated using Markov chain Monte Carlo.\nreff::Union{Real,AbstractArray}: the ratio(s) of effective sample size of log_ratios and the actual sample size reff = ess/(draws * chains), used to account for autocorrelation, e.g. due to Markov chain Monte Carlo. If an array, it must have the size (parameters...,) to match log_ratios.\n\nKeywords\n\nwarn=true: If true, warning messages are delivered\nnormalize=true: If true, the log-weights will be log-normalized so that exp.(log_weights) sums to 1 along the sample dimensions.\n\nReturns\n\nresult: a PSISResult object containing the results of the Pareto-smoothing.\n\nA warning is raised if the Pareto shape parameter k 07. See PSISResult for details and PSISPlots.paretoshapeplot for a diagnostic plot.\n\n[VehtariSimpson2021]: Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO]\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PSIS.psis!","page":"Stats","title":"PSIS.psis!","text":"psis(log_ratios, reff = 1.0; kwargs...) -> PSISResult\npsis!(log_ratios, reff = 1.0; kwargs...) -> PSISResult\n\nCompute Pareto smoothed importance sampling (PSIS) log weights [VehtariSimpson2021].\n\nWhile psis computes smoothed log weights out-of-place, psis! smooths them in-place.\n\nArguments\n\nlog_ratios: an array of logarithms of importance ratios, with size (draws, [chains, [parameters...]]), where chains>1 would be used when chains are generated using Markov chain Monte Carlo.\nreff::Union{Real,AbstractArray}: the ratio(s) of effective sample size of log_ratios and the actual sample size reff = ess/(draws * chains), used to account for autocorrelation, e.g. due to Markov chain Monte Carlo. If an array, it must have the size (parameters...,) to match log_ratios.\n\nKeywords\n\nwarn=true: If true, warning messages are delivered\nnormalize=true: If true, the log-weights will be log-normalized so that exp.(log_weights) sums to 1 along the sample dimensions.\n\nReturns\n\nresult: a PSISResult object containing the results of the Pareto-smoothing.\n\nA warning is raised if the Pareto shape parameter k 07. See PSISResult for details and PSISPlots.paretoshapeplot for a diagnostic plot.\n\n[VehtariSimpson2021]: Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO]\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#LOO-and-WAIC","page":"Stats","title":"LOO and WAIC","text":"","category":"section"},{"location":"api/stats/","page":"Stats","title":"Stats","text":"AbstractELPDResult\nPSISLOOResult\nWAICResult\nelpd_estimates\ninformation_criterion\nloo\nwaic","category":"page"},{"location":"api/stats/#PosteriorStats.AbstractELPDResult","page":"Stats","title":"PosteriorStats.AbstractELPDResult","text":"abstract type AbstractELPDResult\n\nAn abstract type representing the result of an ELPD computation.\n\nEvery subtype stores estimates of both the expected log predictive density (elpd) and the effective number of parameters p, as well as standard errors and pointwise estimates of each, from which other relevant estimates can be computed.\n\nSubtypes implement the following functions:\n\nelpd_estimates\ninformation_criterion\n\n\n\n\n\n","category":"type"},{"location":"api/stats/#PosteriorStats.PSISLOOResult","page":"Stats","title":"PosteriorStats.PSISLOOResult","text":"Results of Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO).\n\nSee also: loo, AbstractELPDResult\n\nestimates: Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p)\npointwise: Pointwise estimates\npsis_result: Pareto-smoothed importance sampling (PSIS) results\n\n\n\n\n\n","category":"type"},{"location":"api/stats/#PosteriorStats.WAICResult","page":"Stats","title":"PosteriorStats.WAICResult","text":"Results of computing the widely applicable information criterion (WAIC).\n\nSee also: waic, AbstractELPDResult\n\nestimates: Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p)\npointwise: Pointwise estimates\n\n\n\n\n\n","category":"type"},{"location":"api/stats/#PosteriorStats.elpd_estimates","page":"Stats","title":"PosteriorStats.elpd_estimates","text":"elpd_estimates(result::AbstractELPDResult; pointwise=false) -> (; elpd, elpd_mcse, lpd)\n\nReturn the (E)LPD estimates from the result.\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PosteriorStats.information_criterion","page":"Stats","title":"PosteriorStats.information_criterion","text":"information_criterion(elpd, scale::Symbol)\n\nCompute the information criterion for the given scale from the elpd estimate.\n\nscale must be one of (:deviance, :log, :negative_log).\n\nSee also: loo, waic\n\n\n\n\n\ninformation_criterion(result::AbstractELPDResult, scale::Symbol; pointwise=false)\n\nCompute information criterion for the given scale from the existing ELPD result.\n\nscale must be one of (:deviance, :log, :negative_log).\n\nIf pointwise=true, then pointwise estimates are returned.\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PosteriorStats.loo","page":"Stats","title":"PosteriorStats.loo","text":"loo(data::Dataset; [var_name::Symbol,] kwargs...) -> PSISLOOResult{<:NamedTuple,<:Dataset}\nloo(data::InferenceData; [var_name::Symbol,] kwargs...) -> PSISLOOResult{<:NamedTuple,<:Dataset}\n\nCompute PSIS-LOO from log-likelihood values in data.\n\nIf more than one log-likelihood variable is present, then var_name must be provided.\n\nExamples\n\nCalculate PSIS-LOO of a model:\n\njulia> using ArviZExampleData, PosteriorStats\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> loo(idata)\nPSISLOOResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.34\n\nand PSISResult with 500 draws, 4 chains, and 8 parameters\nPareto shape (k) diagnostic values:\n Count Min. ESS\n (-Inf, 0.5] good 6 (75.0%) 135\n (0.5, 0.7] okay 2 (25.0%) 421\n\n\n\n\n\nloo(log_likelihood; reff=nothing, kwargs...) -> PSISLOOResult{<:NamedTuple,<:NamedTuple}\n\nCompute the Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO). [Vehtari2017][LOOFAQ]\n\nlog_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]).\n\nKeywords\n\nreff::Union{Real,AbstractArray{<:Real}}: The relative effective sample size(s) of the likelihood values. If an array, it must have the same data dimensions as the corresponding log-likelihood variable. If not provided, then this is estimated using MCMCDiagnosticTools.ess.\nkwargs: Remaining keywords are forwarded to [PSIS.psis].\n\nSee also: PSISLOOResult, waic\n\n[Vehtari2017]: Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544\n\n[LOOFAQ]: Aki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html\n\nExamples\n\nManually compute R_mathrmeff and calculate PSIS-LOO of a model:\n\njulia> using ArviZExampleData, MCMCDiagnosticTools\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> reff = ess(log_like; kind=:basic, split_chains=1, relative=true);\n\njulia> loo(log_like; reff)\nPSISLOOResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.34\n\nand PSISResult with 500 draws, 4 chains, and 8 parameters\nPareto shape (k) diagnostic values:\n Count Min. ESS\n (-Inf, 0.5] good 7 (87.5%) 151\n (0.5, 0.7] okay 1 (12.5%) 446\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PosteriorStats.waic","page":"Stats","title":"PosteriorStats.waic","text":"waic(data::Dataset; [var_name::Symbol]) -> WAICResult{<:NamedTuple,<:Dataset}\nwaic(data::InferenceData; [var_name::Symbol]) -> WAICResult{<:NamedTuple,<:Dataset}\n\nCompute WAIC from log-likelihood values in data.\n\nIf more than one log-likelihood variable is present, then var_name must be provided.\n\nExamples\n\nCalculate WAIC of a model:\n\njulia> using ArviZExampleData, PosteriorStats\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> waic(idata)\nWAICResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.33\n\n\n\n\n\nwaic(log_likelihood::AbstractArray) -> WAICResult{<:NamedTuple,<:NamedTuple}\n\nCompute the widely applicable information criterion (WAIC).[Watanabe2010][Vehtari2017][LOOFAQ]\n\nlog_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]).\n\nSee also: WAICResult, loo\n\n[Watanabe2010]: Watanabe, S. Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory. 11(116):3571−3594, 2010. https://jmlr.csail.mit.edu/papers/v11/watanabe10a.html\n\n[Vehtari2017]: Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544\n\n[LOOFAQ]: Aki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html\n\nExamples\n\nCalculate WAIC of a model:\n\njulia> using ArviZExampleData\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> waic(log_like)\nWAICResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.33\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#Model-comparison","page":"Stats","title":"Model comparison","text":"","category":"section"},{"location":"api/stats/","page":"Stats","title":"Stats","text":"ModelComparisonResult\ncompare\nmodel_weights","category":"page"},{"location":"api/stats/#PosteriorStats.ModelComparisonResult","page":"Stats","title":"PosteriorStats.ModelComparisonResult","text":"ModelComparisonResult\n\nResult of model comparison using ELPD.\n\nThis struct implements the Tables and TableTraits interfaces.\n\nEach field returns a collection of the corresponding entry for each model:\n\nname: Names of the models, if provided.\nrank: Ranks of the models (ordered by decreasing ELPD)\nelpd_diff: ELPD of a model subtracted from the largest ELPD of any model\nelpd_diff_mcse: Monte Carlo standard error of the ELPD difference\nweight: Model weights computed with weights_method\nelpd_result: AbstactELPDResults for each model, which can be used to access useful stats like ELPD estimates, pointwise estimates, and Pareto shape values for PSIS-LOO\nweights_method: Method used to compute model weights with model_weights\n\n\n\n\n\n","category":"type"},{"location":"api/stats/#PosteriorStats.compare","page":"Stats","title":"PosteriorStats.compare","text":"compare(models; kwargs...) -> ModelComparisonResult\n\nCompare models based on their expected log pointwise predictive density (ELPD).\n\nThe ELPD is estimated either by Pareto smoothed importance sampling leave-one-out cross-validation (LOO) or using the widely applicable information criterion (WAIC). We recommend loo. Read more theory here - in a paper by some of the leading authorities on model comparison dx.doi.org/10.1111/1467-9868.00353\n\nArguments\n\nmodels: a Tuple, NamedTuple, or AbstractVector whose values are either AbstractELPDResult entries or any argument to elpd_method.\n\nKeywords\n\nweights_method::AbstractModelWeightsMethod=Stacking(): the method to be used to weight the models. See model_weights for details\nelpd_method=loo: a method that computes an AbstractELPDResult from an argument in models.\nsort::Bool=true: Whether to sort models by decreasing ELPD.\n\nReturns\n\nModelComparisonResult: A container for the model comparison results. The fields contain a similar collection to models.\n\nExamples\n\nCompare the centered and non centered models of the eight school problem using the defaults: loo and Stacking weights. A custom myloo method formates the inputs as expected by loo.\n\njulia> using ArviZExampleData\n\njulia> models = (\n centered=load_example_data(\"centered_eight\"),\n non_centered=load_example_data(\"non_centered_eight\"),\n );\n\njulia> function myloo(idata)\n log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1))\n return loo(log_like)\n end;\n\njulia> mc = compare(models; elpd_method=myloo)\n┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.\n└ @ PSIS ~/.julia/packages/PSIS/...\nModelComparisonResult with Stacking weights\n rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯\n non_centered 1 -31 1.4 0 0.0 1.0 0.9 ⋯\n centered 2 -31 1.4 0.06 0.067 0.0 0.9 ⋯\n 1 column omitted\njulia> mc.weight |> pairs\npairs(::NamedTuple) with 2 entries:\n :non_centered => 1.0\n :centered => 5.34175e-19\n\nCompare the same models from pre-computed PSIS-LOO results and computing BootstrappedPseudoBMA weights:\n\njulia> elpd_results = mc.elpd_result;\n\njulia> compare(elpd_results; weights_method=BootstrappedPseudoBMA())\nModelComparisonResult with BootstrappedPseudoBMA weights\n rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯\n non_centered 1 -31 1.4 0 0.0 0.52 0.9 ⋯\n centered 2 -31 1.4 0.06 0.067 0.48 0.9 ⋯\n 1 column omitted\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#PosteriorStats.model_weights","page":"Stats","title":"PosteriorStats.model_weights","text":"model_weights(elpd_results; method=Stacking())\nmodel_weights(method::AbstractModelWeightsMethod, elpd_results)\n\nCompute weights for each model in elpd_results using method.\n\nelpd_results is a Tuple, NamedTuple, or AbstractVector with AbstractELPDResult entries. The weights are returned in the same type of collection.\n\nStacking is the recommended approach, as it performs well even when the true data generating process is not included among the candidate models. See [YaoVehtari2018] for details.\n\nSee also: AbstractModelWeightsMethod, compare\n\n[YaoVehtari2018]: Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030\n\nExamples\n\nCompute Stacking weights for two models:\n\njulia> using ArviZExampleData\n\njulia> models = (\n centered=load_example_data(\"centered_eight\"),\n non_centered=load_example_data(\"non_centered_eight\"),\n );\n\njulia> elpd_results = map(models) do idata\n log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1))\n return loo(log_like)\n end;\n┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.\n└ @ PSIS ~/.julia/packages/PSIS/...\n\njulia> model_weights(elpd_results; method=Stacking()) |> pairs\npairs(::NamedTuple) with 2 entries:\n :centered => 5.34175e-19\n :non_centered => 1.0\n\nNow we compute BootstrappedPseudoBMA weights for the same models:\n\njulia> model_weights(elpd_results; method=BootstrappedPseudoBMA()) |> pairs\npairs(::NamedTuple) with 2 entries:\n :centered => 0.483723\n :non_centered => 0.516277\n\n\n\n\n\n","category":"function"},{"location":"api/stats/","page":"Stats","title":"Stats","text":"The following model weighting methods are available","category":"page"},{"location":"api/stats/","page":"Stats","title":"Stats","text":"AbstractModelWeightsMethod\nBootstrappedPseudoBMA\nPseudoBMA\nStacking","category":"page"},{"location":"api/stats/#PosteriorStats.AbstractModelWeightsMethod","page":"Stats","title":"PosteriorStats.AbstractModelWeightsMethod","text":"abstract type AbstractModelWeightsMethod\n\nAn abstract type representing methods for computing model weights.\n\nSubtypes implement model_weights(method, elpd_results).\n\n\n\n\n\n","category":"type"},{"location":"api/stats/#PosteriorStats.BootstrappedPseudoBMA","page":"Stats","title":"PosteriorStats.BootstrappedPseudoBMA","text":"struct BootstrappedPseudoBMA{R<:Random.AbstractRNG, T<:Real} <: AbstractModelWeightsMethod\n\nModel weighting method using pseudo Bayesian Model Averaging using Akaike-type weighting with the Bayesian bootstrap (pseudo-BMA+)[YaoVehtari2018].\n\nThe Bayesian bootstrap stabilizes the model weights.\n\nBootstrappedPseudoBMA(; rng=Random.default_rng(), samples=1_000, alpha=1)\nBootstrappedPseudoBMA(rng, samples, alpha)\n\nConstruct the method.\n\nrng::Random.AbstractRNG: The random number generator to use for the Bayesian bootstrap\nsamples::Int64: The number of samples to draw for bootstrapping\nalpha::Real: The shape parameter in the Dirichlet distribution used for the Bayesian bootstrap. The default (1) corresponds to a uniform distribution on the simplex.\n\nSee also: Stacking\n\n[YaoVehtari2018]: Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030\n\n\n\n\n\n","category":"type"},{"location":"api/stats/#PosteriorStats.PseudoBMA","page":"Stats","title":"PosteriorStats.PseudoBMA","text":"struct PseudoBMA <: AbstractModelWeightsMethod\n\nModel weighting method using pseudo Bayesian Model Averaging (pseudo-BMA) and Akaike-type weighting.\n\nPseudoBMA(; regularize=false)\nPseudoBMA(regularize)\n\nConstruct the method with optional regularization of the weights using the standard error of the ELPD estimate.\n\nnote: Note\nThis approach is not recommended, as it produces unstable weight estimates. It is recommended to instead use BootstrappedPseudoBMA to stabilize the weights or Stacking. For details, see [YaoVehtari2018].\n\n[YaoVehtari2018]: Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030\n\nSee also: Stacking\n\n\n\n\n\n","category":"type"},{"location":"api/stats/#PosteriorStats.Stacking","page":"Stats","title":"PosteriorStats.Stacking","text":"struct Stacking{O<:Optim.AbstractOptimizer} <: AbstractModelWeightsMethod\n\nModel weighting using stacking of predictive distributions[YaoVehtari2018].\n\nStacking(; optimizer=Optim.LBFGS(), options=Optim.Options()\nStacking(optimizer[, options])\n\nConstruct the method, optionally customizing the optimization.\n\noptimizer::Optim.AbstractOptimizer: The optimizer to use for the optimization of the weights. The optimizer must support projected gradient optimization via a manifold field.\noptions::Optim.Options: The Optim options to use for the optimization of the weights.\n\nSee also: BootstrappedPseudoBMA\n\n[YaoVehtari2018]: Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030\n\n\n\n\n\n","category":"type"},{"location":"api/stats/#Predictive-checks","page":"Stats","title":"Predictive checks","text":"","category":"section"},{"location":"api/stats/","page":"Stats","title":"Stats","text":"loo_pit","category":"page"},{"location":"api/stats/#PosteriorStats.loo_pit","page":"Stats","title":"PosteriorStats.loo_pit","text":"loo_pit(idata::InferenceData, log_weights; kwargs...) -> DimArray\n\nCompute LOO-PIT values using existing normalized log LOO importance weights.\n\nKeywords\n\ny_name: Name of observed data variable in idata.observed_data. If not provided, then the only observed data variable is used.\ny_pred_name: Name of posterior predictive variable in idata.posterior_predictive. If not provided, then y_name is used.\nkwargs: Remaining keywords are forwarded to the base method of loo_pit.\n\nExamples\n\nCalculate LOO-PIT values using already computed log weights.\n\njulia> using ArviZExampleData, PosteriorStats\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> loo_result = loo(idata; var_name=:obs);\n\njulia> loo_pit(idata, loo_result.psis_result.log_weights; y_name=:obs)\n8-element DimArray{Float64,1} loo_pit_obs with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.943511\n \"Deerfield\" 0.63797\n \"Phillips Andover\" 0.316697\n \"Phillips Exeter\" 0.582252\n \"Hotchkiss\" 0.295321\n \"Lawrenceville\" 0.403318\n \"St. Paul's\" 0.902508\n \"Mt. Hermon\" 0.655275\n\n\n\n\n\nloo_pit(idata::InferenceData; kwargs...) -> DimArray\n\nCompute LOO-PIT from groups in idata using PSIS-LOO.\n\nKeywords\n\ny_name: Name of observed data variable in idata.observed_data. If not provided, then the only observed data variable is used.\ny_pred_name: Name of posterior predictive variable in idata.posterior_predictive. If not provided, then y_name is used.\nlog_likelihood_name: Name of log-likelihood variable in idata.log_likelihood. If not provided, then y_name is used if idata has a log_likelihood group, otherwise the only variable is used.\nreff::Union{Real,AbstractArray{<:Real}}: The relative effective sample size(s) of the likelihood values. If an array, it must have the same data dimensions as the corresponding log-likelihood variable. If not provided, then this is estimated using ess.\nkwargs: Remaining keywords are forwarded to the base method of loo_pit.\n\nExamples\n\nCalculate LOO-PIT values using as test quantity the observed values themselves.\n\njulia> using ArviZExampleData, PosteriorStats\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> loo_pit(idata; y_name=:obs)\n8-element DimArray{Float64,1} loo_pit_obs with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.943511\n \"Deerfield\" 0.63797\n \"Phillips Andover\" 0.316697\n \"Phillips Exeter\" 0.582252\n \"Hotchkiss\" 0.295321\n \"Lawrenceville\" 0.403318\n \"St. Paul's\" 0.902508\n \"Mt. Hermon\" 0.655275\n\n\n\n\n\nloo_pit(y, y_pred, log_weights; kwargs...) -> Union{Real,AbstractArray}\n\nCompute leave-one-out probability integral transform (LOO-PIT) checks.\n\nArguments\n\ny: array of observations with shape (params...,)\ny_pred: array of posterior predictive samples with shape (draws, chains, params...).\nlog_weights: array of normalized log LOO importance weights with shape (draws, chains, params...).\n\nKeywords\n\nis_discrete: If not provided, then it is set to true iff elements of y and y_pred are all integer-valued. If true, then data are smoothed using smooth_data to make them non-discrete before estimating LOO-PIT values.\nkwargs: Remaining keywords are forwarded to smooth_data if data is discrete.\n\nReturns\n\npitvals: LOO-PIT values with same size as y. If y is a scalar, then pitvals is a scalar.\n\nLOO-PIT is a marginal posterior predictive check. If y_-i is the array y of observations with the ith observation left out, and y_i^* is a posterior prediction of the ith observation, then the LOO-PIT value for the ith observation is defined as\n\nP(y_i^* le y_i mid y_-i) = int_-infty^y_i p(y_i^* mid y_-i) mathrmd y_i^*\n\nThe LOO posterior predictions and the corresponding observations should have similar distributions, so if conditional predictive distributions are well-calibrated, then all LOO-PIT values should be approximately uniformly distributed on 0 1.[Gabry2019]\n\n[Gabry2019]: Gabry, J., Simpson, D., Vehtari, A., Betancourt, M. & Gelman, A. Visualization in Bayesian Workflow. J. R. Stat. Soc. Ser. A Stat. Soc. 182, 389–402 (2019). doi: 10.1111/rssa.12378 arXiv: 1709.01449\n\nExamples\n\nCalculate LOO-PIT values using as test quantity the observed values themselves.\n\njulia> using ArviZExampleData\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> y = idata.observed_data.obs;\n\njulia> y_pred = PermutedDimsArray(idata.posterior_predictive.obs, (:draw, :chain, :school));\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> log_weights = loo(log_like).psis_result.log_weights;\n\njulia> loo_pit(y, y_pred, log_weights)\n8-element DimArray{Float64,1} with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.943511\n \"Deerfield\" 0.63797\n \"Phillips Andover\" 0.316697\n \"Phillips Exeter\" 0.582252\n \"Hotchkiss\" 0.295321\n \"Lawrenceville\" 0.403318\n \"St. Paul's\" 0.902508\n \"Mt. Hermon\" 0.655275\n\nCalculate LOO-PIT values using as test quantity the square of the difference between each observation and mu.\n\njulia> using Statistics\n\njulia> mu = idata.posterior.mu;\n\njulia> T = y .- median(mu);\n\njulia> T_pred = y_pred .- mu;\n\njulia> loo_pit(T .^ 2, T_pred .^ 2, log_weights)\n8-element DimArray{Float64,1} with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.873577\n \"Deerfield\" 0.243686\n \"Phillips Andover\" 0.357563\n \"Phillips Exeter\" 0.149908\n \"Hotchkiss\" 0.435094\n \"Lawrenceville\" 0.220627\n \"St. Paul's\" 0.775086\n \"Mt. Hermon\" 0.296706\n\n\n\n\n\n","category":"function"},{"location":"api/stats/#Utilities","page":"Stats","title":"Utilities","text":"","category":"section"},{"location":"api/stats/","page":"Stats","title":"Stats","text":"PosteriorStats.smooth_data","category":"page"},{"location":"api/stats/#PosteriorStats.smooth_data","page":"Stats","title":"PosteriorStats.smooth_data","text":"smooth_data(y; dims=:, interp_method=CubicSpline, offset_frac=0.01)\n\nSmooth y along dims using interp_method.\n\ninterp_method is a 2-argument callabale that takes the arguments y and x and returns a DataInterpolations.jl interpolation method, defaulting to a cubic spline interpolator.\n\noffset_frac is the fraction of the length of y to use as an offset when interpolating.\n\n\n\n\n\n","category":"function"},{"location":"api/dataset/#dataset-api","page":"Dataset","title":"Dataset","text":"","category":"section"},{"location":"api/dataset/","page":"Dataset","title":"Dataset","text":"Pages = [\"dataset.md\"]","category":"page"},{"location":"api/dataset/#Type-definition","page":"Dataset","title":"Type definition","text":"","category":"section"},{"location":"api/dataset/","page":"Dataset","title":"Dataset","text":"Dataset","category":"page"},{"location":"api/dataset/#InferenceObjects.Dataset","page":"Dataset","title":"InferenceObjects.Dataset","text":"Dataset{L} <: DimensionalData.AbstractDimStack{L}\n\nContainer of dimensional arrays sharing some dimensions.\n\nThis type is an DimensionalData.AbstractDimStack that implements the same interface as DimensionalData.DimStack and has identical usage.\n\nWhen a Dataset is passed to Python, it is converted to an xarray.Dataset without copying the data. That is, the Python object shares the same memory as the Julia object. However, if an xarray.Dataset is passed to Julia, its data must be copied.\n\nConstructors\n\nDataset(data::DimensionalData.AbstractDimArray...)\nDataset(data::Tuple{Vararg{<:DimensionalData.AbstractDimArray}})\nDataset(data::NamedTuple{Keys,Vararg{<:DimensionalData.AbstractDimArray}})\nDataset(\n data::NamedTuple,\n dims::Tuple{Vararg{DimensionalData.Dimension}};\n metadata=DimensionalData.NoMetadata(),\n)\n\nIn most cases, use convert_to_dataset to create a Dataset instead of directly using a constructor.\n\n\n\n\n\n","category":"type"},{"location":"api/dataset/#General-conversion","page":"Dataset","title":"General conversion","text":"","category":"section"},{"location":"api/dataset/","page":"Dataset","title":"Dataset","text":"convert_to_dataset\nnamedtuple_to_dataset","category":"page"},{"location":"api/dataset/#InferenceObjects.convert_to_dataset","page":"Dataset","title":"InferenceObjects.convert_to_dataset","text":"convert_to_dataset(obj; group = :posterior, kwargs...) -> Dataset\n\nConvert a supported object to a Dataset.\n\nIn most cases, this function calls convert_to_inference_data and returns the corresponding group.\n\n\n\n\n\n","category":"function"},{"location":"api/dataset/#InferenceObjects.namedtuple_to_dataset","page":"Dataset","title":"InferenceObjects.namedtuple_to_dataset","text":"namedtuple_to_dataset(data; kwargs...) -> Dataset\n\nConvert NamedTuple mapping variable names to arrays to a Dataset.\n\nAny non-array values will be converted to a 0-dimensional array.\n\nKeywords\n\nattrs::AbstractDict{<:AbstractString}: a collection of metadata to attach to the dataset, in addition to defaults. Values should be JSON serializable.\nlibrary::Union{String,Module}: library used for performing inference. Will be attached to the attrs metadata.\ndims: a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are:\nSymbol: dimension name\nType{<:DimensionsionalData.Dimension}: dimension type\nDimensionsionalData.Dimension: dimension, potentially with indices\nNothing: no dimension name provided, dimension name is automatically generated\ncoords: a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated.\n\n\n\n\n\n","category":"function"},{"location":"api/dataset/#DimensionalData","page":"Dataset","title":"DimensionalData","text":"","category":"section"},{"location":"api/dataset/","page":"Dataset","title":"Dataset","text":"As a DimensionalData.AbstractDimStack, Dataset also implements the AbstractDimStack API and can be used like a DimStack. See DimensionalData's documentation for example usage.","category":"page"},{"location":"api/dataset/#Tables-inteface","page":"Dataset","title":"Tables inteface","text":"","category":"section"},{"location":"api/dataset/","page":"Dataset","title":"Dataset","text":"Dataset implements the Tables interface. This allows Datasets to be used as sources for any function that can accept a table. For example, it's straightforward to:","category":"page"},{"location":"api/dataset/","page":"Dataset","title":"Dataset","text":"write to CSV with CSV.jl\nflatten to a DataFrame with DataFrames.jl\nplot with StatsPlots.jl\nplot with AlgebraOfGraphics.jl","category":"page"},{"location":"#arvizjl","page":"Home","title":"ArviZ.jl: Exploratory analysis of Bayesian models in Julia","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"ArviZ.jl is a Julia meta-package for exploratory analysis of Bayesian models. It is part of the ArviZ project, which also includes a related Python package.","category":"page"},{"location":"","page":"Home","title":"Home","text":"ArviZ consists of and re-exports the following subpackages, along with extensions integrating them with InferenceObjects:","category":"page"},{"location":"","page":"Home","title":"Home","text":"InferenceObjects.jl: a base package implementing the InferenceData type with utilities for building, saving, and working with it\nMCMCDiagnosticTools.jl: diagnostics for Markov Chain Monte Carlo methods\nPSIS.jl: Pareto-smoothed importance sampling\nPosteriorStats.jl: common statistical analyses for the Bayesian workflow","category":"page"},{"location":"","page":"Home","title":"Home","text":"Additional functionality can be loaded with the following packages:","category":"page"},{"location":"","page":"Home","title":"Home","text":"ArviZExampleData.jl: example InferenceData objects, useful for demonstration and testing\nArviZPythonPlots.jl: Python ArviZ's library of plotting functions for Julia types","category":"page"},{"location":"","page":"Home","title":"Home","text":"See the navigation bar for more useful packages.","category":"page"},{"location":"#installation","page":"Home","title":"Installation","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"From the Julia REPL, type ] to enter the Pkg REPL mode and run","category":"page"},{"location":"","page":"Home","title":"Home","text":"pkg> add ArviZ","category":"page"},{"location":"#usage","page":"Home","title":"Usage","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"See the Quickstart for example usage and the API Overview for description of functions.","category":"page"},{"location":"#extendingarviz","page":"Home","title":"Extending ArviZ.jl","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"To use a custom data type with ArviZ.jl, simply overload InferenceObjects.convert_to_inference_data to convert your input(s) to an InferenceObjects.InferenceData.","category":"page"},{"location":"working_with_inference_data/#working-with-inference-data","page":"Working with InferenceData","title":"Working with InferenceData","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"using ArviZ, ArviZExampleData, DimensionalData, Statistics","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Here we present a collection of common manipulations you can use while working with InferenceData.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Let's load one of ArviZ's example datasets. posterior, posterior_predictive, etc are the groups stored in idata, and they are stored as Datasets. In this HTML view, you can click a group name to expand a summary of the group.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"idata = load_example_data(\"centered_eight\")","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"info: Info\nDatasets are DimensionalData.AbstractDimStacks and can be used identically. The variables a Dataset contains are called \"layers\", and dimensions of the same name that appear in more than one layer within a Dataset must have the same indices.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"InferenceData behaves like a NamedTuple and can be used similarly. Note that unlike a NamedTuple, the groups always appear in a specific order.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"length(idata) # number of groups","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"keys(idata) # group names","category":"page"},{"location":"working_with_inference_data/#Get-the-dataset-corresponding-to-a-single-group","page":"Working with InferenceData","title":"Get the dataset corresponding to a single group","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Group datasets can be accessed both as properties or as indexed items.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"post = idata.posterior","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"post is the dataset itself, so this is a non-allocating operation.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"idata[:posterior] === post","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"InferenceData supports a more advanced indexing syntax, which we'll see later.","category":"page"},{"location":"working_with_inference_data/#Getting-a-new-InferenceData-with-a-subset-of-groups","page":"Working with InferenceData","title":"Getting a new InferenceData with a subset of groups","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"We can index by a collection of group names to get a new InferenceData with just those groups. This is also non-allocating.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"idata_sub = idata[(:posterior, :posterior_predictive)]","category":"page"},{"location":"working_with_inference_data/#Adding-groups-to-an-InferenceData","page":"Working with InferenceData","title":"Adding groups to an InferenceData","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"InferenceData is immutable, so to add or replace groups we use merge to create a new object.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"merge(idata_sub, idata[(:observed_data, :prior)])","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"We can also use Base.setindex to out-of-place add or replace a single group.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Base.setindex(idata_sub, idata.prior, :prior)","category":"page"},{"location":"working_with_inference_data/#Add-a-new-variable","page":"Working with InferenceData","title":"Add a new variable","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Dataset is also immutable. So while the values within the underlying data arrays can be mutated, layers cannot be added or removed from Datasets, and groups cannot be added/removed from InferenceData.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Instead, we do this out-of-place also using merge.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"merge(post, (log_tau=log.(post[:tau]),))","category":"page"},{"location":"working_with_inference_data/#Obtain-an-array-for-a-given-parameter","page":"Working with InferenceData","title":"Obtain an array for a given parameter","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Let’s say we want to get the values for mu as an array. Parameters can be accessed with either property or index syntax.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"post.tau","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"post[:tau] === post.tau","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"To remove the dimensions, just use parent to retrieve the underlying array.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"parent(post.tau)","category":"page"},{"location":"working_with_inference_data/#Get-the-dimension-lengths","page":"Working with InferenceData","title":"Get the dimension lengths","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Let’s check how many groups are in our hierarchical model.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"size(idata.observed_data, :school)","category":"page"},{"location":"working_with_inference_data/#Get-coordinate/index-values","page":"Working with InferenceData","title":"Get coordinate/index values","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"What are the names of the groups in our hierarchical model? You can access them from the coordinate name school in this case.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"DimensionalData.index(idata.observed_data, :school)","category":"page"},{"location":"working_with_inference_data/#Get-a-subset-of-chains","page":"Working with InferenceData","title":"Get a subset of chains","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Let’s keep only chain 0 here. For the subset to take effect on all relevant InferenceData groups – posterior, sample_stats, log_likelihood, and posterior_predictive – we will index InferenceData instead of Dataset.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Here we use DimensionalData's At selector. Its other selectors are also supported.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"idata[chain=At(0)]","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Note that in this case, prior only has a chain of 0. If it also had the other chains, we could have passed chain=At([0, 2]) to subset by chains 0 and 2.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"warning: Warning\nIf we used idata[chain=[0, 2]] without the At selector, this is equivalent to idata[chain=DimensionalData.index(idata.posterior, :chain)[0, 2]], that is, [0, 2] indexes an array of dimension indices, which here would error. But if we had requested idata[chain=[1, 2]] we would not hit an error, but we would index the wrong chains. So it's important to always use a selector to index by values of dimension indices.","category":"page"},{"location":"working_with_inference_data/#Remove-the-first-n-draws-(burn-in)","page":"Working with InferenceData","title":"Remove the first n draws (burn-in)","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Let’s say we want to remove the first 100 draws from all the chains and all InferenceData groups with draws. To do this we use the .. syntax from IntervalSets.jl, which is exported by DimensionalData.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"idata[draw=100 .. Inf]","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"If you check the object you will see that the groups posterior, posterior_predictive, prior, and sample_stats have 400 draws compared to idata, which has 500. The group observed_data has not been affected because it does not have the draw dimension.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Alternatively, you can change a subset of groups by combining indexing styles with merge. Here we use this to build a new InferenceData where we have discarded the first 100 draws only from posterior.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"merge(idata, idata[(:posterior,), draw=100 .. Inf])","category":"page"},{"location":"working_with_inference_data/#Compute-posterior-mean-values-along-draw-and-chain-dimensions","page":"Working with InferenceData","title":"Compute posterior mean values along draw and chain dimensions","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"To compute the mean value of the posterior samples, do the following:","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"mean(post)","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"This computes the mean along all dimensions, discarding all dimensions and returning the result as a NamedTuple. This may be what you wanted for mu and tau, which have only two dimensions (chain and draw), but maybe not what you expected for theta, which has one more dimension school.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"You can specify along which dimension you want to compute the mean (or other functions), which instead returns a Dataset.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"mean(post; dims=(:chain, :draw))","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"The singleton dimensions of chain and draw now contain meaningless indices, so you may want to discard them, which you can do with dropdims.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"dropdims(mean(post; dims=(:chain, :draw)); dims=(:chain, :draw))","category":"page"},{"location":"working_with_inference_data/#Renaming-a-dimension","page":"Working with InferenceData","title":"Renaming a dimension","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"We can rename a dimension in a Dataset using DimensionalData's set method:","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"theta_bis = set(post.theta; school=:school_bis)","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"We can use this, for example, to broadcast functions across multiple arrays, automatically matching up shared dimensions, using DimensionalData.broadcast_dims.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"theta_school_diff = broadcast_dims(-, post.theta, theta_bis)","category":"page"},{"location":"working_with_inference_data/#Compute-and-store-posterior-pushforward-quantities","page":"Working with InferenceData","title":"Compute and store posterior pushforward quantities","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"We use “posterior pushfoward quantities” to refer to quantities that are not variables in the posterior but deterministic computations using posterior variables.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"You can compute these pushforward operations and store them as a new variable in a copy of the posterior group.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Here we'll create a new InferenceData with theta_school_diff in the posterior:","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"idata_new = Base.setindex(idata, merge(post, (; theta_school_diff)), :posterior)","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Once you have these pushforward quantities in an InferenceData, you’ll then be able to plot them with ArviZ functions, calculate stats and diagnostics on them, or save and share the InferenceData object with the pushforward quantities included.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Here we compute the mcse of theta_school_diff:","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"mcse(idata_new.posterior).theta_school_diff","category":"page"},{"location":"working_with_inference_data/#Advanced-subsetting","page":"Working with InferenceData","title":"Advanced subsetting","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"To select the value corresponding to the difference between the Choate and Deerfield schools do:","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"school_idx = [\"Choate\", \"Hotchkiss\", \"Mt. Hermon\"]\nschool_bis_idx = [\"Deerfield\", \"Choate\", \"Lawrenceville\"]\ntheta_school_diff[school=At(school_idx), school_bis=At(school_bis_idx)]","category":"page"},{"location":"working_with_inference_data/#Add-new-chains-using-cat","page":"Working with InferenceData","title":"Add new chains using cat","text":"","category":"section"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"Suppose after checking the mcse and realizing you need more samples, you rerun the model with two chains and obtain an idata_rerun object.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"idata_rerun = InferenceData(; posterior=set(post[chain=At([0, 1])]; chain=[4, 5]))","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"You can combine the two using cat.","category":"page"},{"location":"working_with_inference_data/","page":"Working with InferenceData","title":"Working with InferenceData","text":"cat(idata[[:posterior]], idata_rerun; dims=:chain)","category":"page"}] } diff --git a/ArviZ/dev/working_with_inference_data/index.html b/ArviZ/dev/working_with_inference_data/index.html index 8fe596758..f9b2e7969 100644 --- a/ArviZ/dev/working_with_inference_data/index.html +++ b/ArviZ/dev/working_with_inference_data/index.html @@ -833,4 +833,4 @@ "sampling_time" => 7.48011 "tuning_steps" => 1000 "arviz_version" => "0.13.0.dev0" - "inference_library" => "pymc" \ No newline at end of file + "inference_library" => "pymc" \ No newline at end of file diff --git a/ArviZExampleData/dev/.documenter-siteinfo.json b/ArviZExampleData/dev/.documenter-siteinfo.json index db4907f72..57c8b8a2d 100644 --- a/ArviZExampleData/dev/.documenter-siteinfo.json +++ b/ArviZExampleData/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-12-22T01:13:45","documenter_version":"1.2.1"}} \ No newline at end of file +{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-12-23T01:10:26","documenter_version":"1.2.1"}} \ No newline at end of file diff --git a/ArviZExampleData/dev/api/index.html b/ArviZExampleData/dev/api/index.html index 921ca7b97..ec61e4c9d 100644 --- a/ArviZExampleData/dev/api/index.html +++ b/ArviZExampleData/dev/api/index.html @@ -30,4 +30,4 @@ > prior > prior_predictive > observed_data - > constant_datasource \ No newline at end of file + > constant_datasource \ No newline at end of file diff --git a/ArviZExampleData/dev/datasets/index.html b/ArviZExampleData/dev/datasets/index.html index f92e20af0..64131ea40 100644 --- a/ArviZExampleData/dev/datasets/index.html +++ b/ArviZExampleData/dev/datasets/index.html @@ -87,4 +87,4 @@ This model uses a Von Mises distribution to propose torsion angles for the structure of a glycan molecule (pdb id: 2LIQ), and a Potential to estimate the proposed structure's energy. Said Potential is bound by Boltzman's law. -remote: http://ndownloader.figshare.com/files/22882652 \ No newline at end of file +remote: http://ndownloader.figshare.com/files/22882652 \ No newline at end of file diff --git a/ArviZExampleData/dev/for_developers/index.html b/ArviZExampleData/dev/for_developers/index.html index 40b706764..a464bea9d 100644 --- a/ArviZExampleData/dev/for_developers/index.html +++ b/ArviZExampleData/dev/for_developers/index.html @@ -4,4 +4,4 @@ julia> tarball_url = "https://github.com/arviz-devs/arviz_example_data/archive/refs/tags/v$version.tar.gz"; -julia> add_artifact!("Artifacts.toml", "arviz_example_data", tarball_url; force=true); \ No newline at end of file +julia> add_artifact!("Artifacts.toml", "arviz_example_data", tarball_url; force=true); \ No newline at end of file diff --git a/ArviZExampleData/dev/index.html b/ArviZExampleData/dev/index.html index b32957362..b9d4656ad 100644 --- a/ArviZExampleData/dev/index.html +++ b/ArviZExampleData/dev/index.html @@ -1 +1 @@ -Home · ArviZExampleData.jl
GitHub
\ No newline at end of file +Home · ArviZExampleData.jl
GitHub
\ No newline at end of file diff --git a/InferenceObjects/dev/.documenter-siteinfo.json b/InferenceObjects/dev/.documenter-siteinfo.json index 45f8e0eb9..c330d9e72 100644 --- a/InferenceObjects/dev/.documenter-siteinfo.json +++ b/InferenceObjects/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-12-22T00:46:20","documenter_version":"1.2.1"}} \ No newline at end of file +{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-12-23T21:46:15","documenter_version":"1.2.1"}} \ No newline at end of file diff --git a/InferenceObjects/dev/dataset/index.html b/InferenceObjects/dev/dataset/index.html index 1df59967f..4e20dd8b5 100644 --- a/InferenceObjects/dev/dataset/index.html +++ b/InferenceObjects/dev/dataset/index.html @@ -5,4 +5,4 @@ data::NamedTuple, dims::Tuple{Vararg{DimensionalData.Dimension}}; metadata=DimensionalData.NoMetadata(), -)

In most cases, use convert_to_dataset to create a Dataset instead of directly using a constructor.

source

General conversion

InferenceObjects.convert_to_dataset — Function
convert_to_dataset(obj; group = :posterior, kwargs...) -> Dataset

Convert a supported object to a Dataset.

In most cases, this function calls convert_to_inference_data and returns the corresponding group.

source
InferenceObjects.namedtuple_to_dataset — Function
namedtuple_to_dataset(data; kwargs...) -> Dataset

Convert NamedTuple mapping variable names to arrays to a Dataset.

Any non-array values will be converted to a 0-dimensional array.

Keywords

  • attrs::AbstractDict{<:AbstractString}: a collection of metadata to attach to the dataset, in addition to defaults. Values should be JSON serializable.
  • library::Union{String,Module}: library used for performing inference. Will be attached to the attrs metadata.
  • dims: a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are:
    • Symbol: dimension name
    • Type{<:DimensionsionalData.Dimension}: dimension type
    • DimensionsionalData.Dimension: dimension, potentially with indices
    • Nothing: no dimension name provided, dimension name is automatically generated
  • coords: a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated.
source

DimensionalData

As a DimensionalData.AbstractDimStack, Dataset also implements the AbstractDimStack API and can be used like a DimStack. See DimensionalData's documentation for example usage.

Tables inteface

Dataset implements the Tables interface. This allows Datasets to be used as sources for any function that can accept a table. For example, it's straightforward to:

\ No newline at end of file +)

In most cases, use convert_to_dataset to create a Dataset instead of directly using a constructor.

source

General conversion

InferenceObjects.convert_to_dataset — Function
convert_to_dataset(obj; group = :posterior, kwargs...) -> Dataset

Convert a supported object to a Dataset.

In most cases, this function calls convert_to_inference_data and returns the corresponding group.

source
InferenceObjects.namedtuple_to_dataset — Function
namedtuple_to_dataset(data; kwargs...) -> Dataset

Convert NamedTuple mapping variable names to arrays to a Dataset.

Any non-array values will be converted to a 0-dimensional array.

Keywords

  • attrs::AbstractDict{<:AbstractString}: a collection of metadata to attach to the dataset, in addition to defaults. Values should be JSON serializable.
  • library::Union{String,Module}: library used for performing inference. Will be attached to the attrs metadata.
  • dims: a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are:
    • Symbol: dimension name
    • Type{<:DimensionsionalData.Dimension}: dimension type
    • DimensionsionalData.Dimension: dimension, potentially with indices
    • Nothing: no dimension name provided, dimension name is automatically generated
  • coords: a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated.
source

DimensionalData

As a DimensionalData.AbstractDimStack, Dataset also implements the AbstractDimStack API and can be used like a DimStack. See DimensionalData's documentation for example usage.

Tables inteface

Dataset implements the Tables interface. This allows Datasets to be used as sources for any function that can accept a table. For example, it's straightforward to:

\ No newline at end of file diff --git a/InferenceObjects/dev/index.html b/InferenceObjects/dev/index.html index 892ba67b0..60534d660 100644 --- a/InferenceObjects/dev/index.html +++ b/InferenceObjects/dev/index.html @@ -1 +1 @@ -Home · InferenceObjects.jl
GitHub

InferenceObjects

InferenceObjects.jl is a Julia implementation of the InferenceData schema for storing results of Bayesian inference. Its purpose is to serve the following three goals:

  1. Usefulness in the analysis of Bayesian inference results.
  2. Reproducibility of Bayesian inference analysis.
  3. Interoperability between different inference backends and programming languages.

The implementation consists primarily of the InferenceData and Dataset structures. InferenceObjects also provides the function convert_to_inference_data, which may be overloaded by inference packages to define how various inference outputs can be converted to an InferenceData.

For examples of how InferenceData can be used, see the ArviZ.jl documentation.

\ No newline at end of file +Home · InferenceObjects.jl
GitHub

InferenceObjects

InferenceObjects.jl is a Julia implementation of the InferenceData schema for storing results of Bayesian inference. Its purpose is to serve the following three goals:

  1. Usefulness in the analysis of Bayesian inference results.
  2. Reproducibility of Bayesian inference analysis.
  3. Interoperability between different inference backends and programming languages.

The implementation consists primarily of the InferenceData and Dataset structures. InferenceObjects also provides the function convert_to_inference_data, which may be overloaded by inference packages to define how various inference outputs can be converted to an InferenceData.

For examples of how InferenceData can be used, see the ArviZ.jl documentation.

\ No newline at end of file diff --git a/InferenceObjects/dev/inference_data/index.html b/InferenceObjects/dev/inference_data/index.html index 90eeed835..f02da3b5a 100644 --- a/InferenceObjects/dev/inference_data/index.html +++ b/InferenceObjects/dev/inference_data/index.html @@ -1,5 +1,5 @@ InferenceData · InferenceObjects.jl
GitHub

InferenceData

Type definition

InferenceObjects.InferenceData — Type
InferenceData{group_names,group_types}

Container for inference data storage using DimensionalData.

This object implements the InferenceData schema.

Internally, groups are stored in a NamedTuple, which can be accessed using parent(::InferenceData).

Constructors

InferenceData(groups::NamedTuple)
-InferenceData(; groups...)

Construct an inference data from either a NamedTuple or keyword arguments of groups.

Groups must be Dataset objects.

Instead of directly creating an InferenceData, use the exported from_xyz functions or convert_to_inference_data.

source

Property interface

Base.getproperty — Function
getproperty(data::InferenceData, name::Symbol) -> Dataset

Get group with the specified name.

source

Indexing interface

Base.getindex — Function
Base.getindex(data::InferenceData, groups::Symbol; coords...) -> Dataset
+InferenceData(; groups...)

Construct an inference data from either a NamedTuple or keyword arguments of groups.

Groups must be Dataset objects.

Instead of directly creating an InferenceData, use the exported from_xyz functions or convert_to_inference_data.

source

Property interface

Base.getproperty — Function
getproperty(data::InferenceData, name::Symbol) -> Dataset

Get group with the specified name.

source

Indexing interface

Base.getindex — Function
Base.getindex(data::InferenceData, groups::Symbol; coords...) -> Dataset
 Base.getindex(data::InferenceData, groups; coords...) -> InferenceData

Return a new InferenceData containing the specified groups sliced to the specified coords.

coords specifies a dimension name mapping to an index, a DimensionalData.Selector, or an IntervalSets.AbstractInterval.

If one or more groups lack the specified dimension, a warning is raised but can be ignored. All groups that contain the dimension must also contain the specified indices, or an exception will be raised.

Examples

Select data from all groups for just the specified id values.

julia> using InferenceObjects, DimensionalData
 
 julia> idata = from_namedtuple(
@@ -49,7 +49,7 @@
   :y Float64 dims: Dim{:id} (1)
 
 with metadata Dict{String, Any} with 1 entry:
-  "created_at" => "2022-08-11T11:19:25.982"

Note that if a single index is provided, the behavior is still to slice so that the dimension is preserved.

source
Base.setindex — Function
Base.setindex(data::InferenceData, group::Dataset, name::Symbol) -> InferenceData

Create a new InferenceData containing the group with the specified name.

If a group with name is already in data, it is replaced.

source

Iteration interface

InferenceData also implements the same iteration interface as its underlying NamedTuple. That is, iterating over an InferenceData iterates over its groups.

General conversion

InferenceObjects.convert_to_inference_data — Function
convert_to_inference_data(obj; group, kwargs...) -> InferenceData

Convert a supported object to an InferenceData object.

If obj converts to a single dataset, group specifies which dataset in the resulting InferenceData that is.

See convert_to_dataset

Arguments

  • obj can be many objects. Basic supported types are:
    • InferenceData: return unchanged
    • Dataset/DimensionalData.AbstractDimStack: add to InferenceData as the only group
    • NamedTuple/AbstractDict: create a Dataset as the only group
    • AbstractArray{<:Real}: create a Dataset as the only group, given an arbitrary name, if the name is not set

More specific types may be documented separately.

Keywords

  • group::Symbol = :posterior: If obj converts to a single dataset, assign the resulting dataset to this group.

  • dims: a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are:

    • Symbol: dimension name
    • Type{<:DimensionsionalData.Dimension}: dimension type
    • DimensionsionalData.Dimension: dimension, potentially with indices
    • Nothing: no dimension name provided, dimension name is automatically generated

  • coords: a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated.

  • kwargs: remaining keywords forwarded to converter functions

source
InferenceObjects.from_dict — Function
from_dict(posterior::AbstractDict; kwargs...) -> InferenceData

Convert a Dict to an InferenceData.

Arguments

  • posterior: The data to be converted. Its strings must be Symbol or AbstractString, and its values must be arrays.

Keywords

  • posterior_predictive::Any=nothing: Draws from the posterior predictive distribution
  • sample_stats::Any=nothing: Statistics of the posterior sampling process
  • predictions::Any=nothing: Out-of-sample predictions for the posterior.
  • prior::Dict=nothing: Draws from the prior
  • prior_predictive::Any=nothing: Draws from the prior predictive distribution
  • sample_stats_prior::Any=nothing: Statistics of the prior sampling process
  • observed_data::NamedTuple: Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values.
  • constant_data::NamedTuple: Model constants, data included in the model which is not modeled as a random variable. Keys are parameter names and values.
  • predictions_constant_data::NamedTuple: Constants relevant to the model predictions (i.e. new x values in a linear regression).
  • log_likelihood: Pointwise log-likelihood for the data. It is recommended to use this argument as a NamedTuple whose keys are observed variable names and whose values are log likelihood arrays.
  • library: Name of library that generated the draws
  • coords: Map from named dimension to named indices
  • dims: Map from variable name to names of its dimensions

Returns

  • InferenceData: The data with groups corresponding to the provided data

Examples

using InferenceObjects
+  "created_at" => "2022-08-11T11:19:25.982"

Note that if a single index is provided, the behavior is still to slice so that the dimension is preserved.

source
Base.setindex — Function
Base.setindex(data::InferenceData, group::Dataset, name::Symbol) -> InferenceData

Create a new InferenceData containing the group with the specified name.

If a group with name is already in data, it is replaced.

source

Iteration interface

InferenceData also implements the same iteration interface as its underlying NamedTuple. That is, iterating over an InferenceData iterates over its groups.

General conversion

InferenceObjects.convert_to_inference_data — Function
convert_to_inference_data(obj; group, kwargs...) -> InferenceData

Convert a supported object to an InferenceData object.

If obj converts to a single dataset, group specifies which dataset in the resulting InferenceData that is.

See convert_to_dataset

Arguments

  • obj can be many objects. Basic supported types are:
    • InferenceData: return unchanged
    • Dataset/DimensionalData.AbstractDimStack: add to InferenceData as the only group
    • NamedTuple/AbstractDict: create a Dataset as the only group
    • AbstractArray{<:Real}: create a Dataset as the only group, given an arbitrary name, if the name is not set

More specific types may be documented separately.

Keywords

  • group::Symbol = :posterior: If obj converts to a single dataset, assign the resulting dataset to this group.

  • dims: a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are:

    • Symbol: dimension name
    • Type{<:DimensionsionalData.Dimension}: dimension type
    • DimensionsionalData.Dimension: dimension, potentially with indices
    • Nothing: no dimension name provided, dimension name is automatically generated

  • coords: a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated.

  • kwargs: remaining keywords forwarded to converter functions

source
InferenceObjects.from_dict — Function
from_dict(posterior::AbstractDict; kwargs...) -> InferenceData

Convert a Dict to an InferenceData.

Arguments

  • posterior: The data to be converted. Its strings must be Symbol or AbstractString, and its values must be arrays.

Keywords

  • posterior_predictive::Any=nothing: Draws from the posterior predictive distribution
  • sample_stats::Any=nothing: Statistics of the posterior sampling process
  • predictions::Any=nothing: Out-of-sample predictions for the posterior.
  • prior::Dict=nothing: Draws from the prior
  • prior_predictive::Any=nothing: Draws from the prior predictive distribution
  • sample_stats_prior::Any=nothing: Statistics of the prior sampling process
  • observed_data::NamedTuple: Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values.
  • constant_data::NamedTuple: Model constants, data included in the model which is not modeled as a random variable. Keys are parameter names and values.
  • predictions_constant_data::NamedTuple: Constants relevant to the model predictions (i.e. new x values in a linear regression).
  • log_likelihood: Pointwise log-likelihood for the data. It is recommended to use this argument as a NamedTuple whose keys are observed variable names and whose values are log likelihood arrays.
  • library: Name of library that generated the draws
  • coords: Map from named dimension to named indices
  • dims: Map from variable name to names of its dimensions

Returns

  • InferenceData: The data with groups corresponding to the provided data

Examples

using InferenceObjects
 nchains = 2
 ndraws = 100
 
@@ -58,7 +58,7 @@
     :y => randn(2, ndraws, nchains),
     :z => randn(3, 2, ndraws, nchains),
 )
-idata = from_dict(data)
source
InferenceObjects.from_namedtuple — Function
from_namedtuple(posterior::NamedTuple; kwargs...) -> InferenceData
 from_namedtuple(posterior::Vector{Vector{<:NamedTuple}}; kwargs...) -> InferenceData
 from_namedtuple(
     posterior::NamedTuple,
@@ -77,7 +77,7 @@
 idata1 = from_namedtuple(data1)
 
 data2 = [[(x=rand(), y=randn(2), z=randn(3, 2)) for _ in 1:ndraws] for _ in 1:nchains];
-idata2 = from_namedtuple(data2)
source

General functions

Base.cat — Function
cat(data::InferenceData...; [groups=keys(data[1]),] dims) -> InferenceData

Concatenate InferenceData objects along the specified dimension dims.

Only the groups in groups are concatenated. Remaining groups are merged into the new InferenceData object.

Examples

Here is how we can concatenate all groups of two InferenceData objects along the existing chain dimension:

julia> coords = (; a_dim=["x", "y", "z"]);
+idata2 = from_namedtuple(data2)
source

General functions

Base.cat — Function
cat(data::InferenceData...; [groups=keys(data[1]),] dims) -> InferenceData

Concatenate InferenceData objects along the specified dimension dims.

Only the groups in groups are concatenated. Remaining groups are merged into the new InferenceData object.

Examples

Here is how we can concatenate all groups of two InferenceData objects along the existing chain dimension:

julia> coords = (; a_dim=["x", "y", "z"]);
 
 julia> dims = dims=(; a=[:a_dim]);
 
@@ -147,7 +147,7 @@
   :y Float64 dims: Dim{:y_dim_1} (10)
 
 with metadata Dict{String, Any} with 1 entry:
-  "created_at" => "2023-02-17T15:11:00.59"
source
Base.merge — Function
merge(data::InferenceData...) -> InferenceData

Merge InferenceData objects.

The result contains all groups in data and others. If a group appears more than once, the one that occurs last is kept.

See also: cat

Examples

Here we merge an InferenceData containing only a posterior group with one containing only a prior group to create a new one containing both groups.

julia> idata1 = from_dict(Dict(:a => randn(100, 4, 3), :b => randn(100, 4)))
+  "created_at" => "2023-02-17T15:11:00.59"
source
Base.merge — Function
merge(data::InferenceData...) -> InferenceData

Merge InferenceData objects.

The result contains all groups in data and others. If a group appears more than once, the one that occurs last is kept.

See also: cat

Examples

Here we merge an InferenceData containing only a posterior group with one containing only a prior group to create a new one containing both groups.

julia> idata1 = from_dict(Dict(:a => randn(100, 4, 3), :b => randn(100, 4)))
 InferenceData with groups:
   > posterior
 
@@ -158,7 +158,7 @@
 julia> idata_merged = merge(idata1, idata2)
 InferenceData with groups:
   > posterior
-  > prior
source

I/O extensions

The following types of storage are provided via extensions.

NetCDF I/O using NCDatasets.jl

InferenceObjects.from_netcdf — Function
from_netcdf(path::AbstractString; kwargs...) -> InferenceData

Load an InferenceData from an unopened NetCDF file.

Remaining kwargs are passed to NCDatasets.NCDataset. This method loads data eagerly. To instead load data lazily, pass an opened NCDataset to from_netcdf.

Note

This method requires that NCDatasets is loaded before it can be used.

Examples

julia> using InferenceObjects, NCDatasets
+  > prior
source

I/O extensions

The following types of storage are provided via extensions.

NetCDF I/O using NCDatasets.jl

InferenceObjects.from_netcdf — Function
from_netcdf(path::AbstractString; kwargs...) -> InferenceData

Load an InferenceData from an unopened NetCDF file.

Remaining kwargs are passed to NCDatasets.NCDataset. This method loads data eagerly. To instead load data lazily, pass an opened NCDataset to from_netcdf.

Note

This method requires that NCDatasets is loaded before it can be used.

Examples

julia> using InferenceObjects, NCDatasets
 
 julia> idata = from_netcdf("centered_eight.nc")
 InferenceData with groups:
@@ -182,7 +182,7 @@
 
 julia> idata_copy = copy(idata); # disconnect from the loaded dataset
 
-julia> close(ds);
source
InferenceObjects.to_netcdf — Function
to_netcdf(data, dest::AbstractString; group::Symbol=:posterior, kwargs...)
 to_netcdf(data, dest::NCDatasets.NCDataset; group::Symbol=:posterior)

Write data to a NetCDF file.

data is any type that can be converted to an InferenceData using convert_to_inference_data. If not an InferenceData, then group specifies which group the data represents.

dest specifies either the path to the NetCDF file or an opened NetCDF file. If dest is a path, remaining kwargs are passed to NCDatasets.NCDataset.

Note

This method requires that NCDatasets is loaded before it can be used.

Examples

julia> using InferenceObjects, NCDatasets
 
 julia> idata = from_namedtuple((; x = randn(4, 100, 3), z = randn(4, 100)))
@@ -190,4 +190,4 @@
   > posterior
 
 julia> to_netcdf(idata, "data.nc")
-"data.nc"
source
\ No newline at end of file +"data.nc"source \ No newline at end of file diff --git a/InferenceObjects/stable b/InferenceObjects/stable index 18c1a8eb6..81b9d2db3 120000 --- a/InferenceObjects/stable +++ b/InferenceObjects/stable @@ -1 +1 @@ -v0.3.14 \ No newline at end of file +v0.3.15 \ No newline at end of file diff --git a/InferenceObjects/v0.3 b/InferenceObjects/v0.3 index 18c1a8eb6..81b9d2db3 120000 --- a/InferenceObjects/v0.3 +++ b/InferenceObjects/v0.3 @@ -1 +1 @@ -v0.3.14 \ No newline at end of file +v0.3.15 \ No newline at end of file diff --git a/InferenceObjects/v0.3.15/.documenter-siteinfo.json b/InferenceObjects/v0.3.15/.documenter-siteinfo.json new file mode 100644 index 000000000..a665b00c6 --- /dev/null +++ b/InferenceObjects/v0.3.15/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-12-23T22:06:45","documenter_version":"1.2.1"}} \ No newline at end of file diff --git a/InferenceObjects/v0.3.15/assets/documenter.js b/InferenceObjects/v0.3.15/assets/documenter.js new file mode 100644 index 000000000..f5311607b --- /dev/null +++ b/InferenceObjects/v0.3.15/assets/documenter.js @@ -0,0 +1,889 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'minisearch': 'https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function () { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'minisearch'], function($, minisearch) { + +// In general, most search related things will have "search" as a prefix. +// To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +let results = []; +let timer = undefined; + +let data = documenterSearchIndex["docs"].map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; +}); + +// list below is the lunr 2.1.3 list minus the intersect with names(Base) +// (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) +// ideally we'd just filter the original list but it's not available as a variable +const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", +]); + +let index = new minisearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with search results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + boost: { title: 100 }, + fuzzy: 2, + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + tokenize: (string) => string.split(/[\s\-\.]+/), + }, +}); + +index.addAll(data); + +let filters = [...new Set(data.map((x) => x.category))]; +var modal_filters = make_modal_body_filters(filters); +var filter_results = []; + +$(document).on("keyup", ".documenter-search-input", function (event) { + // Adding a debounce to prevent disruptions from super-speed typing! + debounce(() => update_search(filter_results), 300); +}); + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + $(this).removeClass("search-filter-selected"); + } else { + $(this).addClass("search-filter-selected"); + } + + // Adding a debounce to prevent disruptions from crazy clicking! + debounce(() => get_filters(), 300); +}); + +/** + * A debounce function, takes a function and an optional timeout in milliseconds + * + * @function callback + * @param {number} timeout + */ +function debounce(callback, timeout = 300) { + clearTimeout(timer); + timer = setTimeout(callback, timeout); +} + +/** + * Make/Update the search component + * + * @param {string[]} selected_filters + */ +function update_search(selected_filters = []) { + let initial_search_body = ` +
Type something to get started!
+ `; + + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + results = index.search(querystring, { + filter: (result) => { + // Filtering results + if (selected_filters.length === 0) { + return result.score >= 1; + } else { + return ( + result.score >= 1 && selected_filters.includes(result.category) + ); + } + }, + }); + + let search_result_container = ``; + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + results.forEach(function (result) { + if (result.location) { + // Checking for duplication of results for the same page + if (!links.includes(result.location)) { + search_results += make_search_result(result, querystring); + count++; + } + + links.push(result.location); + } + }); + + let result_count = `
${count} result(s)
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + filter_results = []; + modal_filters = make_modal_body_filters(filters, filter_results); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(initial_search_body); + } +} + +/** + * Make the modal filter html + * + * @param {string[]} filters + * @param {string[]} selected_filters + * @returns string + */ +function make_modal_body_filters(filters, selected_filters = []) { + let str = ``; + + filters.forEach((val) => { + if (selected_filters.includes(val)) { + str += `${val}`; + } else { + str += `${val}`; + } + }); + + let filter_html = ` +
+ Filters: + ${str} +
+ `; + + return filter_html; +} + +/** + * Make the result component given a minisearch result data object and the value of the search input as queryString. + * To view the result object structure, refer: https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ +function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + + let textindex = new RegExp(`\\b${querystring}\\b`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`\\b${querystring}\\b`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${result.title}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; +} + +/** + * Get selected filters, remake the filter html and lastly update the search modal + */ +function get_filters() { + let ele = $(".search-filters .search-filter-selected").get(); + filter_results = ele.map((x) => $(x).text().toLowerCase()); + modal_filters = make_modal_body_filters(filters, filter_results); + update_search(filter_results); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+`; + +let initial_search_body = ` +
Type something to get started!
+`; + +let search_modal_footer = ` + +`; + +$(document.body).append( + ` + + ` +); + +document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); +}); + +document.querySelector(".close-search-modal").addEventListener("click", () => { + closeModal(); +}); + +$(document).on("click", ".search-result-link", function () { + closeModal(); +}); + +document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; +}); + +// Functions to open and close a modal +function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); +} + +function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); +} + +document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/InferenceObjects/v0.3.15/assets/themes/documenter-dark.css b/InferenceObjects/v0.3.15/assets/themes/documenter-dark.css new file mode 100644 index 000000000..9f5449f4b --- /dev/null +++ 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.button.is-link.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-link.is-outlined{background-color:transparent;border-color:#1abc9c;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-outlined:hover,html.theme--documenter-dark .button.is-link.is-outlined.is-hovered,html.theme--documenter-dark .button.is-link.is-outlined:focus,html.theme--documenter-dark .button.is-link.is-outlined.is-focused{background-color:#1abc9c;border-color:#1abc9c;color:#fff}html.theme--documenter-dark .button.is-link.is-outlined.is-loading::after{border-color:transparent transparent #1abc9c #1abc9c !important}html.theme--documenter-dark .button.is-link.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-link.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-link.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-link.is-outlined{background-color:transparent;border-color:#1abc9c;box-shadow:none;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-focused{background-color:#fff;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #1abc9c #1abc9c !important}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-link.is-light{background-color:#edfdf9;color:#15987e}html.theme--documenter-dark .button.is-link.is-light:hover,html.theme--documenter-dark .button.is-link.is-light.is-hovered{background-color:#e2fbf6;border-color:transparent;color:#15987e}html.theme--documenter-dark .button.is-link.is-light:active,html.theme--documenter-dark .button.is-link.is-light.is-active{background-color:#d7f9f3;border-color:transparent;color:#15987e}html.theme--documenter-dark .button.is-info{background-color:#024c7d;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-info:hover,html.theme--documenter-dark .button.is-info.is-hovered{background-color:#024470;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-info:focus,html.theme--documenter-dark .button.is-info.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-info:focus:not(:active),html.theme--documenter-dark .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(2,76,125,0.25)}html.theme--documenter-dark .button.is-info:active,html.theme--documenter-dark .button.is-info.is-active{background-color:#023d64;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-info[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-info{background-color:#024c7d;border-color:#024c7d;box-shadow:none}html.theme--documenter-dark .button.is-info.is-inverted{background-color:#fff;color:#024c7d}html.theme--documenter-dark .button.is-info.is-inverted:hover,html.theme--documenter-dark .button.is-info.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#024c7d}html.theme--documenter-dark .button.is-info.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-info.is-outlined{background-color:transparent;border-color:#024c7d;color:#024c7d}html.theme--documenter-dark .button.is-info.is-outlined:hover,html.theme--documenter-dark .button.is-info.is-outlined.is-hovered,html.theme--documenter-dark .button.is-info.is-outlined:focus,html.theme--documenter-dark .button.is-info.is-outlined.is-focused{background-color:#024c7d;border-color:#024c7d;color:#fff}html.theme--documenter-dark .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #024c7d #024c7d !important}html.theme--documenter-dark .button.is-info.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-info.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-info.is-outlined{background-color:transparent;border-color:#024c7d;box-shadow:none;color:#024c7d}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-focused{background-color:#fff;color:#024c7d}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #024c7d #024c7d !important}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-info.is-light{background-color:#ebf7ff;color:#0e9dfb}html.theme--documenter-dark .button.is-info.is-light:hover,html.theme--documenter-dark .button.is-info.is-light.is-hovered{background-color:#def2fe;border-color:transparent;color:#0e9dfb}html.theme--documenter-dark .button.is-info.is-light:active,html.theme--documenter-dark .button.is-info.is-light.is-active{background-color:#d2edfe;border-color:transparent;color:#0e9dfb}html.theme--documenter-dark .button.is-success{background-color:#008438;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success:hover,html.theme--documenter-dark .button.is-success.is-hovered{background-color:#073;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success:focus,html.theme--documenter-dark .button.is-success.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success:focus:not(:active),html.theme--documenter-dark .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(0,132,56,0.25)}html.theme--documenter-dark .button.is-success:active,html.theme--documenter-dark .button.is-success.is-active{background-color:#006b2d;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success{background-color:#008438;border-color:#008438;box-shadow:none}html.theme--documenter-dark .button.is-success.is-inverted{background-color:#fff;color:#008438}html.theme--documenter-dark .button.is-success.is-inverted:hover,html.theme--documenter-dark .button.is-success.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#008438}html.theme--documenter-dark .button.is-success.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-success.is-outlined{background-color:transparent;border-color:#008438;color:#008438}html.theme--documenter-dark .button.is-success.is-outlined:hover,html.theme--documenter-dark .button.is-success.is-outlined.is-hovered,html.theme--documenter-dark .button.is-success.is-outlined:focus,html.theme--documenter-dark .button.is-success.is-outlined.is-focused{background-color:#008438;border-color:#008438;color:#fff}html.theme--documenter-dark .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #008438 #008438 !important}html.theme--documenter-dark .button.is-success.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-outlined{background-color:transparent;border-color:#008438;box-shadow:none;color:#008438}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#008438}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #008438 #008438 !important}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-success.is-light{background-color:#ebfff3;color:#00eb64}html.theme--documenter-dark .button.is-success.is-light:hover,html.theme--documenter-dark .button.is-success.is-light.is-hovered{background-color:#deffec;border-color:transparent;color:#00eb64}html.theme--documenter-dark .button.is-success.is-light:active,html.theme--documenter-dark .button.is-success.is-light.is-active{background-color:#d1ffe5;border-color:transparent;color:#00eb64}html.theme--documenter-dark .button.is-warning{background-color:#ad8100;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-warning:hover,html.theme--documenter-dark .button.is-warning.is-hovered{background-color:#a07700;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-warning:focus,html.theme--documenter-dark .button.is-warning.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-warning:focus:not(:active),html.theme--documenter-dark .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(173,129,0,0.25)}html.theme--documenter-dark .button.is-warning:active,html.theme--documenter-dark .button.is-warning.is-active{background-color:#946e00;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-warning[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning{background-color:#ad8100;border-color:#ad8100;box-shadow:none}html.theme--documenter-dark .button.is-warning.is-inverted{background-color:#fff;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#ad8100;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-outlined.is-focused{background-color:#ad8100;border-color:#ad8100;color:#fff}html.theme--documenter-dark .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #ad8100 #ad8100 !important}html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#ad8100;box-shadow:none;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ad8100 #ad8100 !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-warning.is-light{background-color:#fffaeb;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:hover,html.theme--documenter-dark .button.is-warning.is-light.is-hovered{background-color:#fff7de;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:active,html.theme--documenter-dark .button.is-warning.is-light.is-active{background-color:#fff3d1;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-danger{background-color:#9e1b0d;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:hover,html.theme--documenter-dark .button.is-danger.is-hovered{background-color:#92190c;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus,html.theme--documenter-dark .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus:not(:active),html.theme--documenter-dark .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(158,27,13,0.25)}html.theme--documenter-dark .button.is-danger:active,html.theme--documenter-dark .button.is-danger.is-active{background-color:#86170b;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger{background-color:#9e1b0d;border-color:#9e1b0d;box-shadow:none}html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#9e1b0d;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-outlined.is-focused{background-color:#9e1b0d;border-color:#9e1b0d;color:#fff}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#9e1b0d;box-shadow:none;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark 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.button.is-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark 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.button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons 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.button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark 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h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter 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.docs-logo>img.is-5by4{padding-top:80%}html.theme--documenter-dark .image.is-4by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--documenter-dark .image.is-3by2,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2{padding-top:66.6666%}html.theme--documenter-dark .image.is-5by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3{padding-top:60%}html.theme--documenter-dark .image.is-16by9,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9{padding-top:56.25%}html.theme--documenter-dark .image.is-2by1,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by1{padding-top:50%}html.theme--documenter-dark .image.is-3by1,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--documenter-dark .image.is-4by5,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by5{padding-top:125%}html.theme--documenter-dark .image.is-3by4,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--documenter-dark .image.is-2by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--documenter-dark .image.is-3by5,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--documenter-dark .image.is-9by16,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-9by16{padding-top:177.7777%}html.theme--documenter-dark .image.is-1by2,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by2{padding-top:200%}html.theme--documenter-dark .image.is-1by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by3{padding-top:300%}html.theme--documenter-dark .image.is-16x16,html.theme--documenter-dark #documenter .docs-sidebar 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Gets put into the tag.. +function set_theme_from_local_storage() { + // Initialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if (window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the users preference is for dark color scheme + var darkPreference = + window.matchMedia("(prefers-color-scheme: dark)").matches === true; + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; + var disabled = []; + var primaryLightTheme = null; + var primaryDarkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + if (ss.ownerNode.getAttribute("data-theme-primary") !== null) { + primaryLightTheme = themename; + } + // Check if the theme is primary dark theme so that we could store its name in darkTheme + if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) { + primaryDarkTheme = themename; + } + // If we find a matching theme (and it's not the default), we'll set active to non-null + if (themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if (themename !== theme) disabled.push(ss); + } + var activeTheme = null; + if (active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName("html")[0].className = "theme--" + theme; + activeTheme = theme; + } else { + // If we did _not_ find an active theme, then we need to fall back to the primary theme + // which can either be dark or light, depending on the user's OS preference. + var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme; + // In case it somehow happens that the relevant primary theme was not found in the + // preceding loop, we abort without doing anything. + if (activeTheme === null) { + console.error("Unable to determine primary theme."); + return; + } + // When switching to the primary light theme, then we must not have a class name + // for the tag. That's only for non-primary or the primary dark theme. + if (darkPreference) { + document.getElementsByTagName("html")[0].className = + "theme--" + activeTheme; + } else { + document.getElementsByTagName("html")[0].className = ""; + } + } + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // we'll disable all the stylesheets, except for the active one + ss.disabled = !(themename == activeTheme); + } +} +set_theme_from_local_storage(); diff --git a/InferenceObjects/v0.3.15/assets/warner.js b/InferenceObjects/v0.3.15/assets/warner.js new file mode 100644 index 000000000..3f6f5d008 --- /dev/null +++ b/InferenceObjects/v0.3.15/assets/warner.js @@ -0,0 +1,52 @@ +function maybeAddWarning() { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return; + } + + // Current version is not a version number, so we can't tell if it's the newest version. Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return; + } + + // Current version is newest version, so no need to add a warning. + if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { + return; + } + + // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. + if (document.body.querySelector('meta[name="robots"]') === null) { + const meta = document.createElement("meta"); + meta.name = "robots"; + meta.content = "noindex"; + + document.getElementsByTagName("head")[0].appendChild(meta); + } + + const div = document.createElement("div"); + div.classList.add("outdated-warning-overlay"); + const closer = document.createElement("button"); + closer.classList.add("outdated-warning-closer", "delete"); + closer.addEventListener("click", function () { + document.body.removeChild(div); + }); + const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE; + div.innerHTML = + 'This documentation is not for the latest stable release, but for either the development version or an older release.
Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", maybeAddWarning); +} else { + maybeAddWarning(); +} diff --git a/InferenceObjects/v0.3.15/dataset/index.html b/InferenceObjects/v0.3.15/dataset/index.html new file mode 100644 index 000000000..45485cabb --- /dev/null +++ b/InferenceObjects/v0.3.15/dataset/index.html @@ -0,0 +1,8 @@ +Dataset · InferenceObjects.jl
GitHub

Dataset

Type definition

InferenceObjects.Dataset — Type
Dataset{L} <: DimensionalData.AbstractDimStack{L}

Container of dimensional arrays sharing some dimensions.

This type is an DimensionalData.AbstractDimStack that implements the same interface as DimensionalData.DimStack and has identical usage.

When a Dataset is passed to Python, it is converted to an xarray.Dataset without copying the data. That is, the Python object shares the same memory as the Julia object. However, if an xarray.Dataset is passed to Julia, its data must be copied.

Constructors

Dataset(data::DimensionalData.AbstractDimArray...)
+Dataset(data::Tuple{Vararg{<:DimensionalData.AbstractDimArray}})
+Dataset(data::NamedTuple{Keys,Vararg{<:DimensionalData.AbstractDimArray}})
+Dataset(
+    data::NamedTuple,
+    dims::Tuple{Vararg{DimensionalData.Dimension}};
+    metadata=DimensionalData.NoMetadata(),
+)

In most cases, use convert_to_dataset to create a Dataset instead of directly using a constructor.

source

General conversion

InferenceObjects.namedtuple_to_dataset — Function
namedtuple_to_dataset(data; kwargs...) -> Dataset

Convert NamedTuple mapping variable names to arrays to a Dataset.

Any non-array values will be converted to a 0-dimensional array.

Keywords

  • attrs::AbstractDict{<:AbstractString}: a collection of metadata to attach to the dataset, in addition to defaults. Values should be JSON serializable.
  • library::Union{String,Module}: library used for performing inference. Will be attached to the attrs metadata.
  • dims: a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are:
    • Symbol: dimension name
    • Type{<:DimensionsionalData.Dimension}: dimension type
    • DimensionsionalData.Dimension: dimension, potentially with indices
    • Nothing: no dimension name provided, dimension name is automatically generated
  • coords: a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated.
source

DimensionalData

As a DimensionalData.AbstractDimStack, Dataset also implements the AbstractDimStack API and can be used like a DimStack. See DimensionalData's documentation for example usage.

Tables inteface

Dataset implements the Tables interface. This allows Datasets to be used as sources for any function that can accept a table. For example, it's straightforward to:

  • write to CSV with CSV.jl
  • flatten to a DataFrame with DataFrames.jl
  • plot with StatsPlots.jl
  • plot with AlgebraOfGraphics.jl
\ No newline at end of file diff --git a/InferenceObjects/v0.3.15/index.html b/InferenceObjects/v0.3.15/index.html new file mode 100644 index 000000000..41e4bdcf4 --- /dev/null +++ b/InferenceObjects/v0.3.15/index.html @@ -0,0 +1 @@ +Home · InferenceObjects.jl
GitHub

InferenceObjects

InferenceObjects.jl is a Julia implementation of the InferenceData schema for storing results of Bayesian inference. Its purpose is to serve the following three goals:

  1. Usefulness in the analysis of Bayesian inference results.
  2. Reproducibility of Bayesian inference analysis.
  3. Interoperability between different inference backends and programming languages.

The implementation consists primarily of the InferenceData and Dataset structures. InferenceObjects also provides the function convert_to_inference_data, which may be overloaded by inference packages to define how various inference outputs can be converted to an InferenceData.

For examples of how InferenceData can be used, see the ArviZ.jl documentation.

\ No newline at end of file diff --git a/InferenceObjects/v0.3.15/inference_data/index.html b/InferenceObjects/v0.3.15/inference_data/index.html new file mode 100644 index 000000000..f1c3f5630 --- /dev/null +++ b/InferenceObjects/v0.3.15/inference_data/index.html @@ -0,0 +1,193 @@ +InferenceData · InferenceObjects.jl
GitHub

InferenceData

Type definition

InferenceObjects.InferenceData — Type
InferenceData{group_names,group_types}

Container for inference data storage using DimensionalData.

This object implements the InferenceData schema.

Internally, groups are stored in a NamedTuple, which can be accessed using parent(::InferenceData).

Constructors

InferenceData(groups::NamedTuple)
+InferenceData(; groups...)

Construct an inference data from either a NamedTuple or keyword arguments of groups.

Groups must be Dataset objects.

Instead of directly creating an InferenceData, use the exported from_xyz functions or convert_to_inference_data.

source

Property interface

Base.getproperty — Function
getproperty(data::InferenceData, name::Symbol) -> Dataset

Get group with the specified name.

source

Indexing interface

Base.getindex — Function
Base.getindex(data::InferenceData, groups::Symbol; coords...) -> Dataset
+Base.getindex(data::InferenceData, groups; coords...) -> InferenceData

Return a new InferenceData containing the specified groups sliced to the specified coords.

coords specifies a dimension name mapping to an index, a DimensionalData.Selector, or an IntervalSets.AbstractInterval.

If one or more groups lack the specified dimension, a warning is raised but can be ignored. All groups that contain the dimension must also contain the specified indices, or an exception will be raised.

Examples

Select data from all groups for just the specified id values.

julia> using InferenceObjects, DimensionalData
+
+julia> idata = from_namedtuple(
+           (θ=randn(4, 100, 4), τ=randn(4, 100));
+           prior=(θ=randn(4, 100, 4), τ=randn(4, 100)),
+           observed_data=(y=randn(4),),
+           dims=(θ=[:id], y=[:id]),
+           coords=(id=["a", "b", "c", "d"],),
+       )
+InferenceData with groups:
+  > posterior
+  > prior
+  > observed_data
+
+julia> idata.posterior
+Dataset with dimensions:
+  Dim{:chain} Sampled 1:4 ForwardOrdered Regular Points,
+  Dim{:draw} Sampled 1:100 ForwardOrdered Regular Points,
+  Dim{:id} Categorical String[a, b, c, d] ForwardOrdered
+and 2 layers:
+  :θ Float64 dims: Dim{:chain}, Dim{:draw}, Dim{:id} (4×100×4)
+  :τ Float64 dims: Dim{:chain}, Dim{:draw} (4×100)
+
+with metadata Dict{String, Any} with 1 entry:
+  "created_at" => "2022-08-11T11:15:21.4"
+
+julia> idata_sel = idata[id=At(["a", "b"])]
+InferenceData with groups:
+  > posterior
+  > prior
+  > observed_data
+
+julia> idata_sel.posterior
+Dataset with dimensions:
+  Dim{:chain} Sampled 1:4 ForwardOrdered Regular Points,
+  Dim{:draw} Sampled 1:100 ForwardOrdered Regular Points,
+  Dim{:id} Categorical String[a, b] ForwardOrdered
+and 2 layers:
+  :θ Float64 dims: Dim{:chain}, Dim{:draw}, Dim{:id} (4×100×2)
+  :τ Float64 dims: Dim{:chain}, Dim{:draw} (4×100)
+
+with metadata Dict{String, Any} with 1 entry:
+  "created_at" => "2022-08-11T11:15:21.4"

Select data from just the posterior, returning a Dataset if the indices index more than one element from any of the variables:

julia> idata[:observed_data, id=At(["a"])]
+Dataset with dimensions:
+  Dim{:id} Categorical String[a] ForwardOrdered
+and 1 layer:
+  :y Float64 dims: Dim{:id} (1)
+
+with metadata Dict{String, Any} with 1 entry:
+  "created_at" => "2022-08-11T11:19:25.982"

Note that if a single index is provided, the behavior is still to slice so that the dimension is preserved.

source
Base.setindex — Function
Base.setindex(data::InferenceData, group::Dataset, name::Symbol) -> InferenceData

Create a new InferenceData containing the group with the specified name.

If a group with name is already in data, it is replaced.

source

Iteration interface

InferenceData also implements the same iteration interface as its underlying NamedTuple. That is, iterating over an InferenceData iterates over its groups.

General conversion

InferenceObjects.convert_to_inference_data — Function
convert_to_inference_data(obj; group, kwargs...) -> InferenceData

Convert a supported object to an InferenceData object.

If obj converts to a single dataset, group specifies which dataset in the resulting InferenceData that is.

See convert_to_dataset

Arguments

  • obj can be many objects. Basic supported types are:
    • InferenceData: return unchanged
    • Dataset/DimensionalData.AbstractDimStack: add to InferenceData as the only group
    • NamedTuple/AbstractDict: create a Dataset as the only group
    • AbstractArray{<:Real}: create a Dataset as the only group, given an arbitrary name, if the name is not set

More specific types may be documented separately.

Keywords

  • group::Symbol = :posterior: If obj converts to a single dataset, assign the resulting dataset to this group.

  • dims: a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are:

    • Symbol: dimension name
    • Type{<:DimensionsionalData.Dimension}: dimension type
    • DimensionsionalData.Dimension: dimension, potentially with indices
    • Nothing: no dimension name provided, dimension name is automatically generated

  • coords: a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated.

  • kwargs: remaining keywords forwarded to converter functions

source
InferenceObjects.from_dict — Function
from_dict(posterior::AbstractDict; kwargs...) -> InferenceData

Convert a Dict to an InferenceData.

Arguments

  • posterior: The data to be converted. Its strings must be Symbol or AbstractString, and its values must be arrays.

Keywords

  • posterior_predictive::Any=nothing: Draws from the posterior predictive distribution
  • sample_stats::Any=nothing: Statistics of the posterior sampling process
  • predictions::Any=nothing: Out-of-sample predictions for the posterior.
  • prior::Dict=nothing: Draws from the prior
  • prior_predictive::Any=nothing: Draws from the prior predictive distribution
  • sample_stats_prior::Any=nothing: Statistics of the prior sampling process
  • observed_data::NamedTuple: Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values.
  • constant_data::NamedTuple: Model constants, data included in the model which is not modeled as a random variable. Keys are parameter names and values.
  • predictions_constant_data::NamedTuple: Constants relevant to the model predictions (i.e. new x values in a linear regression).
  • log_likelihood: Pointwise log-likelihood for the data. It is recommended to use this argument as a NamedTuple whose keys are observed variable names and whose values are log likelihood arrays.
  • library: Name of library that generated the draws
  • coords: Map from named dimension to named indices
  • dims: Map from variable name to names of its dimensions

Returns

  • InferenceData: The data with groups corresponding to the provided data

Examples

using InferenceObjects
+nchains = 2
+ndraws = 100
+
+data = Dict(
+    :x => rand(ndraws, nchains),
+    :y => randn(2, ndraws, nchains),
+    :z => randn(3, 2, ndraws, nchains),
+)
+idata = from_dict(data)
source
InferenceObjects.from_namedtuple — Function
from_namedtuple(posterior::NamedTuple; kwargs...) -> InferenceData
+from_namedtuple(posterior::Vector{Vector{<:NamedTuple}}; kwargs...) -> InferenceData
+from_namedtuple(
+    posterior::NamedTuple,
+    sample_stats::Any,
+    posterior_predictive::Any,
+    predictions::Any,
+    log_likelihood::Any;
+    kwargs...
+) -> InferenceData

Convert a NamedTuple or container of NamedTuples to an InferenceData.

If containers are passed, they are flattened into a single NamedTuple with array elements whose first dimensions correspond to the dimensions of the containers.

Arguments

  • posterior: The data to be converted. It may be of the following types:

    • ::NamedTuple: The keys are the variable names and the values are arrays with dimensions (ndraws, nchains[, sizes...]).
    • ::Vector{Vector{<:NamedTuple}}: A vector of length nchains whose elements have length ndraws.

Keywords

  • posterior_predictive::Any=nothing: Draws from the posterior predictive distribution
  • sample_stats::Any=nothing: Statistics of the posterior sampling process
  • predictions::Any=nothing: Out-of-sample predictions for the posterior.
  • prior=nothing: Draws from the prior. Accepts the same types as posterior.
  • prior_predictive::Any=nothing: Draws from the prior predictive distribution
  • sample_stats_prior::Any=nothing: Statistics of the prior sampling process
  • observed_data::NamedTuple: Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values.
  • constant_data::NamedTuple: Model constants, data included in the model which is not modeled as a random variable. Keys are parameter names and values.
  • predictions_constant_data::NamedTuple: Constants relevant to the model predictions (i.e. new x values in a linear regression).
  • log_likelihood: Pointwise log-likelihood for the data. It is recommended to use this argument as a NamedTuple whose keys are observed variable names and whose values are log likelihood arrays.
  • library: Name of library that generated the draws
  • coords: Map from named dimension to named indices
  • dims: Map from variable name to names of its dimensions

Returns

  • InferenceData: The data with groups corresponding to the provided data
Note

If a NamedTuple is provided for observed_data, constant_data, or predictionsconstantdata`, any non-array values (e.g. integers) are converted to 0-dimensional arrays.

Examples

using InferenceObjects
+nchains = 2
+ndraws = 100
+
+data1 = (
+    x=rand(ndraws, nchains), y=randn(ndraws, nchains, 2), z=randn(ndraws, nchains, 3, 2)
+)
+idata1 = from_namedtuple(data1)
+
+data2 = [[(x=rand(), y=randn(2), z=randn(3, 2)) for _ in 1:ndraws] for _ in 1:nchains];
+idata2 = from_namedtuple(data2)
source

General functions

Base.cat — Function
cat(data::InferenceData...; [groups=keys(data[1]),] dims) -> InferenceData

Concatenate InferenceData objects along the specified dimension dims.

Only the groups in groups are concatenated. Remaining groups are merged into the new InferenceData object.

Examples

Here is how we can concatenate all groups of two InferenceData objects along the existing chain dimension:

julia> coords = (; a_dim=["x", "y", "z"]);
+
+julia> dims = dims=(; a=[:a_dim]);
+
+julia> data = Dict(:a => randn(100, 4, 3), :b => randn(100, 4));
+
+julia> idata = from_dict(data; coords=coords, dims=dims)
+InferenceData with groups:
+  > posterior
+
+julia> idata_cat1 = cat(idata, idata; dims=:chain)
+InferenceData with groups:
+  > posterior
+
+julia> idata_cat1.posterior
+Dataset with dimensions:
+  Dim{:draw},
+  Dim{:chain},
+  Dim{:a_dim} Categorical{String} String["x", "y", "z"] ForwardOrdered
+and 2 layers:
+  :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim} (100×8×3)
+  :b Float64 dims: Dim{:draw}, Dim{:chain} (100×8)
+
+with metadata Dict{String, Any} with 1 entry:
+  "created_at" => "2023-04-03T18:41:35.779"

Alternatively, we can concatenate along a new run dimension, which will be created.

julia> idata_cat2 = cat(idata, idata; dims=:run)
+InferenceData with groups:
+  > posterior
+
+julia> idata_cat2.posterior
+Dataset with dimensions:
+  Dim{:draw},
+  Dim{:chain},
+  Dim{:a_dim} Categorical{String} String["x", "y", "z"] ForwardOrdered,
+  Dim{:run}
+and 2 layers:
+  :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim}, Dim{:run} (100×4×3×2)
+  :b Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:run} (100×4×2)
+
+with metadata Dict{String, Any} with 1 entry:
+  "created_at" => "2023-04-03T18:41:35.779"

We can also concatenate only a subset of groups and merge the rest, which is useful when some groups are present only in some of the InferenceData objects or will be identical in all of them:

julia> observed_data = Dict(:y => randn(10));
+
+julia> idata2 = from_dict(data; observed_data=observed_data, coords=coords, dims=dims)
+InferenceData with groups:
+  > posterior
+  > observed_data
+
+julia> idata_cat3 = cat(idata, idata2; groups=(:posterior,), dims=:run)
+InferenceData with groups:
+  > posterior
+  > observed_data
+
+julia> idata_cat3.posterior
+Dataset with dimensions:
+  Dim{:draw},
+  Dim{:chain},
+  Dim{:a_dim} Categorical{String} String["x", "y", "z"] ForwardOrdered,
+  Dim{:run}
+and 2 layers:
+  :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim}, Dim{:run} (100×4×3×2)
+  :b Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:run} (100×4×2)
+
+with metadata Dict{String, Any} with 1 entry:
+  "created_at" => "2023-04-03T18:41:35.779"
+
+julia> idata_cat3.observed_data
+Dataset with dimensions: Dim{:y_dim_1}
+and 1 layer:
+  :y Float64 dims: Dim{:y_dim_1} (10)
+
+with metadata Dict{String, Any} with 1 entry:
+  "created_at" => "2023-02-17T15:11:00.59"
source
Base.merge — Function
merge(data::InferenceData...) -> InferenceData

Merge InferenceData objects.

The result contains all groups in data and others. If a group appears more than once, the one that occurs last is kept.

See also: cat

Examples

Here we merge an InferenceData containing only a posterior group with one containing only a prior group to create a new one containing both groups.

julia> idata1 = from_dict(Dict(:a => randn(100, 4, 3), :b => randn(100, 4)))
+InferenceData with groups:
+  > posterior
+
+julia> idata2 = from_dict(; prior=Dict(:a => randn(100, 1, 3), :c => randn(100, 1)))
+InferenceData with groups:
+  > prior
+
+julia> idata_merged = merge(idata1, idata2)
+InferenceData with groups:
+  > posterior
+  > prior
source

I/O extensions

The following types of storage are provided via extensions.

NetCDF I/O using NCDatasets.jl

InferenceObjects.from_netcdf — Function
from_netcdf(path::AbstractString; kwargs...) -> InferenceData

Load an InferenceData from an unopened NetCDF file.

Remaining kwargs are passed to NCDatasets.NCDataset. This method loads data eagerly. To instead load data lazily, pass an opened NCDataset to from_netcdf.

Note

This method requires that NCDatasets is loaded before it can be used.

Examples

julia> using InferenceObjects, NCDatasets
+
+julia> idata = from_netcdf("centered_eight.nc")
+InferenceData with groups:
+  > posterior
+  > posterior_predictive
+  > sample_stats
+  > prior
+  > observed_data
from_netcdf(ds::NCDatasets.NCDataset; load_mode) -> InferenceData

Load an InferenceData from an opened NetCDF file.

load_mode defaults to :lazy, which avoids reading variables into memory. Operations on these arrays will be slow. load_mode can also be :eager, which copies all variables into memory. It is then safe to close ds. If load_mode is :lazy and ds is closed after constructing InferenceData, using the variable arrays will have undefined behavior.

Examples

Here is how we might load an InferenceData from an InferenceData lazily from a web-hosted NetCDF file.

julia> using HTTP, InferenceObjects, NCDatasets
+
+julia> resp = HTTP.get("https://github.com/arviz-devs/arviz_example_data/blob/main/data/centered_eight.nc?raw=true");
+
+julia> ds = NCDataset("centered_eight", "r"; memory = resp.body);
+
+julia> idata = from_netcdf(ds)
+InferenceData with groups:
+  > posterior
+  > posterior_predictive
+  > sample_stats
+  > prior
+  > observed_data
+
+julia> idata_copy = copy(idata); # disconnect from the loaded dataset
+
+julia> close(ds);
source
InferenceObjects.to_netcdf — Function
to_netcdf(data, dest::AbstractString; group::Symbol=:posterior, kwargs...)
+to_netcdf(data, dest::NCDatasets.NCDataset; group::Symbol=:posterior)

Write data to a NetCDF file.

data is any type that can be converted to an InferenceData using convert_to_inference_data. If not an InferenceData, then group specifies which group the data represents.

dest specifies either the path to the NetCDF file or an opened NetCDF file. If dest is a path, remaining kwargs are passed to NCDatasets.NCDataset.

Note

This method requires that NCDatasets is loaded before it can be used.

Examples

julia> using InferenceObjects, NCDatasets
+
+julia> idata = from_namedtuple((; x = randn(4, 100, 3), z = randn(4, 100)))
+InferenceData with groups:
+  > posterior
+
+julia> to_netcdf(idata, "data.nc")
+"data.nc"
source
\ No newline at end of file diff --git a/InferenceObjects/v0.3.15/search_index.js b/InferenceObjects/v0.3.15/search_index.js new file mode 100644 index 000000000..f46f00303 --- /dev/null +++ b/InferenceObjects/v0.3.15/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"dataset/#Dataset","page":"Dataset","title":"Dataset","text":"","category":"section"},{"location":"dataset/","page":"Dataset","title":"Dataset","text":"Pages = [\"dataset.md\"]","category":"page"},{"location":"dataset/#Type-definition","page":"Dataset","title":"Type definition","text":"","category":"section"},{"location":"dataset/","page":"Dataset","title":"Dataset","text":"Dataset","category":"page"},{"location":"dataset/#InferenceObjects.Dataset","page":"Dataset","title":"InferenceObjects.Dataset","text":"Dataset{L} <: DimensionalData.AbstractDimStack{L}\n\nContainer of dimensional arrays sharing some dimensions.\n\nThis type is an DimensionalData.AbstractDimStack that implements the same interface as DimensionalData.DimStack and has identical usage.\n\nWhen a Dataset is passed to Python, it is converted to an xarray.Dataset without copying the data. That is, the Python object shares the same memory as the Julia object. However, if an xarray.Dataset is passed to Julia, its data must be copied.\n\nConstructors\n\nDataset(data::DimensionalData.AbstractDimArray...)\nDataset(data::Tuple{Vararg{<:DimensionalData.AbstractDimArray}})\nDataset(data::NamedTuple{Keys,Vararg{<:DimensionalData.AbstractDimArray}})\nDataset(\n data::NamedTuple,\n dims::Tuple{Vararg{DimensionalData.Dimension}};\n metadata=DimensionalData.NoMetadata(),\n)\n\nIn most cases, use convert_to_dataset to create a Dataset instead of directly using a constructor.\n\n\n\n\n\n","category":"type"},{"location":"dataset/#General-conversion","page":"Dataset","title":"General conversion","text":"","category":"section"},{"location":"dataset/","page":"Dataset","title":"Dataset","text":"convert_to_dataset\nnamedtuple_to_dataset","category":"page"},{"location":"dataset/#InferenceObjects.convert_to_dataset","page":"Dataset","title":"InferenceObjects.convert_to_dataset","text":"convert_to_dataset(obj; group = :posterior, kwargs...) -> Dataset\n\nConvert a supported object to a Dataset.\n\nIn most cases, this function calls convert_to_inference_data and returns the corresponding group.\n\n\n\n\n\n","category":"function"},{"location":"dataset/#InferenceObjects.namedtuple_to_dataset","page":"Dataset","title":"InferenceObjects.namedtuple_to_dataset","text":"namedtuple_to_dataset(data; kwargs...) -> Dataset\n\nConvert NamedTuple mapping variable names to arrays to a Dataset.\n\nAny non-array values will be converted to a 0-dimensional array.\n\nKeywords\n\nattrs::AbstractDict{<:AbstractString}: a collection of metadata to attach to the dataset, in addition to defaults. Values should be JSON serializable.\nlibrary::Union{String,Module}: library used for performing inference. Will be attached to the attrs metadata.\ndims: a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are:\nSymbol: dimension name\nType{<:DimensionsionalData.Dimension}: dimension type\nDimensionsionalData.Dimension: dimension, potentially with indices\nNothing: no dimension name provided, dimension name is automatically generated\ncoords: a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. 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For example, it's straightforward to:","category":"page"},{"location":"dataset/","page":"Dataset","title":"Dataset","text":"write to CSV with CSV.jl\nflatten to a DataFrame with DataFrames.jl\nplot with StatsPlots.jl\nplot with AlgebraOfGraphics.jl","category":"page"},{"location":"inference_data/#InferenceData","page":"InferenceData","title":"InferenceData","text":"","category":"section"},{"location":"inference_data/","page":"InferenceData","title":"InferenceData","text":"Pages = [\"inference_data.md\"]","category":"page"},{"location":"inference_data/#Type-definition","page":"InferenceData","title":"Type definition","text":"","category":"section"},{"location":"inference_data/","page":"InferenceData","title":"InferenceData","text":"InferenceData","category":"page"},{"location":"inference_data/#InferenceObjects.InferenceData","page":"InferenceData","title":"InferenceObjects.InferenceData","text":"InferenceData{group_names,group_types}\n\nContainer for inference data storage using DimensionalData.\n\nThis object implements the InferenceData schema.\n\nInternally, groups are stored in a NamedTuple, which can be accessed using parent(::InferenceData).\n\nConstructors\n\nInferenceData(groups::NamedTuple)\nInferenceData(; groups...)\n\nConstruct an inference data from either a NamedTuple or keyword arguments of groups.\n\nGroups must be Dataset objects.\n\nInstead of directly creating an InferenceData, use the exported from_xyz functions or convert_to_inference_data.\n\n\n\n\n\n","category":"type"},{"location":"inference_data/#Property-interface","page":"InferenceData","title":"Property interface","text":"","category":"section"},{"location":"inference_data/","page":"InferenceData","title":"InferenceData","text":"getproperty\npropertynames","category":"page"},{"location":"inference_data/#Base.getproperty","page":"InferenceData","title":"Base.getproperty","text":"getproperty(data::InferenceData, name::Symbol) -> Dataset\n\nGet group with the specified name.\n\n\n\n\n\n","category":"function"},{"location":"inference_data/#Base.propertynames","page":"InferenceData","title":"Base.propertynames","text":"propertynames(data::InferenceData) -> Tuple{Symbol}\n\nGet names of groups\n\n\n\n\n\n","category":"function"},{"location":"inference_data/#Indexing-interface","page":"InferenceData","title":"Indexing interface","text":"","category":"section"},{"location":"inference_data/","page":"InferenceData","title":"InferenceData","text":"getindex\nBase.setindex","category":"page"},{"location":"inference_data/#Base.getindex","page":"InferenceData","title":"Base.getindex","text":"Base.getindex(data::InferenceData, groups::Symbol; coords...) -> Dataset\nBase.getindex(data::InferenceData, groups; coords...) -> InferenceData\n\nReturn a new InferenceData containing the specified groups sliced to the specified coords.\n\ncoords specifies a dimension name mapping to an index, a DimensionalData.Selector, or an IntervalSets.AbstractInterval.\n\nIf one or more groups lack the specified dimension, a warning is raised but can be ignored. All groups that contain the dimension must also contain the specified indices, or an exception will be raised.\n\nExamples\n\nSelect data from all groups for just the specified id values.\n\njulia> using InferenceObjects, DimensionalData\n\njulia> idata = from_namedtuple(\n (θ=randn(4, 100, 4), τ=randn(4, 100));\n prior=(θ=randn(4, 100, 4), τ=randn(4, 100)),\n observed_data=(y=randn(4),),\n dims=(θ=[:id], y=[:id]),\n coords=(id=[\"a\", \"b\", \"c\", \"d\"],),\n )\nInferenceData with groups:\n > posterior\n > prior\n > observed_data\n\njulia> idata.posterior\nDataset with dimensions:\n Dim{:chain} Sampled 1:4 ForwardOrdered Regular Points,\n Dim{:draw} Sampled 1:100 ForwardOrdered Regular Points,\n Dim{:id} Categorical String[a, b, c, d] ForwardOrdered\nand 2 layers:\n :θ Float64 dims: Dim{:chain}, Dim{:draw}, Dim{:id} (4×100×4)\n :τ Float64 dims: Dim{:chain}, Dim{:draw} (4×100)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2022-08-11T11:15:21.4\"\n\njulia> idata_sel = idata[id=At([\"a\", \"b\"])]\nInferenceData with groups:\n > posterior\n > prior\n > observed_data\n\njulia> idata_sel.posterior\nDataset with dimensions:\n Dim{:chain} Sampled 1:4 ForwardOrdered Regular Points,\n Dim{:draw} Sampled 1:100 ForwardOrdered Regular Points,\n Dim{:id} Categorical String[a, b] ForwardOrdered\nand 2 layers:\n :θ Float64 dims: Dim{:chain}, Dim{:draw}, Dim{:id} (4×100×2)\n :τ Float64 dims: Dim{:chain}, Dim{:draw} (4×100)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2022-08-11T11:15:21.4\"\n\nSelect data from just the posterior, returning a Dataset if the indices index more than one element from any of the variables:\n\njulia> idata[:observed_data, id=At([\"a\"])]\nDataset with dimensions:\n Dim{:id} Categorical String[a] ForwardOrdered\nand 1 layer:\n :y Float64 dims: Dim{:id} (1)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2022-08-11T11:19:25.982\"\n\nNote that if a single index is provided, the behavior is still to slice so that the dimension is preserved.\n\n\n\n\n\n","category":"function"},{"location":"inference_data/#Base.setindex","page":"InferenceData","title":"Base.setindex","text":"Base.setindex(data::InferenceData, group::Dataset, name::Symbol) -> InferenceData\n\nCreate a new InferenceData containing the group with the specified name.\n\nIf a group with name is already in data, it is replaced.\n\n\n\n\n\n","category":"function"},{"location":"inference_data/#Iteration-interface","page":"InferenceData","title":"Iteration interface","text":"","category":"section"},{"location":"inference_data/","page":"InferenceData","title":"InferenceData","text":"InferenceData also implements the same iteration interface as its underlying NamedTuple. That is, iterating over an InferenceData iterates over its groups.","category":"page"},{"location":"inference_data/#General-conversion","page":"InferenceData","title":"General conversion","text":"","category":"section"},{"location":"inference_data/","page":"InferenceData","title":"InferenceData","text":"convert_to_inference_data\nfrom_dict\nfrom_namedtuple","category":"page"},{"location":"inference_data/#InferenceObjects.convert_to_inference_data","page":"InferenceData","title":"InferenceObjects.convert_to_inference_data","text":"convert_to_inference_data(obj; group, kwargs...) -> InferenceData\n\nConvert a supported object to an InferenceData object.\n\nIf obj converts to a single dataset, group specifies which dataset in the resulting InferenceData that is.\n\nSee convert_to_dataset\n\nArguments\n\nobj can be many objects. Basic supported types are:\nInferenceData: return unchanged\nDataset/DimensionalData.AbstractDimStack: add to InferenceData as the only group\nNamedTuple/AbstractDict: create a Dataset as the only group\nAbstractArray{<:Real}: create a Dataset as the only group, given an arbitrary name, if the name is not set\n\nMore specific types may be documented separately.\n\nKeywords\n\ngroup::Symbol = :posterior: If obj converts to a single dataset, assign the resulting dataset to this group.\ndims: a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are:\nSymbol: dimension name\nType{<:DimensionsionalData.Dimension}: dimension type\nDimensionsionalData.Dimension: dimension, potentially with indices\nNothing: no dimension name provided, dimension name is automatically generated\ncoords: a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated.\nkwargs: remaining keywords forwarded to converter functions\n\n\n\n\n\n","category":"function"},{"location":"inference_data/#InferenceObjects.from_dict","page":"InferenceData","title":"InferenceObjects.from_dict","text":"from_dict(posterior::AbstractDict; kwargs...) -> InferenceData\n\nConvert a Dict to an InferenceData.\n\nArguments\n\nposterior: The data to be converted. Its strings must be Symbol or AbstractString, and its values must be arrays.\n\nKeywords\n\nposterior_predictive::Any=nothing: Draws from the posterior predictive distribution\nsample_stats::Any=nothing: Statistics of the posterior sampling process\npredictions::Any=nothing: Out-of-sample predictions for the posterior.\nprior::Dict=nothing: Draws from the prior\nprior_predictive::Any=nothing: Draws from the prior predictive distribution\nsample_stats_prior::Any=nothing: Statistics of the prior sampling process\nobserved_data::NamedTuple: Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values.\nconstant_data::NamedTuple: Model constants, data included in the model which is not modeled as a random variable. Keys are parameter names and values.\npredictions_constant_data::NamedTuple: Constants relevant to the model predictions (i.e. new x values in a linear regression).\nlog_likelihood: Pointwise log-likelihood for the data. It is recommended to use this argument as a NamedTuple whose keys are observed variable names and whose values are log likelihood arrays.\nlibrary: Name of library that generated the draws\ncoords: Map from named dimension to named indices\ndims: Map from variable name to names of its dimensions\n\nReturns\n\nInferenceData: The data with groups corresponding to the provided data\n\nExamples\n\nusing InferenceObjects\nnchains = 2\nndraws = 100\n\ndata = Dict(\n :x => rand(ndraws, nchains),\n :y => randn(2, ndraws, nchains),\n :z => randn(3, 2, ndraws, nchains),\n)\nidata = from_dict(data)\n\n\n\n\n\n","category":"function"},{"location":"inference_data/#InferenceObjects.from_namedtuple","page":"InferenceData","title":"InferenceObjects.from_namedtuple","text":"from_namedtuple(posterior::NamedTuple; kwargs...) -> InferenceData\nfrom_namedtuple(posterior::Vector{Vector{<:NamedTuple}}; kwargs...) -> InferenceData\nfrom_namedtuple(\n posterior::NamedTuple,\n sample_stats::Any,\n posterior_predictive::Any,\n predictions::Any,\n log_likelihood::Any;\n kwargs...\n) -> InferenceData\n\nConvert a NamedTuple or container of NamedTuples to an InferenceData.\n\nIf containers are passed, they are flattened into a single NamedTuple with array elements whose first dimensions correspond to the dimensions of the containers.\n\nArguments\n\nposterior: The data to be converted. It may be of the following types:\n::NamedTuple: The keys are the variable names and the values are arrays with dimensions (ndraws, nchains[, sizes...]).\n::Vector{Vector{<:NamedTuple}}: A vector of length nchains whose elements have length ndraws.\n\nKeywords\n\nposterior_predictive::Any=nothing: Draws from the posterior predictive distribution\nsample_stats::Any=nothing: Statistics of the posterior sampling process\npredictions::Any=nothing: Out-of-sample predictions for the posterior.\nprior=nothing: Draws from the prior. Accepts the same types as posterior.\nprior_predictive::Any=nothing: Draws from the prior predictive distribution\nsample_stats_prior::Any=nothing: Statistics of the prior sampling process\nobserved_data::NamedTuple: Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values.\nconstant_data::NamedTuple: Model constants, data included in the model which is not modeled as a random variable. Keys are parameter names and values.\npredictions_constant_data::NamedTuple: Constants relevant to the model predictions (i.e. new x values in a linear regression).\nlog_likelihood: Pointwise log-likelihood for the data. It is recommended to use this argument as a NamedTuple whose keys are observed variable names and whose values are log likelihood arrays.\nlibrary: Name of library that generated the draws\ncoords: Map from named dimension to named indices\ndims: Map from variable name to names of its dimensions\n\nReturns\n\nInferenceData: The data with groups corresponding to the provided data\n\nnote: Note\nIf a NamedTuple is provided for observed_data, constant_data, or predictionsconstantdata`, any non-array values (e.g. integers) are converted to 0-dimensional arrays.\n\nExamples\n\nusing InferenceObjects\nnchains = 2\nndraws = 100\n\ndata1 = (\n x=rand(ndraws, nchains), y=randn(ndraws, nchains, 2), z=randn(ndraws, nchains, 3, 2)\n)\nidata1 = from_namedtuple(data1)\n\ndata2 = [[(x=rand(), y=randn(2), z=randn(3, 2)) for _ in 1:ndraws] for _ in 1:nchains];\nidata2 = from_namedtuple(data2)\n\n\n\n\n\n","category":"function"},{"location":"inference_data/#General-functions","page":"InferenceData","title":"General functions","text":"","category":"section"},{"location":"inference_data/","page":"InferenceData","title":"InferenceData","text":"cat\nmerge","category":"page"},{"location":"inference_data/#Base.cat","page":"InferenceData","title":"Base.cat","text":"cat(data::InferenceData...; [groups=keys(data[1]),] dims) -> InferenceData\n\nConcatenate InferenceData objects along the specified dimension dims.\n\nOnly the groups in groups are concatenated. Remaining groups are merged into the new InferenceData object.\n\nExamples\n\nHere is how we can concatenate all groups of two InferenceData objects along the existing chain dimension:\n\njulia> coords = (; a_dim=[\"x\", \"y\", \"z\"]);\n\njulia> dims = dims=(; a=[:a_dim]);\n\njulia> data = Dict(:a => randn(100, 4, 3), :b => randn(100, 4));\n\njulia> idata = from_dict(data; coords=coords, dims=dims)\nInferenceData with groups:\n > posterior\n\njulia> idata_cat1 = cat(idata, idata; dims=:chain)\nInferenceData with groups:\n > posterior\n\njulia> idata_cat1.posterior\nDataset with dimensions:\n Dim{:draw},\n Dim{:chain},\n Dim{:a_dim} Categorical{String} String[\"x\", \"y\", \"z\"] ForwardOrdered\nand 2 layers:\n :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim} (100×8×3)\n :b Float64 dims: Dim{:draw}, Dim{:chain} (100×8)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-04-03T18:41:35.779\"\n\nAlternatively, we can concatenate along a new run dimension, which will be created.\n\njulia> idata_cat2 = cat(idata, idata; dims=:run)\nInferenceData with groups:\n > posterior\n\njulia> idata_cat2.posterior\nDataset with dimensions:\n Dim{:draw},\n Dim{:chain},\n Dim{:a_dim} Categorical{String} String[\"x\", \"y\", \"z\"] ForwardOrdered,\n Dim{:run}\nand 2 layers:\n :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim}, Dim{:run} (100×4×3×2)\n :b Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:run} (100×4×2)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-04-03T18:41:35.779\"\n\nWe can also concatenate only a subset of groups and merge the rest, which is useful when some groups are present only in some of the InferenceData objects or will be identical in all of them:\n\njulia> observed_data = Dict(:y => randn(10));\n\njulia> idata2 = from_dict(data; observed_data=observed_data, coords=coords, dims=dims)\nInferenceData with groups:\n > posterior\n > observed_data\n\njulia> idata_cat3 = cat(idata, idata2; groups=(:posterior,), dims=:run)\nInferenceData with groups:\n > posterior\n > observed_data\n\njulia> idata_cat3.posterior\nDataset with dimensions:\n Dim{:draw},\n Dim{:chain},\n Dim{:a_dim} Categorical{String} String[\"x\", \"y\", \"z\"] ForwardOrdered,\n Dim{:run}\nand 2 layers:\n :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim}, Dim{:run} (100×4×3×2)\n :b Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:run} (100×4×2)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-04-03T18:41:35.779\"\n\njulia> idata_cat3.observed_data\nDataset with dimensions: Dim{:y_dim_1}\nand 1 layer:\n :y Float64 dims: Dim{:y_dim_1} (10)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-02-17T15:11:00.59\"\n\n\n\n\n\n","category":"function"},{"location":"inference_data/#Base.merge","page":"InferenceData","title":"Base.merge","text":"merge(data::InferenceData...) -> InferenceData\n\nMerge InferenceData objects.\n\nThe result contains all groups in data and others. If a group appears more than once, the one that occurs last is kept.\n\nSee also: cat\n\nExamples\n\nHere we merge an InferenceData containing only a posterior group with one containing only a prior group to create a new one containing both groups.\n\njulia> idata1 = from_dict(Dict(:a => randn(100, 4, 3), :b => randn(100, 4)))\nInferenceData with groups:\n > posterior\n\njulia> idata2 = from_dict(; prior=Dict(:a => randn(100, 1, 3), :c => randn(100, 1)))\nInferenceData with groups:\n > prior\n\njulia> idata_merged = merge(idata1, idata2)\nInferenceData with groups:\n > posterior\n > prior\n\n\n\n\n\n","category":"function"},{"location":"inference_data/#I/O-extensions","page":"InferenceData","title":"I/O extensions","text":"","category":"section"},{"location":"inference_data/","page":"InferenceData","title":"InferenceData","text":"The following types of storage are provided via extensions.","category":"page"},{"location":"inference_data/#NetCDF-I/O-using-NCDatasets.jl","page":"InferenceData","title":"NetCDF I/O using NCDatasets.jl","text":"","category":"section"},{"location":"inference_data/","page":"InferenceData","title":"InferenceData","text":"from_netcdf\nto_netcdf","category":"page"},{"location":"inference_data/#InferenceObjects.from_netcdf","page":"InferenceData","title":"InferenceObjects.from_netcdf","text":"from_netcdf(path::AbstractString; kwargs...) -> InferenceData\n\nLoad an InferenceData from an unopened NetCDF file.\n\nRemaining kwargs are passed to NCDatasets.NCDataset. This method loads data eagerly. To instead load data lazily, pass an opened NCDataset to from_netcdf.\n\nnote: Note\nThis method requires that NCDatasets is loaded before it can be used.\n\nExamples\n\njulia> using InferenceObjects, NCDatasets\n\njulia> idata = from_netcdf(\"centered_eight.nc\")\nInferenceData with groups:\n > posterior\n > posterior_predictive\n > sample_stats\n > prior\n > observed_data\n\nfrom_netcdf(ds::NCDatasets.NCDataset; load_mode) -> InferenceData\n\nLoad an InferenceData from an opened NetCDF file.\n\nload_mode defaults to :lazy, which avoids reading variables into memory. Operations on these arrays will be slow. load_mode can also be :eager, which copies all variables into memory. It is then safe to close ds. If load_mode is :lazy and ds is closed after constructing InferenceData, using the variable arrays will have undefined behavior.\n\nExamples\n\nHere is how we might load an InferenceData from an InferenceData lazily from a web-hosted NetCDF file.\n\njulia> using HTTP, InferenceObjects, NCDatasets\n\njulia> resp = HTTP.get(\"https://github.com/arviz-devs/arviz_example_data/blob/main/data/centered_eight.nc?raw=true\");\n\njulia> ds = NCDataset(\"centered_eight\", \"r\"; memory = resp.body);\n\njulia> idata = from_netcdf(ds)\nInferenceData with groups:\n > posterior\n > posterior_predictive\n > sample_stats\n > prior\n > observed_data\n\njulia> idata_copy = copy(idata); # disconnect from the loaded dataset\n\njulia> close(ds);\n\n\n\n\n\n","category":"function"},{"location":"inference_data/#InferenceObjects.to_netcdf","page":"InferenceData","title":"InferenceObjects.to_netcdf","text":"to_netcdf(data, dest::AbstractString; group::Symbol=:posterior, kwargs...)\nto_netcdf(data, dest::NCDatasets.NCDataset; group::Symbol=:posterior)\n\nWrite data to a NetCDF file.\n\ndata is any type that can be converted to an InferenceData using convert_to_inference_data. If not an InferenceData, then group specifies which group the data represents.\n\ndest specifies either the path to the NetCDF file or an opened NetCDF file. If dest is a path, remaining kwargs are passed to NCDatasets.NCDataset.\n\nnote: Note\nThis method requires that NCDatasets is loaded before it can be used.\n\nExamples\n\njulia> using InferenceObjects, NCDatasets\n\njulia> idata = from_namedtuple((; x = randn(4, 100, 3), z = randn(4, 100)))\nInferenceData with groups:\n > posterior\n\njulia> to_netcdf(idata, \"data.nc\")\n\"data.nc\"\n\n\n\n\n\n","category":"function"},{"location":"","page":"Home","title":"Home","text":"CurrentModule = InferenceObjects","category":"page"},{"location":"#InferenceObjects","page":"Home","title":"InferenceObjects","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"InferenceObjects.jl is a Julia implementation of the InferenceData schema for storing results of Bayesian inference. Its purpose is to serve the following three goals:","category":"page"},{"location":"","page":"Home","title":"Home","text":"Usefulness in the analysis of Bayesian inference results.\nReproducibility of Bayesian inference analysis.\nInteroperability between different inference backends and programming languages.","category":"page"},{"location":"","page":"Home","title":"Home","text":"The implementation consists primarily of the InferenceData and Dataset structures. InferenceObjects also provides the function convert_to_inference_data, which may be overloaded by inference packages to define how various inference outputs can be converted to an InferenceData.","category":"page"},{"location":"","page":"Home","title":"Home","text":"For examples of how InferenceData can be used, see the ArviZ.jl documentation.","category":"page"}] +} diff --git a/InferenceObjects/v0.3.15/siteinfo.js b/InferenceObjects/v0.3.15/siteinfo.js new file mode 100644 index 000000000..f7a231086 --- /dev/null +++ b/InferenceObjects/v0.3.15/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v0.3.15"; diff --git a/InferenceObjects/versions.js b/InferenceObjects/versions.js index acd2a1c62..345c0172b 100644 --- a/InferenceObjects/versions.js +++ b/InferenceObjects/versions.js @@ -5,5 +5,5 @@ var DOC_VERSIONS = [ "v0.1", "dev", ]; -var DOCUMENTER_NEWEST = "v0.3.14"; +var DOCUMENTER_NEWEST = "v0.3.15"; var DOCUMENTER_STABLE = "stable"; diff --git a/PSIS/dev/.documenter-siteinfo.json b/PSIS/dev/.documenter-siteinfo.json index 9930977c3..efadb3829 100644 --- a/PSIS/dev/.documenter-siteinfo.json +++ b/PSIS/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-12-22T00:44:53","documenter_version":"1.2.1"}} \ No newline at end of file +{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-12-23T00:39:32","documenter_version":"1.2.1"}} \ No newline at end of file diff --git a/PSIS/dev/api/index.html b/PSIS/dev/api/index.html index fc328813a..88532d902 100644 --- a/PSIS/dev/api/index.html +++ b/PSIS/dev/api/index.html @@ -6,4 +6,4 @@ x = rand(proposal, 1_000, 100) log_ratios = logpdf.(target, x) .- logpdf.(proposal, x) result = psis(log_ratios) -paretoshapeplot(result)

We can also plot the Pareto shape parameters directly:

paretoshapeplot(result.pareto_shape)

We can also use plot directly:

plot(result.pareto_shape; showlines=true)
source
\ No newline at end of file +paretoshapeplot(result)

We can also plot the Pareto shape parameters directly:

paretoshapeplot(result.pareto_shape)

We can also use plot directly:

plot(result.pareto_shape; showlines=true)
source
\ No newline at end of file diff --git a/PSIS/dev/index.html b/PSIS/dev/index.html index aa46122cd..0d89f5432 100644 --- a/PSIS/dev/index.html +++ b/PSIS/dev/index.html @@ -13,4 +13,4 @@ (-Inf, 0.5] good 7 (23.3%) 959 (0.5, 0.7] okay 14 (46.7%) 927 (0.7, 1] bad 8 (26.7%) —— - (1, Inf) very bad 1 (3.3%) ——

As indicated by the warnings, this is a poor choice of a proposal distribution, and estimates are unlikely to converge (see PSISResult for an explanation of the shape thresholds).

When running PSIS with many parameters, it is useful to plot the Pareto shape values to diagnose convergence. See Plotting PSIS results for examples.

\ No newline at end of file + (1, Inf) very bad 1 (3.3%) ——

As indicated by the warnings, this is a poor choice of a proposal distribution, and estimates are unlikely to converge (see PSISResult for an explanation of the shape thresholds).

When running PSIS with many parameters, it is useful to plot the Pareto shape values to diagnose convergence. See Plotting PSIS results for examples.

\ No newline at end of file diff --git a/PSIS/dev/internal/index.html b/PSIS/dev/internal/index.html index 6651df24c..a86959a8d 100644 --- a/PSIS/dev/internal/index.html +++ b/PSIS/dev/internal/index.html @@ -1 +1 @@ -Internal · PSIS.jl
GitHub

Internal

PSIS.GeneralizedPareto — Type
GeneralizedPareto{T<:Real}

The generalized Pareto distribution.

This is equivalent to Distributions.GeneralizedPareto and can be converted to one with convert(Distributions.GeneralizedPareto, d).

Constructor

GeneralizedPareto(μ, σ, k)

Construct the generalized Pareto distribution (GPD) with location parameter $μ$, scale parameter $σ$ and shape parameter $k$.

Note

The shape parameter $k$ is equivalent to the commonly used shape parameter $ξ$. This is the same parameterization used by [VehtariSimpson2021] and is related to that used by [ZhangStephens2009] as $k \mapsto -k$.

source
PSIS.fit_gpd — Method
fit_gpd(x; μ=0, kwargs...)

Fit a GeneralizedPareto with location μ to the data x.

The fit is performed using the Empirical Bayes method of [ZhangStephens2009].

Keywords

  • prior_adjusted::Bool=true, If true, a weakly informative Normal prior centered on $\frac{1}{2}$ is used for the shape $k$.
  • sorted::Bool=issorted(x): If true, x is assumed to be sorted. If false, a sorted copy of x is made.
  • min_points::Int=30: The minimum number of quadrature points to use when estimating the posterior mean of $\theta = \frac{\xi}{\sigma}$.
source
\ No newline at end of file +Internal · PSIS.jl
GitHub

Internal

PSIS.GeneralizedPareto — Type
GeneralizedPareto{T<:Real}

The generalized Pareto distribution.

This is equivalent to Distributions.GeneralizedPareto and can be converted to one with convert(Distributions.GeneralizedPareto, d).

Constructor

GeneralizedPareto(μ, σ, k)

Construct the generalized Pareto distribution (GPD) with location parameter $μ$, scale parameter $σ$ and shape parameter $k$.

Note

The shape parameter $k$ is equivalent to the commonly used shape parameter $ξ$. This is the same parameterization used by [VehtariSimpson2021] and is related to that used by [ZhangStephens2009] as $k \mapsto -k$.

source
PSIS.fit_gpd — Method
fit_gpd(x; μ=0, kwargs...)

Fit a GeneralizedPareto with location μ to the data x.

The fit is performed using the Empirical Bayes method of [ZhangStephens2009].

Keywords

  • prior_adjusted::Bool=true, If true, a weakly informative Normal prior centered on $\frac{1}{2}$ is used for the shape $k$.
  • sorted::Bool=issorted(x): If true, x is assumed to be sorted. If false, a sorted copy of x is made.
  • min_points::Int=30: The minimum number of quadrature points to use when estimating the posterior mean of $\theta = \frac{\xi}{\sigma}$.
source
\ No newline at end of file diff --git a/PSIS/dev/plotting/29d7ad4e.svg b/PSIS/dev/plotting/7e3d98ae.svg similarity index 76% rename from PSIS/dev/plotting/29d7ad4e.svg rename to PSIS/dev/plotting/7e3d98ae.svg index aa376ddd0..e409ad7bc 100644 --- a/PSIS/dev/plotting/29d7ad4e.svg +++ b/PSIS/dev/plotting/7e3d98ae.svg @@ -1,124 +1,124 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/PSIS/dev/plotting/index.html b/PSIS/dev/plotting/index.html index a17258382..ac6afff9f 100644 --- a/PSIS/dev/plotting/index.html +++ b/PSIS/dev/plotting/index.html @@ -10,4 +10,4 @@ (-Inf, 0.5] good 4 (20.0%) 959 (0.5, 0.7] okay 10 (50.0%) 927 (0.7, 1] bad 6 (30.0%) ——

Plots.jl

PSISResult objects can be plotted directly:

using Plots
-plot(result; showlines=true, marker=:+, legend=false, linewidth=2)
Example block output

This is equivalent to calling PSISPlots.paretoshapeplot(result; kwargs...).

\ No newline at end of file +plot(result; showlines=true, marker=:+, legend=false, linewidth=2)Example block output

This is equivalent to calling PSISPlots.paretoshapeplot(result; kwargs...).

\ No newline at end of file diff --git a/PosteriorStats/dev/.documenter-siteinfo.json b/PosteriorStats/dev/.documenter-siteinfo.json index 5f8fc79ea..c4e2fdf74 100644 --- a/PosteriorStats/dev/.documenter-siteinfo.json +++ b/PosteriorStats/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-12-22T03:02:51","documenter_version":"1.2.1"}} \ No newline at end of file +{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-12-23T19:07:53","documenter_version":"1.2.1"}} \ No newline at end of file diff --git a/PosteriorStats/dev/api/index.html b/PosteriorStats/dev/api/index.html index 3eb2d02ff..caf4b294d 100644 --- a/PosteriorStats/dev/api/index.html +++ b/PosteriorStats/dev/api/index.html @@ -1,4 +1,5 @@ -API · PosteriorStats.jl
GitHub

API

    Summary statistics

    PosteriorStats.SummaryStats — Type

    A container for a column table of values computed by summarize.

    This object implements the Tables and TableTraits interfaces and has a custom show method.

    • name: The name of the collection of summary statistics, used as the table title in display.

    • data: The summary statistics for each parameter, with an optional first column parameter containing the parameter names.

    source
    PosteriorStats.default_diagnostics — Function
    default_diagnostics(focus=Statistics.mean; kwargs...)

    Default diagnostics to be computed with summarize.

    The value of focus determines the diagnostics to be returned:

    • Statistics.mean: mcse_mean, mcse_std, ess_tail, ess_bulk, rhat
    • Statistics.median: mcse_median, ess_tail, ess_bulk, rhat
    source
    PosteriorStats.default_stats — Function
    default_stats(focus=Statistics.mean; prob_interval=0.94, kwargs...)

    Default statistics to be computed with summarize.

    The value of focus determines the statistics to be returned:

    • Statistics.mean: mean, std, hdi_3%, hdi_97%
    • Statistics.median: median, mad, eti_3%, eti_97%

    If prob_interval is set to a different value than the default, then different HDI and ETI statistics are computed accordingly. hdi refers to the highest-density interval, while eti refers to the equal-tailed interval (i.e. the credible interval computed from symmetric quantiles).

    See also: hdi

    source
    PosteriorStats.summarize — Function
    summarize(data, stats_funs...; name="SummaryStats", [var_names]) -> SummaryStats

    Compute the summary statistics in stats_funs on each param in data.

    stats_funs is a collection of functions that reduces a matrix with shape (draws, chains) to a scalar or a collection of scalars. Alternatively, an item in stats_funs may be a Pair of the form name => fun specifying the name to be used for the statistic or of the form (name1, ...) => fun when the function returns a collection. When the function returns a collection, the names in this latter format must be provided.

    If no stats functions are provided, then those specified in default_summary_stats are computed.

    var_names specifies the names of the parameters in data. If not provided, the names are inferred from data.

    To support computing summary statistics from a custom object, overload this method specifying the type of data.

    See also SummaryStats, default_summary_stats, default_stats, default_diagnostics.

    Examples

    Compute mean, std and the Monte Carlo standard error (MCSE) of the mean estimate:

    julia> using Statistics, StatsBase
+API · PosteriorStats.jl
    GitHub
    API
      Summary statistics
      PosteriorStats.SummaryStats — Type
      struct SummaryStats{D, V<:(AbstractVector)}
      A container for a column table of values computed by summarize.
      This object implements the Tables and TableTraits column table interfaces. It has a custom show method.
      SummaryStats behaves like an OrderedDict of columns, where the columns can be accessed using either Symbols or a 1-based integer index.
      • name::String: The name of the collection of summary statistics, used as the table title in display.
      • data::Any: The summary statistics for each parameter. It must implement the Tables interface.
      • parameter_names::AbstractVector: Names of the parameters
      SummaryStats([name::String,] data[, parameter_names])
+SummaryStats(data[, parameter_names]; name::String="SummaryStats")
      Construct a SummaryStats from tabular data with optional stats name and param_names.
      data must not contain a column :parameter, as this is reserved for the parameter names, which are always in the first column.
      source
      PosteriorStats.default_diagnostics — Function
      default_diagnostics(focus=Statistics.mean; kwargs...)
      Default diagnostics to be computed with summarize.
      The value of focus determines the diagnostics to be returned:
      • Statistics.mean: mcse_mean, mcse_std, ess_tail, ess_bulk, rhat
      • Statistics.median: mcse_median, ess_tail, ess_bulk, rhat
      source
      PosteriorStats.default_stats — Function
      default_stats(focus=Statistics.mean; prob_interval=0.94, kwargs...)
      Default statistics to be computed with summarize.
      The value of focus determines the statistics to be returned:
      • Statistics.mean: mean, std, hdi_3%, hdi_97%
      • Statistics.median: median, mad, eti_3%, eti_97%
      If prob_interval is set to a different value than the default, then different HDI and ETI statistics are computed accordingly. hdi refers to the highest-density interval, while eti refers to the equal-tailed interval (i.e. the credible interval computed from symmetric quantiles).
      See also: hdi
      source
      PosteriorStats.summarize — Function
      summarize(data, stats_funs...; name="SummaryStats", [var_names]) -> SummaryStats
      Compute the summary statistics in stats_funs on each param in data.
      stats_funs is a collection of functions that reduces a matrix with shape (draws, chains) to a scalar or a collection of scalars. Alternatively, an item in stats_funs may be a Pair of the form name => fun specifying the name to be used for the statistic or of the form (name1, ...) => fun when the function returns a collection. When the function returns a collection, the names in this latter format must be provided.
      If no stats functions are provided, then those specified in default_summary_stats are computed.
      var_names specifies the names of the parameters in data. If not provided, the names are inferred from data.
      To support computing summary statistics from a custom object, overload this method specifying the type of data.
      See also SummaryStats, default_summary_stats, default_stats, default_diagnostics.
      Examples
      Compute mean, std and the Monte Carlo standard error (MCSE) of the mean estimate:
      julia> using Statistics, StatsBase
 
 julia> x = randn(1000, 4, 3) .+ reshape(0:10:20, 1, 1, :);
 
@@ -28,7 +29,7 @@
     median    mad  eti_3%  eti_97%  mcse_median  ess_tail  ess_median  rhat
  a   0.004  0.978   -1.83     1.89        0.020      3567        3336  1.00
  b  10.02   0.995    8.17    11.9         0.023      3841        3787  1.00
- c  19.99   0.979   18.1     21.9         0.020      3892        3829  1.00
      source
      General statistics
      PosteriorStats.hdi — Function
      hdi(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper)
      Estimate the unimodal highest density interval (HDI) of samples for the probability prob.
      The HDI is the minimum width Bayesian credible interval (BCI). That is, it is the smallest possible interval containing (100*prob)% of the probability mass.[Hyndman1996]
      samples is an array of shape (draws[, chains[, params...]]). If multiple parameters are present, then lower and upper are arrays with the shape (params...,), computed separately for each marginal.
      This implementation uses the algorithm of [ChenShao1999].
      Note
      Any default value of prob is arbitrary. The default value of prob=0.94 instead of a more common default like prob=0.95 is chosen to reminder the user of this arbitrariness.
      Examples
      Here we calculate the 83% HDI for a normal random variable:
      julia> x = randn(2_000);
+ c  19.99   0.979   18.1     21.9         0.020      3892        3829  1.00
      source
      General statistics
      PosteriorStats.hdi — Function
      hdi(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper)
      Estimate the unimodal highest density interval (HDI) of samples for the probability prob.
      The HDI is the minimum width Bayesian credible interval (BCI). That is, it is the smallest possible interval containing (100*prob)% of the probability mass.[Hyndman1996]
      samples is an array of shape (draws[, chains[, params...]]). If multiple parameters are present, then lower and upper are arrays with the shape (params...,), computed separately for each marginal.
      This implementation uses the algorithm of [ChenShao1999].
      Note
      Any default value of prob is arbitrary. The default value of prob=0.94 instead of a more common default like prob=0.95 is chosen to reminder the user of this arbitrariness.
      Examples
      Here we calculate the 83% HDI for a normal random variable:
      julia> x = randn(2_000);
 
 julia> hdi(x; prob=0.83) |> pairs
 pairs(::NamedTuple) with 2 entries:
@@ -38,7 +39,7 @@
 julia> hdi(x) |> pairs
 pairs(::NamedTuple) with 2 entries:
   :lower => [-1.9674, 3.0326, 8.0326]
-  :upper => [1.90028, 6.90028, 11.9003]
      source
      PosteriorStats.hdi! — Function
      hdi!(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper)
      A version of hdi that sorts samples in-place while computing the HDI.
      source
      LOO and WAIC
      PosteriorStats.AbstractELPDResult — Type
      abstract type AbstractELPDResult
      An abstract type representing the result of an ELPD computation.
      Every subtype stores estimates of both the expected log predictive density (elpd) and the effective number of parameters p, as well as standard errors and pointwise estimates of each, from which other relevant estimates can be computed.
      Subtypes implement the following functions:
      source
      PosteriorStats.PSISLOOResult — Type
      Results of Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO).
      See also: loo, AbstractELPDResult
      • estimates: Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p)
      • pointwise: Pointwise estimates
      • psis_result: Pareto-smoothed importance sampling (PSIS) results
      source
      PosteriorStats.WAICResult — Type
      Results of computing the widely applicable information criterion (WAIC).
      See also: waic, AbstractELPDResult
      • estimates: Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p)
      • pointwise: Pointwise estimates
      source
      PosteriorStats.elpd_estimates — Function
      elpd_estimates(result::AbstractELPDResult; pointwise=false) -> (; elpd, elpd_mcse, lpd)
      Return the (E)LPD estimates from the result.
      source
      PosteriorStats.information_criterion — Function
      information_criterion(elpd, scale::Symbol)
      Compute the information criterion for the given scale from the elpd estimate.
      scale must be one of (:deviance, :log, :negative_log).
      See also: loo, waic
      source
      information_criterion(result::AbstractELPDResult, scale::Symbol; pointwise=false)
      Compute information criterion for the given scale from the existing ELPD result.
      scale must be one of (:deviance, :log, :negative_log).
      If pointwise=true, then pointwise estimates are returned.
      source
      PosteriorStats.loo — Function
      loo(log_likelihood; reff=nothing, kwargs...) -> PSISLOOResult{<:NamedTuple,<:NamedTuple}
      Compute the Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO). [Vehtari2017][LOOFAQ]
      log_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]).
      Keywords
      • reff::Union{Real,AbstractArray{<:Real}}: The relative effective sample size(s) of the likelihood values. If an array, it must have the same data dimensions as the corresponding log-likelihood variable. If not provided, then this is estimated using MCMCDiagnosticTools.ess.
      • kwargs: Remaining keywords are forwarded to [PSIS.psis].
      See also: PSISLOOResult, waic
      Examples
      Manually compute $R_\mathrm{eff}$ and calculate PSIS-LOO of a model:
      julia> using ArviZExampleData, MCMCDiagnosticTools
+  :upper => [1.90028, 6.90028, 11.9003]
      source
      PosteriorStats.hdi! — Function
      hdi!(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper)
      A version of hdi that sorts samples in-place while computing the HDI.
      source
      LOO and WAIC
      PosteriorStats.AbstractELPDResult — Type
      abstract type AbstractELPDResult
      An abstract type representing the result of an ELPD computation.
      Every subtype stores estimates of both the expected log predictive density (elpd) and the effective number of parameters p, as well as standard errors and pointwise estimates of each, from which other relevant estimates can be computed.
      Subtypes implement the following functions:
      source
      PosteriorStats.PSISLOOResult — Type
      Results of Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO).
      See also: loo, AbstractELPDResult
      • estimates: Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p)
      • pointwise: Pointwise estimates
      • psis_result: Pareto-smoothed importance sampling (PSIS) results
      source
      PosteriorStats.WAICResult — Type
      Results of computing the widely applicable information criterion (WAIC).
      See also: waic, AbstractELPDResult
      • estimates: Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p)
      • pointwise: Pointwise estimates
      source
      PosteriorStats.elpd_estimates — Function
      elpd_estimates(result::AbstractELPDResult; pointwise=false) -> (; elpd, elpd_mcse, lpd)
      Return the (E)LPD estimates from the result.
      source
      PosteriorStats.information_criterion — Function
      information_criterion(elpd, scale::Symbol)
      Compute the information criterion for the given scale from the elpd estimate.
      scale must be one of (:deviance, :log, :negative_log).
      See also: loo, waic
      source
      information_criterion(result::AbstractELPDResult, scale::Symbol; pointwise=false)
      Compute information criterion for the given scale from the existing ELPD result.
      scale must be one of (:deviance, :log, :negative_log).
      If pointwise=true, then pointwise estimates are returned.
      source
      PosteriorStats.loo — Function
      loo(log_likelihood; reff=nothing, kwargs...) -> PSISLOOResult{<:NamedTuple,<:NamedTuple}
      Compute the Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO). [Vehtari2017][LOOFAQ]
      log_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]).
      Keywords
      • reff::Union{Real,AbstractArray{<:Real}}: The relative effective sample size(s) of the likelihood values. If an array, it must have the same data dimensions as the corresponding log-likelihood variable. If not provided, then this is estimated using MCMCDiagnosticTools.ess.
      • kwargs: Remaining keywords are forwarded to [PSIS.psis].
      See also: PSISLOOResult, waic
      Examples
      Manually compute $R_\mathrm{eff}$ and calculate PSIS-LOO of a model:
      julia> using ArviZExampleData, MCMCDiagnosticTools
 
 julia> idata = load_example_data("centered_eight");
 
@@ -55,7 +56,7 @@
 Pareto shape (k) diagnostic values:
                     Count      Min. ESS
  (-Inf, 0.5]  good  7 (87.5%)  151
-  (0.5, 0.7]  okay  1 (12.5%)  446
      source
      PosteriorStats.waic — Function
      waic(log_likelihood::AbstractArray) -> WAICResult{<:NamedTuple,<:NamedTuple}
      Compute the widely applicable information criterion (WAIC).[Watanabe2010][Vehtari2017][LOOFAQ]
      log_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]).
      See also: WAICResult, loo
      Examples
      Calculate WAIC of a model:
      julia> using ArviZExampleData
+  (0.5, 0.7]  okay  1 (12.5%)  446
      source
      PosteriorStats.waic — Function
      waic(log_likelihood::AbstractArray) -> WAICResult{<:NamedTuple,<:NamedTuple}
      Compute the widely applicable information criterion (WAIC).[Watanabe2010][Vehtari2017][LOOFAQ]
      log_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]).
      See also: WAICResult, loo
      Examples
      Calculate WAIC of a model:
      julia> using ArviZExampleData
 
 julia> idata = load_example_data("centered_eight");
 
@@ -64,7 +65,7 @@
 julia> waic(log_like)
 WAICResult with estimates
  elpd  elpd_mcse    p  p_mcse
-  -31        1.4  0.9    0.33
      source
      Model comparison
      PosteriorStats.ModelComparisonResult — Type
      ModelComparisonResult
      Result of model comparison using ELPD.
      This struct implements the Tables and TableTraits interfaces.
      Each field returns a collection of the corresponding entry for each model:
      • name: Names of the models, if provided.
      • rank: Ranks of the models (ordered by decreasing ELPD)
      • elpd_diff: ELPD of a model subtracted from the largest ELPD of any model
      • elpd_diff_mcse: Monte Carlo standard error of the ELPD difference
      • weight: Model weights computed with weights_method
      • elpd_result: AbstactELPDResults for each model, which can be used to access useful stats like ELPD estimates, pointwise estimates, and Pareto shape values for PSIS-LOO
      • weights_method: Method used to compute model weights with model_weights
      source
      PosteriorStats.compare — Function
      compare(models; kwargs...) -> ModelComparisonResult
      Compare models based on their expected log pointwise predictive density (ELPD).
      The ELPD is estimated either by Pareto smoothed importance sampling leave-one-out cross-validation (LOO) or using the widely applicable information criterion (WAIC). We recommend loo. Read more theory here - in a paper by some of the leading authorities on model comparison dx.doi.org/10.1111/1467-9868.00353
      Arguments
      • models: a Tuple, NamedTuple, or AbstractVector whose values are either AbstractELPDResult entries or any argument to elpd_method.
      Keywords
      • weights_method::AbstractModelWeightsMethod=Stacking(): the method to be used to weight the models. See model_weights for details
      • elpd_method=loo: a method that computes an AbstractELPDResult from an argument in models.
      • sort::Bool=true: Whether to sort models by decreasing ELPD.
      Returns
      • ModelComparisonResult: A container for the model comparison results. The fields contain a similar collection to models.
      Examples
      Compare the centered and non centered models of the eight school problem using the defaults: loo and Stacking weights. A custom myloo method formates the inputs as expected by loo.
      julia> using ArviZExampleData
+  -31        1.4  0.9    0.33
      source
      Model comparison
      PosteriorStats.ModelComparisonResult — Type
      ModelComparisonResult
      Result of model comparison using ELPD.
      This struct implements the Tables and TableTraits interfaces.
      Each field returns a collection of the corresponding entry for each model:
      • name: Names of the models, if provided.
      • rank: Ranks of the models (ordered by decreasing ELPD)
      • elpd_diff: ELPD of a model subtracted from the largest ELPD of any model
      • elpd_diff_mcse: Monte Carlo standard error of the ELPD difference
      • weight: Model weights computed with weights_method
      • elpd_result: AbstactELPDResults for each model, which can be used to access useful stats like ELPD estimates, pointwise estimates, and Pareto shape values for PSIS-LOO
      • weights_method: Method used to compute model weights with model_weights
      source
      PosteriorStats.compare — Function
      compare(models; kwargs...) -> ModelComparisonResult
      Compare models based on their expected log pointwise predictive density (ELPD).
      The ELPD is estimated either by Pareto smoothed importance sampling leave-one-out cross-validation (LOO) or using the widely applicable information criterion (WAIC). We recommend loo. Read more theory here - in a paper by some of the leading authorities on model comparison dx.doi.org/10.1111/1467-9868.00353
      Arguments
      • models: a Tuple, NamedTuple, or AbstractVector whose values are either AbstractELPDResult entries or any argument to elpd_method.
      Keywords
      • weights_method::AbstractModelWeightsMethod=Stacking(): the method to be used to weight the models. See model_weights for details
      • elpd_method=loo: a method that computes an AbstractELPDResult from an argument in models.
      • sort::Bool=true: Whether to sort models by decreasing ELPD.
      Returns
      • ModelComparisonResult: A container for the model comparison results. The fields contain a similar collection to models.
      Examples
      Compare the centered and non centered models of the eight school problem using the defaults: loo and Stacking weights. A custom myloo method formates the inputs as expected by loo.
      julia> using ArviZExampleData
 
 julia> models = (
            centered=load_example_data("centered_eight"),
@@ -94,7 +95,7 @@
                rank  elpd  elpd_mcse  elpd_diff  elpd_diff_mcse  weight    p   ⋯
  non_centered     1   -31        1.4       0              0.0      0.52  0.9   ⋯
  centered         2   -31        1.4       0.06           0.067    0.48  0.9   ⋯
-                                                                1 column omitted
      source
      PosteriorStats.model_weights — Function
      model_weights(elpd_results; method=Stacking())
 model_weights(method::AbstractModelWeightsMethod, elpd_results)
      Compute weights for each model in elpd_results using method.
      elpd_results is a Tuple, NamedTuple, or AbstractVector with AbstractELPDResult entries. The weights are returned in the same type of collection.
      Stacking is the recommended approach, as it performs well even when the true data generating process is not included among the candidate models. See [YaoVehtari2018] for details.
      See also: AbstractModelWeightsMethod, compare
      Examples
      Compute Stacking weights for two models:
      julia> using ArviZExampleData
 
 julia> models = (
@@ -115,10 +116,10 @@
   :non_centered => 1.0
      Now we compute BootstrappedPseudoBMA weights for the same models:
      julia> model_weights(elpd_results; method=BootstrappedPseudoBMA()) |> pairs
 pairs(::NamedTuple) with 2 entries:
   :centered     => 0.483723
-  :non_centered => 0.516277
      source
      The following model weighting methods are available
      PosteriorStats.BootstrappedPseudoBMA — Type
      struct BootstrappedPseudoBMA{R<:Random.AbstractRNG, T<:Real} <: AbstractModelWeightsMethod
      Model weighting method using pseudo Bayesian Model Averaging using Akaike-type weighting with the Bayesian bootstrap (pseudo-BMA+)[YaoVehtari2018].
      The Bayesian bootstrap stabilizes the model weights.
      BootstrappedPseudoBMA(; rng=Random.default_rng(), samples=1_000, alpha=1)
-BootstrappedPseudoBMA(rng, samples, alpha)
      Construct the method.
      • rng::Random.AbstractRNG: The random number generator to use for the Bayesian bootstrap
      • samples::Int64: The number of samples to draw for bootstrapping
      • alpha::Real: The shape parameter in the Dirichlet distribution used for the Bayesian bootstrap. The default (1) corresponds to a uniform distribution on the simplex.
      See also: Stacking
      source
      PosteriorStats.PseudoBMA — Type
      struct PseudoBMA <: AbstractModelWeightsMethod
      Model weighting method using pseudo Bayesian Model Averaging (pseudo-BMA) and Akaike-type weighting.
      PseudoBMA(; regularize=false)
-PseudoBMA(regularize)
      Construct the method with optional regularization of the weights using the standard error of the ELPD estimate.
      Note
      This approach is not recommended, as it produces unstable weight estimates. It is recommended to instead use BootstrappedPseudoBMA to stabilize the weights or Stacking. For details, see [YaoVehtari2018].
      See also: Stacking
      source
      PosteriorStats.Stacking — Type
      struct Stacking{O<:Optim.AbstractOptimizer} <: AbstractModelWeightsMethod
      Model weighting using stacking of predictive distributions[YaoVehtari2018].
      Stacking(; optimizer=Optim.LBFGS(), options=Optim.Options()
-Stacking(optimizer[, options])
      Construct the method, optionally customizing the optimization.
      • optimizer::Optim.AbstractOptimizer: The optimizer to use for the optimization of the weights. The optimizer must support projected gradient optimization via a manifold field.
      • options::Optim.Options: The Optim options to use for the optimization of the weights.
      See also: BootstrappedPseudoBMA
      source
      Predictive checks
      PosteriorStats.loo_pit — Function
      loo_pit(y, y_pred, log_weights; kwargs...) -> Union{Real,AbstractArray}
      Compute leave-one-out probability integral transform (LOO-PIT) checks.
      Arguments
      • y: array of observations with shape (params...,)
      • y_pred: array of posterior predictive samples with shape (draws, chains, params...).
      • log_weights: array of normalized log LOO importance weights with shape (draws, chains, params...).
      Keywords
      • is_discrete: If not provided, then it is set to true iff elements of y and y_pred are all integer-valued. If true, then data are smoothed using smooth_data to make them non-discrete before estimating LOO-PIT values.
      • kwargs: Remaining keywords are forwarded to smooth_data if data is discrete.
      Returns
      • pitvals: LOO-PIT values with same size as y. If y is a scalar, then pitvals is a scalar.
      LOO-PIT is a marginal posterior predictive check. If $y_{-i}$ is the array $y$ of observations with the $i$th observation left out, and $y_i^*$ is a posterior prediction of the $i$th observation, then the LOO-PIT value for the $i$th observation is defined as
      \[P(y_i^* \le y_i \mid y_{-i}) = \int_{-\infty}^{y_i} p(y_i^* \mid y_{-i}) \mathrm{d} y_i^*\]
      The LOO posterior predictions and the corresponding observations should have similar distributions, so if conditional predictive distributions are well-calibrated, then all LOO-PIT values should be approximately uniformly distributed on $[0, 1]$.[Gabry2019]
      Examples
      Calculate LOO-PIT values using as test quantity the observed values themselves.
      julia> using ArviZExampleData
+  :non_centered => 0.516277
      source
      The following model weighting methods are available
      PosteriorStats.BootstrappedPseudoBMA — Type
      struct BootstrappedPseudoBMA{R<:Random.AbstractRNG, T<:Real} <: AbstractModelWeightsMethod
      Model weighting method using pseudo Bayesian Model Averaging using Akaike-type weighting with the Bayesian bootstrap (pseudo-BMA+)[YaoVehtari2018].
      The Bayesian bootstrap stabilizes the model weights.
      BootstrappedPseudoBMA(; rng=Random.default_rng(), samples=1_000, alpha=1)
+BootstrappedPseudoBMA(rng, samples, alpha)
      Construct the method.
      • rng::Random.AbstractRNG: The random number generator to use for the Bayesian bootstrap
      • samples::Int64: The number of samples to draw for bootstrapping
      • alpha::Real: The shape parameter in the Dirichlet distribution used for the Bayesian bootstrap. The default (1) corresponds to a uniform distribution on the simplex.
      See also: Stacking
      source
      PosteriorStats.PseudoBMA — Type
      struct PseudoBMA <: AbstractModelWeightsMethod
      Model weighting method using pseudo Bayesian Model Averaging (pseudo-BMA) and Akaike-type weighting.
      PseudoBMA(; regularize=false)
+PseudoBMA(regularize)
      Construct the method with optional regularization of the weights using the standard error of the ELPD estimate.
      Note
      This approach is not recommended, as it produces unstable weight estimates. It is recommended to instead use BootstrappedPseudoBMA to stabilize the weights or Stacking. For details, see [YaoVehtari2018].
      See also: Stacking
      source
      PosteriorStats.Stacking — Type
      struct Stacking{O<:Optim.AbstractOptimizer} <: AbstractModelWeightsMethod
      Model weighting using stacking of predictive distributions[YaoVehtari2018].
      Stacking(; optimizer=Optim.LBFGS(), options=Optim.Options()
+Stacking(optimizer[, options])
      Construct the method, optionally customizing the optimization.
      • optimizer::Optim.AbstractOptimizer: The optimizer to use for the optimization of the weights. The optimizer must support projected gradient optimization via a manifold field.
      • options::Optim.Options: The Optim options to use for the optimization of the weights.
      See also: BootstrappedPseudoBMA
      source
      Predictive checks
      PosteriorStats.loo_pit — Function
      loo_pit(y, y_pred, log_weights; kwargs...) -> Union{Real,AbstractArray}
      Compute leave-one-out probability integral transform (LOO-PIT) checks.
      Arguments
      • y: array of observations with shape (params...,)
      • y_pred: array of posterior predictive samples with shape (draws, chains, params...).
      • log_weights: array of normalized log LOO importance weights with shape (draws, chains, params...).
      Keywords
      • is_discrete: If not provided, then it is set to true iff elements of y and y_pred are all integer-valued. If true, then data are smoothed using smooth_data to make them non-discrete before estimating LOO-PIT values.
      • kwargs: Remaining keywords are forwarded to smooth_data if data is discrete.
      Returns
      • pitvals: LOO-PIT values with same size as y. If y is a scalar, then pitvals is a scalar.
      LOO-PIT is a marginal posterior predictive check. If $y_{-i}$ is the array $y$ of observations with the $i$th observation left out, and $y_i^*$ is a posterior prediction of the $i$th observation, then the LOO-PIT value for the $i$th observation is defined as
      \[P(y_i^* \le y_i \mid y_{-i}) = \int_{-\infty}^{y_i} p(y_i^* \mid y_{-i}) \mathrm{d} y_i^*\]
      The LOO posterior predictions and the corresponding observations should have similar distributions, so if conditional predictive distributions are well-calibrated, then all LOO-PIT values should be approximately uniformly distributed on $[0, 1]$.[Gabry2019]
      Examples
      Calculate LOO-PIT values using as test quantity the observed values themselves.
      julia> using ArviZExampleData
 
 julia> idata = load_example_data("centered_eight");
 
@@ -158,7 +159,7 @@
  "Hotchkiss"         0.435094
  "Lawrenceville"     0.220627
  "St. Paul's"        0.775086
- "Mt. Hermon"        0.296706
      source
      PosteriorStats.r2_score — Function
      r2_score(y_true::AbstractVector, y_pred::AbstractArray) -> (; r2, r2_std)
      $R²$ for linear Bayesian regression models.[GelmanGoodrich2019]
      Arguments
      • y_true: Observed data of length noutputs
      • y_pred: Predicted data with size (ndraws[, nchains], noutputs)
      Examples
      julia> using ArviZExampleData
+ "Mt. Hermon"        0.296706
      source
      PosteriorStats.r2_score — Function
      r2_score(y_true::AbstractVector, y_pred::AbstractArray) -> (; r2, r2_std)
      $R²$ for linear Bayesian regression models.[GelmanGoodrich2019]
      Arguments
      • y_true: Observed data of length noutputs
      • y_pred: Predicted data with size (ndraws[, nchains], noutputs)
      Examples
      julia> using ArviZExampleData
 
 julia> idata = load_example_data("regression1d");
 
@@ -169,4 +170,4 @@
 julia> r2_score(y_true, y_pred) |> pairs
 pairs(::NamedTuple) with 2 entries:
   :r2     => 0.683197
-  :r2_std => 0.0368838
      source
      Utilities
      PosteriorStats.smooth_data — Function
      smooth_data(y; dims=:, interp_method=CubicSpline, offset_frac=0.01)
      Smooth y along dims using interp_method.
      interp_method is a 2-argument callabale that takes the arguments y and x and returns a DataInterpolations.jl interpolation method, defaulting to a cubic spline interpolator.
      offset_frac is the fraction of the length of y to use as an offset when interpolating.
      source
      • Hyndman1996Rob J. Hyndman (1996) Computing and Graphing Highest Density Regions,             Amer. Stat., 50(2): 120-6.             DOI: 10.1080/00031305.1996.10474359jstor.
      • ChenShao1999Ming-Hui Chen & Qi-Man Shao (1999)              Monte Carlo Estimation of Bayesian Credible and HPD Intervals,              J Comput. Graph. Stat., 8:1, 69-92.              DOI: 10.1080/10618600.1999.10474802jstor.
      • Vehtari2017Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544
      • LOOFAQAki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html
      • Watanabe2010Watanabe, S. Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory. 11(116):3571−3594, 2010. https://jmlr.csail.mit.edu/papers/v11/watanabe10a.html
      • Vehtari2017Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544
      • LOOFAQAki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html
      • YaoVehtari2018Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman.                Using Stacking to Average Bayesian Predictive Distributions.                2018. Bayesian Analysis. 13, 3, 917–1007.                doi: 10.1214/17-BA1091                arXiv: 1704.02030
      • YaoVehtari2018Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman.                Using Stacking to Average Bayesian Predictive Distributions.                2018. Bayesian Analysis. 13, 3, 917–1007.                doi: 10.1214/17-BA1091                arXiv: 1704.02030
      • YaoVehtari2018Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman.                Using Stacking to Average Bayesian Predictive Distributions.                2018. Bayesian Analysis. 13, 3, 917–1007.                doi: 10.1214/17-BA1091                arXiv: 1704.02030
      • YaoVehtari2018Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman.                Using Stacking to Average Bayesian Predictive Distributions.                2018. Bayesian Analysis. 13, 3, 917–1007.                doi: 10.1214/17-BA1091                arXiv: 1704.02030
      • Gabry2019Gabry, J., Simpson, D., Vehtari, A., Betancourt, M. & Gelman, A. Visualization in Bayesian Workflow. J. R. Stat. Soc. Ser. A Stat. Soc. 182, 389–402 (2019). doi: 10.1111/rssa.12378 arXiv: 1709.01449
      • GelmanGoodrich2019Andrew Gelman, Ben Goodrich, Jonah Gabry & Aki Vehtari (2019) R-squared for Bayesian Regression Models, The American Statistician, 73:3, 307-9, DOI: 10.1080/00031305.2018.1549100.
      
\ No newline at end of file
+  :r2_std => 0.0368838
      source

      Utilities

      PosteriorStats.smooth_data — Function
      smooth_data(y; dims=:, interp_method=CubicSpline, offset_frac=0.01)

      Smooth y along dims using interp_method.

      interp_method is a 2-argument callabale that takes the arguments y and x and returns a DataInterpolations.jl interpolation method, defaulting to a cubic spline interpolator.

      offset_frac is the fraction of the length of y to use as an offset when interpolating.

      source
      • Hyndman1996Rob J. Hyndman (1996) Computing and Graphing Highest Density Regions, Amer. Stat., 50(2): 120-6. DOI: 10.1080/00031305.1996.10474359jstor.
      • ChenShao1999Ming-Hui Chen & Qi-Man Shao (1999) Monte Carlo Estimation of Bayesian Credible and HPD Intervals, J Comput. Graph. Stat., 8:1, 69-92. DOI: 10.1080/10618600.1999.10474802jstor.
      • Vehtari2017Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544
      • LOOFAQAki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html
      • Watanabe2010Watanabe, S. Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory. 11(116):3571−3594, 2010. https://jmlr.csail.mit.edu/papers/v11/watanabe10a.html
      • Vehtari2017Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544
      • LOOFAQAki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html
      • YaoVehtari2018Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030
      • YaoVehtari2018Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030
      • YaoVehtari2018Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030
      • YaoVehtari2018Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030
      • Gabry2019Gabry, J., Simpson, D., Vehtari, A., Betancourt, M. & Gelman, A. Visualization in Bayesian Workflow. J. R. Stat. Soc. Ser. A Stat. Soc. 182, 389–402 (2019). doi: 10.1111/rssa.12378 arXiv: 1709.01449
      • GelmanGoodrich2019Andrew Gelman, Ben Goodrich, Jonah Gabry & Aki Vehtari (2019) R-squared for Bayesian Regression Models, The American Statistician, 73:3, 307-9, DOI: 10.1080/00031305.2018.1549100.
      \ No newline at end of file diff --git a/PosteriorStats/dev/index.html b/PosteriorStats/dev/index.html index 6a6ec9ffc..3b65c1ae0 100644 --- a/PosteriorStats/dev/index.html +++ b/PosteriorStats/dev/index.html @@ -1 +1 @@ -Home · PosteriorStats.jl
      GitHub

      PosteriorStats

      PosteriorStats implements widely-used and well-characterized statistical analyses for the Bayesian workflow. These functions generally estimate properties of posterior and/or posterior predictive distributions. The default implementations defined here operate on Monte Carlo samples.

      See the API for details.

      Extending this package

      The methods defined here are intended to be extended by two types of packages.

      • packages that implement data types for storing Monte Carlo samples
      • packages that implement other representations for posterior distributions than Monte Carlo draws
      \ No newline at end of file +Home · PosteriorStats.jl
      GitHub

      PosteriorStats

      PosteriorStats implements widely-used and well-characterized statistical analyses for the Bayesian workflow. These functions generally estimate properties of posterior and/or posterior predictive distributions. The default implementations defined here operate on Monte Carlo samples.

      See the API for details.

      Extending this package

      The methods defined here are intended to be extended by two types of packages.

      • packages that implement data types for storing Monte Carlo samples
      • packages that implement other representations for posterior distributions than Monte Carlo draws
      \ No newline at end of file diff --git a/PosteriorStats/dev/search_index.js b/PosteriorStats/dev/search_index.js index 4dc16e1fa..7a0063106 100644 --- a/PosteriorStats/dev/search_index.js +++ b/PosteriorStats/dev/search_index.js @@ -1,3 +1,3 @@ var documenterSearchIndex = {"docs": -[{"location":"api/#API","page":"API","title":"API","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Pages = [\"stats.md\"]","category":"page"},{"location":"api/#Summary-statistics","page":"API","title":"Summary statistics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"SummaryStats\ndefault_diagnostics\ndefault_stats\ndefault_summary_stats\nsummarize","category":"page"},{"location":"api/#PosteriorStats.SummaryStats","page":"API","title":"PosteriorStats.SummaryStats","text":"A container for a column table of values computed by summarize.\n\nThis object implements the Tables and TableTraits interfaces and has a custom show method.\n\nname: The name of the collection of summary statistics, used as the table title in display.\ndata: The summary statistics for each parameter, with an optional first column parameter containing the parameter names.\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.default_diagnostics","page":"API","title":"PosteriorStats.default_diagnostics","text":"default_diagnostics(focus=Statistics.mean; kwargs...)\n\nDefault diagnostics to be computed with summarize.\n\nThe value of focus determines the diagnostics to be returned:\n\nStatistics.mean: mcse_mean, mcse_std, ess_tail, ess_bulk, rhat\nStatistics.median: mcse_median, ess_tail, ess_bulk, rhat\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.default_stats","page":"API","title":"PosteriorStats.default_stats","text":"default_stats(focus=Statistics.mean; prob_interval=0.94, kwargs...)\n\nDefault statistics to be computed with summarize.\n\nThe value of focus determines the statistics to be returned:\n\nStatistics.mean: mean, std, hdi_3%, hdi_97%\nStatistics.median: median, mad, eti_3%, eti_97%\n\nIf prob_interval is set to a different value than the default, then different HDI and ETI statistics are computed accordingly. hdi refers to the highest-density interval, while eti refers to the equal-tailed interval (i.e. the credible interval computed from symmetric quantiles).\n\nSee also: hdi\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.default_summary_stats","page":"API","title":"PosteriorStats.default_summary_stats","text":"default_summary_stats(focus=Statistics.mean; kwargs...)\n\nCombinatiton of default_stats and default_diagnostics to be used with summarize.\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.summarize","page":"API","title":"PosteriorStats.summarize","text":"summarize(data, stats_funs...; name=\"SummaryStats\", [var_names]) -> SummaryStats\n\nCompute the summary statistics in stats_funs on each param in data.\n\nstats_funs is a collection of functions that reduces a matrix with shape (draws, chains) to a scalar or a collection of scalars. Alternatively, an item in stats_funs may be a Pair of the form name => fun specifying the name to be used for the statistic or of the form (name1, ...) => fun when the function returns a collection. When the function returns a collection, the names in this latter format must be provided.\n\nIf no stats functions are provided, then those specified in default_summary_stats are computed.\n\nvar_names specifies the names of the parameters in data. If not provided, the names are inferred from data.\n\nTo support computing summary statistics from a custom object, overload this method specifying the type of data.\n\nSee also SummaryStats, default_summary_stats, default_stats, default_diagnostics.\n\nExamples\n\nCompute mean, std and the Monte Carlo standard error (MCSE) of the mean estimate:\n\njulia> using Statistics, StatsBase\n\njulia> x = randn(1000, 4, 3) .+ reshape(0:10:20, 1, 1, :);\n\njulia> summarize(x, mean, std, :mcse_mean => sem; name=\"Mean/Std\")\nMean/Std\n mean std mcse_mean\n 1 0.0003 0.990 0.016\n 2 10.02 0.988 0.016\n 3 19.98 0.988 0.016\n\nAvoid recomputing the mean by using mean_and_std, and provide parameter names:\n\njulia> summarize(x, (:mean, :std) => mean_and_std, mad; var_names=[:a, :b, :c])\nSummaryStats\n mean std mad\n a 0.000305 0.990 0.978\n b 10.0 0.988 0.995\n c 20.0 0.988 0.979\n\nNote that when an estimator and its MCSE are both computed, the MCSE is used to determine the number of significant digits that will be displayed.\n\njulia> summarize(x; var_names=[:a, :b, :c])\nSummaryStats\n mean std hdi_3% hdi_97% mcse_mean mcse_std ess_tail ess_bulk r ⋯\n a 0.0003 0.99 -1.92 1.78 0.016 0.012 3567 3663 1 ⋯\n b 10.02 0.99 8.17 11.9 0.016 0.011 3841 3906 1 ⋯\n c 19.98 0.99 18.1 21.9 0.016 0.012 3892 3749 1 ⋯\n 1 column omitted\n\nCompute just the statistics with an 89% HDI on all parameters, and provide the parameter names:\n\njulia> summarize(x, default_stats(; prob_interval=0.89)...; var_names=[:a, :b, :c])\nSummaryStats\n mean std hdi_5.5% hdi_94.5%\n a 0.000305 0.990 -1.63 1.52\n b 10.0 0.988 8.53 11.6\n c 20.0 0.988 18.5 21.6\n\nCompute the summary stats focusing on Statistics.median:\n\njulia> summarize(x, default_summary_stats(median)...; var_names=[:a, :b, :c])\nSummaryStats\n median mad eti_3% eti_97% mcse_median ess_tail ess_median rhat\n a 0.004 0.978 -1.83 1.89 0.020 3567 3336 1.00\n b 10.02 0.995 8.17 11.9 0.023 3841 3787 1.00\n c 19.99 0.979 18.1 21.9 0.020 3892 3829 1.00\n\n\n\n\n\n","category":"function"},{"location":"api/#General-statistics","page":"API","title":"General statistics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"hdi\nhdi!","category":"page"},{"location":"api/#PosteriorStats.hdi","page":"API","title":"PosteriorStats.hdi","text":"hdi(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper)\n\nEstimate the unimodal highest density interval (HDI) of samples for the probability prob.\n\nThe HDI is the minimum width Bayesian credible interval (BCI). That is, it is the smallest possible interval containing (100*prob)% of the probability mass.[Hyndman1996]\n\nsamples is an array of shape (draws[, chains[, params...]]). If multiple parameters are present, then lower and upper are arrays with the shape (params...,), computed separately for each marginal.\n\nThis implementation uses the algorithm of [ChenShao1999].\n\nnote: Note\nAny default value of prob is arbitrary. The default value of prob=0.94 instead of a more common default like prob=0.95 is chosen to reminder the user of this arbitrariness.\n\n[Hyndman1996]: Rob J. Hyndman (1996) Computing and Graphing Highest Density Regions, Amer. Stat., 50(2): 120-6. DOI: 10.1080/00031305.1996.10474359 jstor.\n\n[ChenShao1999]: Ming-Hui Chen & Qi-Man Shao (1999) Monte Carlo Estimation of Bayesian Credible and HPD Intervals, J Comput. Graph. Stat., 8:1, 69-92. DOI: 10.1080/10618600.1999.10474802 jstor.\n\nExamples\n\nHere we calculate the 83% HDI for a normal random variable:\n\njulia> x = randn(2_000);\n\njulia> hdi(x; prob=0.83) |> pairs\npairs(::NamedTuple) with 2 entries:\n :lower => -1.38266\n :upper => 1.25982\n\nWe can also calculate the HDI for a 3-dimensional array of samples:\n\njulia> x = randn(1_000, 1, 1) .+ reshape(0:5:10, 1, 1, :);\n\njulia> hdi(x) |> pairs\npairs(::NamedTuple) with 2 entries:\n :lower => [-1.9674, 3.0326, 8.0326]\n :upper => [1.90028, 6.90028, 11.9003]\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.hdi!","page":"API","title":"PosteriorStats.hdi!","text":"hdi!(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper)\n\nA version of hdi that sorts samples in-place while computing the HDI.\n\n\n\n\n\n","category":"function"},{"location":"api/#LOO-and-WAIC","page":"API","title":"LOO and WAIC","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"AbstractELPDResult\nPSISLOOResult\nWAICResult\nelpd_estimates\ninformation_criterion\nloo\nwaic","category":"page"},{"location":"api/#PosteriorStats.AbstractELPDResult","page":"API","title":"PosteriorStats.AbstractELPDResult","text":"abstract type AbstractELPDResult\n\nAn abstract type representing the result of an ELPD computation.\n\nEvery subtype stores estimates of both the expected log predictive density (elpd) and the effective number of parameters p, as well as standard errors and pointwise estimates of each, from which other relevant estimates can be computed.\n\nSubtypes implement the following functions:\n\nelpd_estimates\ninformation_criterion\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.PSISLOOResult","page":"API","title":"PosteriorStats.PSISLOOResult","text":"Results of Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO).\n\nSee also: loo, AbstractELPDResult\n\nestimates: Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p)\npointwise: Pointwise estimates\npsis_result: Pareto-smoothed importance sampling (PSIS) results\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.WAICResult","page":"API","title":"PosteriorStats.WAICResult","text":"Results of computing the widely applicable information criterion (WAIC).\n\nSee also: waic, AbstractELPDResult\n\nestimates: Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p)\npointwise: Pointwise estimates\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.elpd_estimates","page":"API","title":"PosteriorStats.elpd_estimates","text":"elpd_estimates(result::AbstractELPDResult; pointwise=false) -> (; elpd, elpd_mcse, lpd)\n\nReturn the (E)LPD estimates from the result.\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.information_criterion","page":"API","title":"PosteriorStats.information_criterion","text":"information_criterion(elpd, scale::Symbol)\n\nCompute the information criterion for the given scale from the elpd estimate.\n\nscale must be one of (:deviance, :log, :negative_log).\n\nSee also: loo, waic\n\n\n\n\n\ninformation_criterion(result::AbstractELPDResult, scale::Symbol; pointwise=false)\n\nCompute information criterion for the given scale from the existing ELPD result.\n\nscale must be one of (:deviance, :log, :negative_log).\n\nIf pointwise=true, then pointwise estimates are returned.\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.loo","page":"API","title":"PosteriorStats.loo","text":"loo(log_likelihood; reff=nothing, kwargs...) -> PSISLOOResult{<:NamedTuple,<:NamedTuple}\n\nCompute the Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO). [Vehtari2017][LOOFAQ]\n\nlog_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]).\n\nKeywords\n\nreff::Union{Real,AbstractArray{<:Real}}: The relative effective sample size(s) of the likelihood values. If an array, it must have the same data dimensions as the corresponding log-likelihood variable. If not provided, then this is estimated using MCMCDiagnosticTools.ess.\nkwargs: Remaining keywords are forwarded to [PSIS.psis].\n\nSee also: PSISLOOResult, waic\n\n[Vehtari2017]: Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544\n\n[LOOFAQ]: Aki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html\n\nExamples\n\nManually compute R_mathrmeff and calculate PSIS-LOO of a model:\n\njulia> using ArviZExampleData, MCMCDiagnosticTools\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> reff = ess(log_like; kind=:basic, split_chains=1, relative=true);\n\njulia> loo(log_like; reff)\nPSISLOOResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.34\n\nand PSISResult with 500 draws, 4 chains, and 8 parameters\nPareto shape (k) diagnostic values:\n Count Min. ESS\n (-Inf, 0.5] good 7 (87.5%) 151\n (0.5, 0.7] okay 1 (12.5%) 446\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.waic","page":"API","title":"PosteriorStats.waic","text":"waic(log_likelihood::AbstractArray) -> WAICResult{<:NamedTuple,<:NamedTuple}\n\nCompute the widely applicable information criterion (WAIC).[Watanabe2010][Vehtari2017][LOOFAQ]\n\nlog_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]).\n\nSee also: WAICResult, loo\n\n[Watanabe2010]: Watanabe, S. Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory. 11(116):3571−3594, 2010. https://jmlr.csail.mit.edu/papers/v11/watanabe10a.html\n\n[Vehtari2017]: Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544\n\n[LOOFAQ]: Aki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html\n\nExamples\n\nCalculate WAIC of a model:\n\njulia> using ArviZExampleData\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> waic(log_like)\nWAICResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.33\n\n\n\n\n\n","category":"function"},{"location":"api/#Model-comparison","page":"API","title":"Model comparison","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"ModelComparisonResult\ncompare\nmodel_weights","category":"page"},{"location":"api/#PosteriorStats.ModelComparisonResult","page":"API","title":"PosteriorStats.ModelComparisonResult","text":"ModelComparisonResult\n\nResult of model comparison using ELPD.\n\nThis struct implements the Tables and TableTraits interfaces.\n\nEach field returns a collection of the corresponding entry for each model:\n\nname: Names of the models, if provided.\nrank: Ranks of the models (ordered by decreasing ELPD)\nelpd_diff: ELPD of a model subtracted from the largest ELPD of any model\nelpd_diff_mcse: Monte Carlo standard error of the ELPD difference\nweight: Model weights computed with weights_method\nelpd_result: AbstactELPDResults for each model, which can be used to access useful stats like ELPD estimates, pointwise estimates, and Pareto shape values for PSIS-LOO\nweights_method: Method used to compute model weights with model_weights\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.compare","page":"API","title":"PosteriorStats.compare","text":"compare(models; kwargs...) -> ModelComparisonResult\n\nCompare models based on their expected log pointwise predictive density (ELPD).\n\nThe ELPD is estimated either by Pareto smoothed importance sampling leave-one-out cross-validation (LOO) or using the widely applicable information criterion (WAIC). We recommend loo. Read more theory here - in a paper by some of the leading authorities on model comparison dx.doi.org/10.1111/1467-9868.00353\n\nArguments\n\nmodels: a Tuple, NamedTuple, or AbstractVector whose values are either AbstractELPDResult entries or any argument to elpd_method.\n\nKeywords\n\nweights_method::AbstractModelWeightsMethod=Stacking(): the method to be used to weight the models. See model_weights for details\nelpd_method=loo: a method that computes an AbstractELPDResult from an argument in models.\nsort::Bool=true: Whether to sort models by decreasing ELPD.\n\nReturns\n\nModelComparisonResult: A container for the model comparison results. The fields contain a similar collection to models.\n\nExamples\n\nCompare the centered and non centered models of the eight school problem using the defaults: loo and Stacking weights. A custom myloo method formates the inputs as expected by loo.\n\njulia> using ArviZExampleData\n\njulia> models = (\n centered=load_example_data(\"centered_eight\"),\n non_centered=load_example_data(\"non_centered_eight\"),\n );\n\njulia> function myloo(idata)\n log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1))\n return loo(log_like)\n end;\n\njulia> mc = compare(models; elpd_method=myloo)\n┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.\n└ @ PSIS ~/.julia/packages/PSIS/...\nModelComparisonResult with Stacking weights\n rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯\n non_centered 1 -31 1.4 0 0.0 1.0 0.9 ⋯\n centered 2 -31 1.4 0.06 0.067 0.0 0.9 ⋯\n 1 column omitted\njulia> mc.weight |> pairs\npairs(::NamedTuple) with 2 entries:\n :non_centered => 1.0\n :centered => 5.34175e-19\n\nCompare the same models from pre-computed PSIS-LOO results and computing BootstrappedPseudoBMA weights:\n\njulia> elpd_results = mc.elpd_result;\n\njulia> compare(elpd_results; weights_method=BootstrappedPseudoBMA())\nModelComparisonResult with BootstrappedPseudoBMA weights\n rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯\n non_centered 1 -31 1.4 0 0.0 0.52 0.9 ⋯\n centered 2 -31 1.4 0.06 0.067 0.48 0.9 ⋯\n 1 column omitted\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.model_weights","page":"API","title":"PosteriorStats.model_weights","text":"model_weights(elpd_results; method=Stacking())\nmodel_weights(method::AbstractModelWeightsMethod, elpd_results)\n\nCompute weights for each model in elpd_results using method.\n\nelpd_results is a Tuple, NamedTuple, or AbstractVector with AbstractELPDResult entries. The weights are returned in the same type of collection.\n\nStacking is the recommended approach, as it performs well even when the true data generating process is not included among the candidate models. See [YaoVehtari2018] for details.\n\nSee also: AbstractModelWeightsMethod, compare\n\n[YaoVehtari2018]: Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030\n\nExamples\n\nCompute Stacking weights for two models:\n\njulia> using ArviZExampleData\n\njulia> models = (\n centered=load_example_data(\"centered_eight\"),\n non_centered=load_example_data(\"non_centered_eight\"),\n );\n\njulia> elpd_results = map(models) do idata\n log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1))\n return loo(log_like)\n end;\n┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.\n└ @ PSIS ~/.julia/packages/PSIS/...\n\njulia> model_weights(elpd_results; method=Stacking()) |> pairs\npairs(::NamedTuple) with 2 entries:\n :centered => 5.34175e-19\n :non_centered => 1.0\n\nNow we compute BootstrappedPseudoBMA weights for the same models:\n\njulia> model_weights(elpd_results; method=BootstrappedPseudoBMA()) |> pairs\npairs(::NamedTuple) with 2 entries:\n :centered => 0.483723\n :non_centered => 0.516277\n\n\n\n\n\n","category":"function"},{"location":"api/","page":"API","title":"API","text":"The following model weighting methods are available","category":"page"},{"location":"api/","page":"API","title":"API","text":"AbstractModelWeightsMethod\nBootstrappedPseudoBMA\nPseudoBMA\nStacking","category":"page"},{"location":"api/#PosteriorStats.AbstractModelWeightsMethod","page":"API","title":"PosteriorStats.AbstractModelWeightsMethod","text":"abstract type AbstractModelWeightsMethod\n\nAn abstract type representing methods for computing model weights.\n\nSubtypes implement model_weights(method, elpd_results).\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.BootstrappedPseudoBMA","page":"API","title":"PosteriorStats.BootstrappedPseudoBMA","text":"struct BootstrappedPseudoBMA{R<:Random.AbstractRNG, T<:Real} <: AbstractModelWeightsMethod\n\nModel weighting method using pseudo Bayesian Model Averaging using Akaike-type weighting with the Bayesian bootstrap (pseudo-BMA+)[YaoVehtari2018].\n\nThe Bayesian bootstrap stabilizes the model weights.\n\nBootstrappedPseudoBMA(; rng=Random.default_rng(), samples=1_000, alpha=1)\nBootstrappedPseudoBMA(rng, samples, alpha)\n\nConstruct the method.\n\nrng::Random.AbstractRNG: The random number generator to use for the Bayesian bootstrap\nsamples::Int64: The number of samples to draw for bootstrapping\nalpha::Real: The shape parameter in the Dirichlet distribution used for the Bayesian bootstrap. The default (1) corresponds to a uniform distribution on the simplex.\n\nSee also: Stacking\n\n[YaoVehtari2018]: Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.PseudoBMA","page":"API","title":"PosteriorStats.PseudoBMA","text":"struct PseudoBMA <: AbstractModelWeightsMethod\n\nModel weighting method using pseudo Bayesian Model Averaging (pseudo-BMA) and Akaike-type weighting.\n\nPseudoBMA(; regularize=false)\nPseudoBMA(regularize)\n\nConstruct the method with optional regularization of the weights using the standard error of the ELPD estimate.\n\nnote: Note\nThis approach is not recommended, as it produces unstable weight estimates. It is recommended to instead use BootstrappedPseudoBMA to stabilize the weights or Stacking. For details, see [YaoVehtari2018].\n\n[YaoVehtari2018]: Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030\n\nSee also: Stacking\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.Stacking","page":"API","title":"PosteriorStats.Stacking","text":"struct Stacking{O<:Optim.AbstractOptimizer} <: AbstractModelWeightsMethod\n\nModel weighting using stacking of predictive distributions[YaoVehtari2018].\n\nStacking(; optimizer=Optim.LBFGS(), options=Optim.Options()\nStacking(optimizer[, options])\n\nConstruct the method, optionally customizing the optimization.\n\noptimizer::Optim.AbstractOptimizer: The optimizer to use for the optimization of the weights. The optimizer must support projected gradient optimization via a manifold field.\noptions::Optim.Options: The Optim options to use for the optimization of the weights.\n\nSee also: BootstrappedPseudoBMA\n\n[YaoVehtari2018]: Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030\n\n\n\n\n\n","category":"type"},{"location":"api/#Predictive-checks","page":"API","title":"Predictive checks","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"loo_pit\nr2_score","category":"page"},{"location":"api/#PosteriorStats.loo_pit","page":"API","title":"PosteriorStats.loo_pit","text":"loo_pit(y, y_pred, log_weights; kwargs...) -> Union{Real,AbstractArray}\n\nCompute leave-one-out probability integral transform (LOO-PIT) checks.\n\nArguments\n\ny: array of observations with shape (params...,)\ny_pred: array of posterior predictive samples with shape (draws, chains, params...).\nlog_weights: array of normalized log LOO importance weights with shape (draws, chains, params...).\n\nKeywords\n\nis_discrete: If not provided, then it is set to true iff elements of y and y_pred are all integer-valued. If true, then data are smoothed using smooth_data to make them non-discrete before estimating LOO-PIT values.\nkwargs: Remaining keywords are forwarded to smooth_data if data is discrete.\n\nReturns\n\npitvals: LOO-PIT values with same size as y. If y is a scalar, then pitvals is a scalar.\n\nLOO-PIT is a marginal posterior predictive check. If y_-i is the array y of observations with the ith observation left out, and y_i^* is a posterior prediction of the ith observation, then the LOO-PIT value for the ith observation is defined as\n\nP(y_i^* le y_i mid y_-i) = int_-infty^y_i p(y_i^* mid y_-i) mathrmd y_i^*\n\nThe LOO posterior predictions and the corresponding observations should have similar distributions, so if conditional predictive distributions are well-calibrated, then all LOO-PIT values should be approximately uniformly distributed on 0 1.[Gabry2019]\n\n[Gabry2019]: Gabry, J., Simpson, D., Vehtari, A., Betancourt, M. & Gelman, A. Visualization in Bayesian Workflow. J. R. Stat. Soc. Ser. A Stat. Soc. 182, 389–402 (2019). doi: 10.1111/rssa.12378 arXiv: 1709.01449\n\nExamples\n\nCalculate LOO-PIT values using as test quantity the observed values themselves.\n\njulia> using ArviZExampleData\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> y = idata.observed_data.obs;\n\njulia> y_pred = PermutedDimsArray(idata.posterior_predictive.obs, (:draw, :chain, :school));\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> log_weights = loo(log_like).psis_result.log_weights;\n\njulia> loo_pit(y, y_pred, log_weights)\n8-element DimArray{Float64,1} with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.943511\n \"Deerfield\" 0.63797\n \"Phillips Andover\" 0.316697\n \"Phillips Exeter\" 0.582252\n \"Hotchkiss\" 0.295321\n \"Lawrenceville\" 0.403318\n \"St. Paul's\" 0.902508\n \"Mt. Hermon\" 0.655275\n\nCalculate LOO-PIT values using as test quantity the square of the difference between each observation and mu.\n\njulia> using Statistics\n\njulia> mu = idata.posterior.mu;\n\njulia> T = y .- median(mu);\n\njulia> T_pred = y_pred .- mu;\n\njulia> loo_pit(T .^ 2, T_pred .^ 2, log_weights)\n8-element DimArray{Float64,1} with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.873577\n \"Deerfield\" 0.243686\n \"Phillips Andover\" 0.357563\n \"Phillips Exeter\" 0.149908\n \"Hotchkiss\" 0.435094\n \"Lawrenceville\" 0.220627\n \"St. Paul's\" 0.775086\n \"Mt. Hermon\" 0.296706\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.r2_score","page":"API","title":"PosteriorStats.r2_score","text":"r2_score(y_true::AbstractVector, y_pred::AbstractArray) -> (; r2, r2_std)\n\nR² for linear Bayesian regression models.[GelmanGoodrich2019]\n\nArguments\n\ny_true: Observed data of length noutputs\ny_pred: Predicted data with size (ndraws[, nchains], noutputs)\n\n[GelmanGoodrich2019]: Andrew Gelman, Ben Goodrich, Jonah Gabry & Aki Vehtari (2019) R-squared for Bayesian Regression Models, The American Statistician, 73:3, 307-9, DOI: 10.1080/00031305.2018.1549100.\n\nExamples\n\njulia> using ArviZExampleData\n\njulia> idata = load_example_data(\"regression1d\");\n\njulia> y_true = idata.observed_data.y;\n\njulia> y_pred = PermutedDimsArray(idata.posterior_predictive.y, (:draw, :chain, :y_dim_0));\n\njulia> r2_score(y_true, y_pred) |> pairs\npairs(::NamedTuple) with 2 entries:\n :r2 => 0.683197\n :r2_std => 0.0368838\n\n\n\n\n\n","category":"function"},{"location":"api/#Utilities","page":"API","title":"Utilities","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"PosteriorStats.smooth_data","category":"page"},{"location":"api/#PosteriorStats.smooth_data","page":"API","title":"PosteriorStats.smooth_data","text":"smooth_data(y; dims=:, interp_method=CubicSpline, offset_frac=0.01)\n\nSmooth y along dims using interp_method.\n\ninterp_method is a 2-argument callabale that takes the arguments y and x and returns a DataInterpolations.jl interpolation method, defaulting to a cubic spline interpolator.\n\noffset_frac is the fraction of the length of y to use as an offset when interpolating.\n\n\n\n\n\n","category":"function"},{"location":"","page":"Home","title":"Home","text":"CurrentModule = PosteriorStats","category":"page"},{"location":"#PosteriorStats","page":"Home","title":"PosteriorStats","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"PosteriorStats implements widely-used and well-characterized statistical analyses for the Bayesian workflow. These functions generally estimate properties of posterior and/or posterior predictive distributions. The default implementations defined here operate on Monte Carlo samples.","category":"page"},{"location":"","page":"Home","title":"Home","text":"See the API for details.","category":"page"},{"location":"#Extending-this-package","page":"Home","title":"Extending this package","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"The methods defined here are intended to be extended by two types of packages.","category":"page"},{"location":"","page":"Home","title":"Home","text":"packages that implement data types for storing Monte Carlo samples\npackages that implement other representations for posterior distributions than Monte Carlo draws","category":"page"}] +[{"location":"api/#API","page":"API","title":"API","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Pages = [\"stats.md\"]","category":"page"},{"location":"api/#Summary-statistics","page":"API","title":"Summary statistics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"SummaryStats\ndefault_diagnostics\ndefault_stats\ndefault_summary_stats\nsummarize","category":"page"},{"location":"api/#PosteriorStats.SummaryStats","page":"API","title":"PosteriorStats.SummaryStats","text":"struct SummaryStats{D, V<:(AbstractVector)}\n\nA container for a column table of values computed by summarize.\n\nThis object implements the Tables and TableTraits column table interfaces. It has a custom show method.\n\nSummaryStats behaves like an OrderedDict of columns, where the columns can be accessed using either Symbols or a 1-based integer index.\n\nname::String: The name of the collection of summary statistics, used as the table title in display.\ndata::Any: The summary statistics for each parameter. It must implement the Tables interface.\nparameter_names::AbstractVector: Names of the parameters\n\nSummaryStats([name::String,] data[, parameter_names])\nSummaryStats(data[, parameter_names]; name::String=\"SummaryStats\")\n\nConstruct a SummaryStats from tabular data with optional stats name and param_names.\n\ndata must not contain a column :parameter, as this is reserved for the parameter names, which are always in the first column.\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.default_diagnostics","page":"API","title":"PosteriorStats.default_diagnostics","text":"default_diagnostics(focus=Statistics.mean; kwargs...)\n\nDefault diagnostics to be computed with summarize.\n\nThe value of focus determines the diagnostics to be returned:\n\nStatistics.mean: mcse_mean, mcse_std, ess_tail, ess_bulk, rhat\nStatistics.median: mcse_median, ess_tail, ess_bulk, rhat\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.default_stats","page":"API","title":"PosteriorStats.default_stats","text":"default_stats(focus=Statistics.mean; prob_interval=0.94, kwargs...)\n\nDefault statistics to be computed with summarize.\n\nThe value of focus determines the statistics to be returned:\n\nStatistics.mean: mean, std, hdi_3%, hdi_97%\nStatistics.median: median, mad, eti_3%, eti_97%\n\nIf prob_interval is set to a different value than the default, then different HDI and ETI statistics are computed accordingly. hdi refers to the highest-density interval, while eti refers to the equal-tailed interval (i.e. the credible interval computed from symmetric quantiles).\n\nSee also: hdi\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.default_summary_stats","page":"API","title":"PosteriorStats.default_summary_stats","text":"default_summary_stats(focus=Statistics.mean; kwargs...)\n\nCombinatiton of default_stats and default_diagnostics to be used with summarize.\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.summarize","page":"API","title":"PosteriorStats.summarize","text":"summarize(data, stats_funs...; name=\"SummaryStats\", [var_names]) -> SummaryStats\n\nCompute the summary statistics in stats_funs on each param in data.\n\nstats_funs is a collection of functions that reduces a matrix with shape (draws, chains) to a scalar or a collection of scalars. Alternatively, an item in stats_funs may be a Pair of the form name => fun specifying the name to be used for the statistic or of the form (name1, ...) => fun when the function returns a collection. When the function returns a collection, the names in this latter format must be provided.\n\nIf no stats functions are provided, then those specified in default_summary_stats are computed.\n\nvar_names specifies the names of the parameters in data. If not provided, the names are inferred from data.\n\nTo support computing summary statistics from a custom object, overload this method specifying the type of data.\n\nSee also SummaryStats, default_summary_stats, default_stats, default_diagnostics.\n\nExamples\n\nCompute mean, std and the Monte Carlo standard error (MCSE) of the mean estimate:\n\njulia> using Statistics, StatsBase\n\njulia> x = randn(1000, 4, 3) .+ reshape(0:10:20, 1, 1, :);\n\njulia> summarize(x, mean, std, :mcse_mean => sem; name=\"Mean/Std\")\nMean/Std\n mean std mcse_mean\n 1 0.0003 0.990 0.016\n 2 10.02 0.988 0.016\n 3 19.98 0.988 0.016\n\nAvoid recomputing the mean by using mean_and_std, and provide parameter names:\n\njulia> summarize(x, (:mean, :std) => mean_and_std, mad; var_names=[:a, :b, :c])\nSummaryStats\n mean std mad\n a 0.000305 0.990 0.978\n b 10.0 0.988 0.995\n c 20.0 0.988 0.979\n\nNote that when an estimator and its MCSE are both computed, the MCSE is used to determine the number of significant digits that will be displayed.\n\njulia> summarize(x; var_names=[:a, :b, :c])\nSummaryStats\n mean std hdi_3% hdi_97% mcse_mean mcse_std ess_tail ess_bulk r ⋯\n a 0.0003 0.99 -1.92 1.78 0.016 0.012 3567 3663 1 ⋯\n b 10.02 0.99 8.17 11.9 0.016 0.011 3841 3906 1 ⋯\n c 19.98 0.99 18.1 21.9 0.016 0.012 3892 3749 1 ⋯\n 1 column omitted\n\nCompute just the statistics with an 89% HDI on all parameters, and provide the parameter names:\n\njulia> summarize(x, default_stats(; prob_interval=0.89)...; var_names=[:a, :b, :c])\nSummaryStats\n mean std hdi_5.5% hdi_94.5%\n a 0.000305 0.990 -1.63 1.52\n b 10.0 0.988 8.53 11.6\n c 20.0 0.988 18.5 21.6\n\nCompute the summary stats focusing on Statistics.median:\n\njulia> summarize(x, default_summary_stats(median)...; var_names=[:a, :b, :c])\nSummaryStats\n median mad eti_3% eti_97% mcse_median ess_tail ess_median rhat\n a 0.004 0.978 -1.83 1.89 0.020 3567 3336 1.00\n b 10.02 0.995 8.17 11.9 0.023 3841 3787 1.00\n c 19.99 0.979 18.1 21.9 0.020 3892 3829 1.00\n\n\n\n\n\n","category":"function"},{"location":"api/#General-statistics","page":"API","title":"General statistics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"hdi\nhdi!","category":"page"},{"location":"api/#PosteriorStats.hdi","page":"API","title":"PosteriorStats.hdi","text":"hdi(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper)\n\nEstimate the unimodal highest density interval (HDI) of samples for the probability prob.\n\nThe HDI is the minimum width Bayesian credible interval (BCI). That is, it is the smallest possible interval containing (100*prob)% of the probability mass.[Hyndman1996]\n\nsamples is an array of shape (draws[, chains[, params...]]). If multiple parameters are present, then lower and upper are arrays with the shape (params...,), computed separately for each marginal.\n\nThis implementation uses the algorithm of [ChenShao1999].\n\nnote: Note\nAny default value of prob is arbitrary. The default value of prob=0.94 instead of a more common default like prob=0.95 is chosen to reminder the user of this arbitrariness.\n\n[Hyndman1996]: Rob J. Hyndman (1996) Computing and Graphing Highest Density Regions, Amer. Stat., 50(2): 120-6. DOI: 10.1080/00031305.1996.10474359 jstor.\n\n[ChenShao1999]: Ming-Hui Chen & Qi-Man Shao (1999) Monte Carlo Estimation of Bayesian Credible and HPD Intervals, J Comput. Graph. Stat., 8:1, 69-92. DOI: 10.1080/10618600.1999.10474802 jstor.\n\nExamples\n\nHere we calculate the 83% HDI for a normal random variable:\n\njulia> x = randn(2_000);\n\njulia> hdi(x; prob=0.83) |> pairs\npairs(::NamedTuple) with 2 entries:\n :lower => -1.38266\n :upper => 1.25982\n\nWe can also calculate the HDI for a 3-dimensional array of samples:\n\njulia> x = randn(1_000, 1, 1) .+ reshape(0:5:10, 1, 1, :);\n\njulia> hdi(x) |> pairs\npairs(::NamedTuple) with 2 entries:\n :lower => [-1.9674, 3.0326, 8.0326]\n :upper => [1.90028, 6.90028, 11.9003]\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.hdi!","page":"API","title":"PosteriorStats.hdi!","text":"hdi!(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper)\n\nA version of hdi that sorts samples in-place while computing the HDI.\n\n\n\n\n\n","category":"function"},{"location":"api/#LOO-and-WAIC","page":"API","title":"LOO and WAIC","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"AbstractELPDResult\nPSISLOOResult\nWAICResult\nelpd_estimates\ninformation_criterion\nloo\nwaic","category":"page"},{"location":"api/#PosteriorStats.AbstractELPDResult","page":"API","title":"PosteriorStats.AbstractELPDResult","text":"abstract type AbstractELPDResult\n\nAn abstract type representing the result of an ELPD computation.\n\nEvery subtype stores estimates of both the expected log predictive density (elpd) and the effective number of parameters p, as well as standard errors and pointwise estimates of each, from which other relevant estimates can be computed.\n\nSubtypes implement the following functions:\n\nelpd_estimates\ninformation_criterion\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.PSISLOOResult","page":"API","title":"PosteriorStats.PSISLOOResult","text":"Results of Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO).\n\nSee also: loo, AbstractELPDResult\n\nestimates: Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p)\npointwise: Pointwise estimates\npsis_result: Pareto-smoothed importance sampling (PSIS) results\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.WAICResult","page":"API","title":"PosteriorStats.WAICResult","text":"Results of computing the widely applicable information criterion (WAIC).\n\nSee also: waic, AbstractELPDResult\n\nestimates: Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p)\npointwise: Pointwise estimates\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.elpd_estimates","page":"API","title":"PosteriorStats.elpd_estimates","text":"elpd_estimates(result::AbstractELPDResult; pointwise=false) -> (; elpd, elpd_mcse, lpd)\n\nReturn the (E)LPD estimates from the result.\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.information_criterion","page":"API","title":"PosteriorStats.information_criterion","text":"information_criterion(elpd, scale::Symbol)\n\nCompute the information criterion for the given scale from the elpd estimate.\n\nscale must be one of (:deviance, :log, :negative_log).\n\nSee also: loo, waic\n\n\n\n\n\ninformation_criterion(result::AbstractELPDResult, scale::Symbol; pointwise=false)\n\nCompute information criterion for the given scale from the existing ELPD result.\n\nscale must be one of (:deviance, :log, :negative_log).\n\nIf pointwise=true, then pointwise estimates are returned.\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.loo","page":"API","title":"PosteriorStats.loo","text":"loo(log_likelihood; reff=nothing, kwargs...) -> PSISLOOResult{<:NamedTuple,<:NamedTuple}\n\nCompute the Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO). [Vehtari2017][LOOFAQ]\n\nlog_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]).\n\nKeywords\n\nreff::Union{Real,AbstractArray{<:Real}}: The relative effective sample size(s) of the likelihood values. If an array, it must have the same data dimensions as the corresponding log-likelihood variable. If not provided, then this is estimated using MCMCDiagnosticTools.ess.\nkwargs: Remaining keywords are forwarded to [PSIS.psis].\n\nSee also: PSISLOOResult, waic\n\n[Vehtari2017]: Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544\n\n[LOOFAQ]: Aki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html\n\nExamples\n\nManually compute R_mathrmeff and calculate PSIS-LOO of a model:\n\njulia> using ArviZExampleData, MCMCDiagnosticTools\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> reff = ess(log_like; kind=:basic, split_chains=1, relative=true);\n\njulia> loo(log_like; reff)\nPSISLOOResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.34\n\nand PSISResult with 500 draws, 4 chains, and 8 parameters\nPareto shape (k) diagnostic values:\n Count Min. ESS\n (-Inf, 0.5] good 7 (87.5%) 151\n (0.5, 0.7] okay 1 (12.5%) 446\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.waic","page":"API","title":"PosteriorStats.waic","text":"waic(log_likelihood::AbstractArray) -> WAICResult{<:NamedTuple,<:NamedTuple}\n\nCompute the widely applicable information criterion (WAIC).[Watanabe2010][Vehtari2017][LOOFAQ]\n\nlog_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]).\n\nSee also: WAICResult, loo\n\n[Watanabe2010]: Watanabe, S. Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory. 11(116):3571−3594, 2010. https://jmlr.csail.mit.edu/papers/v11/watanabe10a.html\n\n[Vehtari2017]: Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544\n\n[LOOFAQ]: Aki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html\n\nExamples\n\nCalculate WAIC of a model:\n\njulia> using ArviZExampleData\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> waic(log_like)\nWAICResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.33\n\n\n\n\n\n","category":"function"},{"location":"api/#Model-comparison","page":"API","title":"Model comparison","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"ModelComparisonResult\ncompare\nmodel_weights","category":"page"},{"location":"api/#PosteriorStats.ModelComparisonResult","page":"API","title":"PosteriorStats.ModelComparisonResult","text":"ModelComparisonResult\n\nResult of model comparison using ELPD.\n\nThis struct implements the Tables and TableTraits interfaces.\n\nEach field returns a collection of the corresponding entry for each model:\n\nname: Names of the models, if provided.\nrank: Ranks of the models (ordered by decreasing ELPD)\nelpd_diff: ELPD of a model subtracted from the largest ELPD of any model\nelpd_diff_mcse: Monte Carlo standard error of the ELPD difference\nweight: Model weights computed with weights_method\nelpd_result: AbstactELPDResults for each model, which can be used to access useful stats like ELPD estimates, pointwise estimates, and Pareto shape values for PSIS-LOO\nweights_method: Method used to compute model weights with model_weights\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.compare","page":"API","title":"PosteriorStats.compare","text":"compare(models; kwargs...) -> ModelComparisonResult\n\nCompare models based on their expected log pointwise predictive density (ELPD).\n\nThe ELPD is estimated either by Pareto smoothed importance sampling leave-one-out cross-validation (LOO) or using the widely applicable information criterion (WAIC). We recommend loo. Read more theory here - in a paper by some of the leading authorities on model comparison dx.doi.org/10.1111/1467-9868.00353\n\nArguments\n\nmodels: a Tuple, NamedTuple, or AbstractVector whose values are either AbstractELPDResult entries or any argument to elpd_method.\n\nKeywords\n\nweights_method::AbstractModelWeightsMethod=Stacking(): the method to be used to weight the models. See model_weights for details\nelpd_method=loo: a method that computes an AbstractELPDResult from an argument in models.\nsort::Bool=true: Whether to sort models by decreasing ELPD.\n\nReturns\n\nModelComparisonResult: A container for the model comparison results. The fields contain a similar collection to models.\n\nExamples\n\nCompare the centered and non centered models of the eight school problem using the defaults: loo and Stacking weights. A custom myloo method formates the inputs as expected by loo.\n\njulia> using ArviZExampleData\n\njulia> models = (\n centered=load_example_data(\"centered_eight\"),\n non_centered=load_example_data(\"non_centered_eight\"),\n );\n\njulia> function myloo(idata)\n log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1))\n return loo(log_like)\n end;\n\njulia> mc = compare(models; elpd_method=myloo)\n┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.\n└ @ PSIS ~/.julia/packages/PSIS/...\nModelComparisonResult with Stacking weights\n rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯\n non_centered 1 -31 1.4 0 0.0 1.0 0.9 ⋯\n centered 2 -31 1.4 0.06 0.067 0.0 0.9 ⋯\n 1 column omitted\njulia> mc.weight |> pairs\npairs(::NamedTuple) with 2 entries:\n :non_centered => 1.0\n :centered => 5.34175e-19\n\nCompare the same models from pre-computed PSIS-LOO results and computing BootstrappedPseudoBMA weights:\n\njulia> elpd_results = mc.elpd_result;\n\njulia> compare(elpd_results; weights_method=BootstrappedPseudoBMA())\nModelComparisonResult with BootstrappedPseudoBMA weights\n rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯\n non_centered 1 -31 1.4 0 0.0 0.52 0.9 ⋯\n centered 2 -31 1.4 0.06 0.067 0.48 0.9 ⋯\n 1 column omitted\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.model_weights","page":"API","title":"PosteriorStats.model_weights","text":"model_weights(elpd_results; method=Stacking())\nmodel_weights(method::AbstractModelWeightsMethod, elpd_results)\n\nCompute weights for each model in elpd_results using method.\n\nelpd_results is a Tuple, NamedTuple, or AbstractVector with AbstractELPDResult entries. The weights are returned in the same type of collection.\n\nStacking is the recommended approach, as it performs well even when the true data generating process is not included among the candidate models. See [YaoVehtari2018] for details.\n\nSee also: AbstractModelWeightsMethod, compare\n\n[YaoVehtari2018]: Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030\n\nExamples\n\nCompute Stacking weights for two models:\n\njulia> using ArviZExampleData\n\njulia> models = (\n centered=load_example_data(\"centered_eight\"),\n non_centered=load_example_data(\"non_centered_eight\"),\n );\n\njulia> elpd_results = map(models) do idata\n log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1))\n return loo(log_like)\n end;\n┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.\n└ @ PSIS ~/.julia/packages/PSIS/...\n\njulia> model_weights(elpd_results; method=Stacking()) |> pairs\npairs(::NamedTuple) with 2 entries:\n :centered => 5.34175e-19\n :non_centered => 1.0\n\nNow we compute BootstrappedPseudoBMA weights for the same models:\n\njulia> model_weights(elpd_results; method=BootstrappedPseudoBMA()) |> pairs\npairs(::NamedTuple) with 2 entries:\n :centered => 0.483723\n :non_centered => 0.516277\n\n\n\n\n\n","category":"function"},{"location":"api/","page":"API","title":"API","text":"The following model weighting methods are available","category":"page"},{"location":"api/","page":"API","title":"API","text":"AbstractModelWeightsMethod\nBootstrappedPseudoBMA\nPseudoBMA\nStacking","category":"page"},{"location":"api/#PosteriorStats.AbstractModelWeightsMethod","page":"API","title":"PosteriorStats.AbstractModelWeightsMethod","text":"abstract type AbstractModelWeightsMethod\n\nAn abstract type representing methods for computing model weights.\n\nSubtypes implement model_weights(method, elpd_results).\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.BootstrappedPseudoBMA","page":"API","title":"PosteriorStats.BootstrappedPseudoBMA","text":"struct BootstrappedPseudoBMA{R<:Random.AbstractRNG, T<:Real} <: AbstractModelWeightsMethod\n\nModel weighting method using pseudo Bayesian Model Averaging using Akaike-type weighting with the Bayesian bootstrap (pseudo-BMA+)[YaoVehtari2018].\n\nThe Bayesian bootstrap stabilizes the model weights.\n\nBootstrappedPseudoBMA(; rng=Random.default_rng(), samples=1_000, alpha=1)\nBootstrappedPseudoBMA(rng, samples, alpha)\n\nConstruct the method.\n\nrng::Random.AbstractRNG: The random number generator to use for the Bayesian bootstrap\nsamples::Int64: The number of samples to draw for bootstrapping\nalpha::Real: The shape parameter in the Dirichlet distribution used for the Bayesian bootstrap. The default (1) corresponds to a uniform distribution on the simplex.\n\nSee also: Stacking\n\n[YaoVehtari2018]: Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.PseudoBMA","page":"API","title":"PosteriorStats.PseudoBMA","text":"struct PseudoBMA <: AbstractModelWeightsMethod\n\nModel weighting method using pseudo Bayesian Model Averaging (pseudo-BMA) and Akaike-type weighting.\n\nPseudoBMA(; regularize=false)\nPseudoBMA(regularize)\n\nConstruct the method with optional regularization of the weights using the standard error of the ELPD estimate.\n\nnote: Note\nThis approach is not recommended, as it produces unstable weight estimates. It is recommended to instead use BootstrappedPseudoBMA to stabilize the weights or Stacking. For details, see [YaoVehtari2018].\n\n[YaoVehtari2018]: Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030\n\nSee also: Stacking\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.Stacking","page":"API","title":"PosteriorStats.Stacking","text":"struct Stacking{O<:Optim.AbstractOptimizer} <: AbstractModelWeightsMethod\n\nModel weighting using stacking of predictive distributions[YaoVehtari2018].\n\nStacking(; optimizer=Optim.LBFGS(), options=Optim.Options()\nStacking(optimizer[, options])\n\nConstruct the method, optionally customizing the optimization.\n\noptimizer::Optim.AbstractOptimizer: The optimizer to use for the optimization of the weights. The optimizer must support projected gradient optimization via a manifold field.\noptions::Optim.Options: The Optim options to use for the optimization of the weights.\n\nSee also: BootstrappedPseudoBMA\n\n[YaoVehtari2018]: Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030\n\n\n\n\n\n","category":"type"},{"location":"api/#Predictive-checks","page":"API","title":"Predictive checks","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"loo_pit\nr2_score","category":"page"},{"location":"api/#PosteriorStats.loo_pit","page":"API","title":"PosteriorStats.loo_pit","text":"loo_pit(y, y_pred, log_weights; kwargs...) -> Union{Real,AbstractArray}\n\nCompute leave-one-out probability integral transform (LOO-PIT) checks.\n\nArguments\n\ny: array of observations with shape (params...,)\ny_pred: array of posterior predictive samples with shape (draws, chains, params...).\nlog_weights: array of normalized log LOO importance weights with shape (draws, chains, params...).\n\nKeywords\n\nis_discrete: If not provided, then it is set to true iff elements of y and y_pred are all integer-valued. If true, then data are smoothed using smooth_data to make them non-discrete before estimating LOO-PIT values.\nkwargs: Remaining keywords are forwarded to smooth_data if data is discrete.\n\nReturns\n\npitvals: LOO-PIT values with same size as y. If y is a scalar, then pitvals is a scalar.\n\nLOO-PIT is a marginal posterior predictive check. If y_-i is the array y of observations with the ith observation left out, and y_i^* is a posterior prediction of the ith observation, then the LOO-PIT value for the ith observation is defined as\n\nP(y_i^* le y_i mid y_-i) = int_-infty^y_i p(y_i^* mid y_-i) mathrmd y_i^*\n\nThe LOO posterior predictions and the corresponding observations should have similar distributions, so if conditional predictive distributions are well-calibrated, then all LOO-PIT values should be approximately uniformly distributed on 0 1.[Gabry2019]\n\n[Gabry2019]: Gabry, J., Simpson, D., Vehtari, A., Betancourt, M. & Gelman, A. Visualization in Bayesian Workflow. J. R. Stat. Soc. Ser. A Stat. Soc. 182, 389–402 (2019). doi: 10.1111/rssa.12378 arXiv: 1709.01449\n\nExamples\n\nCalculate LOO-PIT values using as test quantity the observed values themselves.\n\njulia> using ArviZExampleData\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> y = idata.observed_data.obs;\n\njulia> y_pred = PermutedDimsArray(idata.posterior_predictive.obs, (:draw, :chain, :school));\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> log_weights = loo(log_like).psis_result.log_weights;\n\njulia> loo_pit(y, y_pred, log_weights)\n8-element DimArray{Float64,1} with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.943511\n \"Deerfield\" 0.63797\n \"Phillips Andover\" 0.316697\n \"Phillips Exeter\" 0.582252\n \"Hotchkiss\" 0.295321\n \"Lawrenceville\" 0.403318\n \"St. Paul's\" 0.902508\n \"Mt. Hermon\" 0.655275\n\nCalculate LOO-PIT values using as test quantity the square of the difference between each observation and mu.\n\njulia> using Statistics\n\njulia> mu = idata.posterior.mu;\n\njulia> T = y .- median(mu);\n\njulia> T_pred = y_pred .- mu;\n\njulia> loo_pit(T .^ 2, T_pred .^ 2, log_weights)\n8-element DimArray{Float64,1} with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.873577\n \"Deerfield\" 0.243686\n \"Phillips Andover\" 0.357563\n \"Phillips Exeter\" 0.149908\n \"Hotchkiss\" 0.435094\n \"Lawrenceville\" 0.220627\n \"St. Paul's\" 0.775086\n \"Mt. Hermon\" 0.296706\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.r2_score","page":"API","title":"PosteriorStats.r2_score","text":"r2_score(y_true::AbstractVector, y_pred::AbstractArray) -> (; r2, r2_std)\n\nR² for linear Bayesian regression models.[GelmanGoodrich2019]\n\nArguments\n\ny_true: Observed data of length noutputs\ny_pred: Predicted data with size (ndraws[, nchains], noutputs)\n\n[GelmanGoodrich2019]: Andrew Gelman, Ben Goodrich, Jonah Gabry & Aki Vehtari (2019) R-squared for Bayesian Regression Models, The American Statistician, 73:3, 307-9, DOI: 10.1080/00031305.2018.1549100.\n\nExamples\n\njulia> using ArviZExampleData\n\njulia> idata = load_example_data(\"regression1d\");\n\njulia> y_true = idata.observed_data.y;\n\njulia> y_pred = PermutedDimsArray(idata.posterior_predictive.y, (:draw, :chain, :y_dim_0));\n\njulia> r2_score(y_true, y_pred) |> pairs\npairs(::NamedTuple) with 2 entries:\n :r2 => 0.683197\n :r2_std => 0.0368838\n\n\n\n\n\n","category":"function"},{"location":"api/#Utilities","page":"API","title":"Utilities","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"PosteriorStats.smooth_data","category":"page"},{"location":"api/#PosteriorStats.smooth_data","page":"API","title":"PosteriorStats.smooth_data","text":"smooth_data(y; dims=:, interp_method=CubicSpline, offset_frac=0.01)\n\nSmooth y along dims using interp_method.\n\ninterp_method is a 2-argument callabale that takes the arguments y and x and returns a DataInterpolations.jl interpolation method, defaulting to a cubic spline interpolator.\n\noffset_frac is the fraction of the length of y to use as an offset when interpolating.\n\n\n\n\n\n","category":"function"},{"location":"","page":"Home","title":"Home","text":"CurrentModule = PosteriorStats","category":"page"},{"location":"#PosteriorStats","page":"Home","title":"PosteriorStats","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"PosteriorStats implements widely-used and well-characterized statistical analyses for the Bayesian workflow. These functions generally estimate properties of posterior and/or posterior predictive distributions. The default implementations defined here operate on Monte Carlo samples.","category":"page"},{"location":"","page":"Home","title":"Home","text":"See the API for details.","category":"page"},{"location":"#Extending-this-package","page":"Home","title":"Extending this package","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"The methods defined here are intended to be extended by two types of packages.","category":"page"},{"location":"","page":"Home","title":"Home","text":"packages that implement data types for storing Monte Carlo samples\npackages that implement other representations for posterior distributions than Monte Carlo draws","category":"page"}] } diff --git a/PosteriorStats/stable b/PosteriorStats/stable index 7a5e833ee..81fd7ba08 120000 --- a/PosteriorStats/stable +++ b/PosteriorStats/stable @@ -1 +1 @@ -v0.1.4 \ No newline at end of file +v0.2.0 \ No newline at end of file diff --git a/PosteriorStats/v0.2 b/PosteriorStats/v0.2 new file mode 120000 index 000000000..81fd7ba08 --- /dev/null +++ b/PosteriorStats/v0.2 @@ -0,0 +1 @@ +v0.2.0 \ No newline at end of file diff --git a/PosteriorStats/v0.2.0/.documenter-siteinfo.json b/PosteriorStats/v0.2.0/.documenter-siteinfo.json new file mode 100644 index 000000000..617bf5234 --- /dev/null +++ b/PosteriorStats/v0.2.0/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-12-23T19:21:40","documenter_version":"1.2.1"}} \ No newline at end of file diff --git a/PosteriorStats/v0.2.0/api/index.html b/PosteriorStats/v0.2.0/api/index.html new file mode 100644 index 000000000..3370108f0 --- /dev/null +++ b/PosteriorStats/v0.2.0/api/index.html @@ -0,0 +1,173 @@ +API · PosteriorStats.jl
      GitHub

      API

        Summary statistics

        PosteriorStats.SummaryStats — Type
        struct SummaryStats{D, V<:(AbstractVector)}

        A container for a column table of values computed by summarize.

        This object implements the Tables and TableTraits column table interfaces. It has a custom show method.

        SummaryStats behaves like an OrderedDict of columns, where the columns can be accessed using either Symbols or a 1-based integer index.

        • name::String: The name of the collection of summary statistics, used as the table title in display.

        • data::Any: The summary statistics for each parameter. It must implement the Tables interface.

        • parameter_names::AbstractVector: Names of the parameters

        SummaryStats([name::String,] data[, parameter_names])
+SummaryStats(data[, parameter_names]; name::String="SummaryStats")

        Construct a SummaryStats from tabular data with optional stats name and param_names.

        data must not contain a column :parameter, as this is reserved for the parameter names, which are always in the first column.

        source
        PosteriorStats.default_diagnostics — Function
        default_diagnostics(focus=Statistics.mean; kwargs...)

        Default diagnostics to be computed with summarize.

        The value of focus determines the diagnostics to be returned:

        • Statistics.mean: mcse_mean, mcse_std, ess_tail, ess_bulk, rhat
        • Statistics.median: mcse_median, ess_tail, ess_bulk, rhat
        source
        PosteriorStats.default_stats — Function
        default_stats(focus=Statistics.mean; prob_interval=0.94, kwargs...)

        Default statistics to be computed with summarize.

        The value of focus determines the statistics to be returned:

        • Statistics.mean: mean, std, hdi_3%, hdi_97%
        • Statistics.median: median, mad, eti_3%, eti_97%

        If prob_interval is set to a different value than the default, then different HDI and ETI statistics are computed accordingly. hdi refers to the highest-density interval, while eti refers to the equal-tailed interval (i.e. the credible interval computed from symmetric quantiles).

        See also: hdi

        source
        PosteriorStats.summarize — Function
        summarize(data, stats_funs...; name="SummaryStats", [var_names]) -> SummaryStats

        Compute the summary statistics in stats_funs on each param in data.

        stats_funs is a collection of functions that reduces a matrix with shape (draws, chains) to a scalar or a collection of scalars. Alternatively, an item in stats_funs may be a Pair of the form name => fun specifying the name to be used for the statistic or of the form (name1, ...) => fun when the function returns a collection. When the function returns a collection, the names in this latter format must be provided.

        If no stats functions are provided, then those specified in default_summary_stats are computed.

        var_names specifies the names of the parameters in data. If not provided, the names are inferred from data.

        To support computing summary statistics from a custom object, overload this method specifying the type of data.

        See also SummaryStats, default_summary_stats, default_stats, default_diagnostics.

        Examples

        Compute mean, std and the Monte Carlo standard error (MCSE) of the mean estimate:

        julia> using Statistics, StatsBase
+
+julia> x = randn(1000, 4, 3) .+ reshape(0:10:20, 1, 1, :);
+
+julia> summarize(x, mean, std, :mcse_mean => sem; name="Mean/Std")
+Mean/Std
+       mean    std  mcse_mean
+ 1   0.0003  0.990      0.016
+ 2  10.02    0.988      0.016
+ 3  19.98    0.988      0.016

        Avoid recomputing the mean by using mean_and_std, and provide parameter names:

        julia> summarize(x, (:mean, :std) => mean_and_std, mad; var_names=[:a, :b, :c])
+SummaryStats
+         mean    std    mad
+ a   0.000305  0.990  0.978
+ b  10.0       0.988  0.995
+ c  20.0       0.988  0.979

        Note that when an estimator and its MCSE are both computed, the MCSE is used to determine the number of significant digits that will be displayed.

        julia> summarize(x; var_names=[:a, :b, :c])
+SummaryStats
+       mean   std  hdi_3%  hdi_97%  mcse_mean  mcse_std  ess_tail  ess_bulk  r ⋯
+ a   0.0003  0.99   -1.92     1.78      0.016     0.012      3567      3663  1 ⋯
+ b  10.02    0.99    8.17    11.9       0.016     0.011      3841      3906  1 ⋯
+ c  19.98    0.99   18.1     21.9       0.016     0.012      3892      3749  1 ⋯
+                                                                1 column omitted

        Compute just the statistics with an 89% HDI on all parameters, and provide the parameter names:

        julia> summarize(x, default_stats(; prob_interval=0.89)...; var_names=[:a, :b, :c])
+SummaryStats
+         mean    std  hdi_5.5%  hdi_94.5%
+ a   0.000305  0.990     -1.63       1.52
+ b  10.0       0.988      8.53      11.6
+ c  20.0       0.988     18.5       21.6

        Compute the summary stats focusing on Statistics.median:

        julia> summarize(x, default_summary_stats(median)...; var_names=[:a, :b, :c])
+SummaryStats
+    median    mad  eti_3%  eti_97%  mcse_median  ess_tail  ess_median  rhat
+ a   0.004  0.978   -1.83     1.89        0.020      3567        3336  1.00
+ b  10.02   0.995    8.17    11.9         0.023      3841        3787  1.00
+ c  19.99   0.979   18.1     21.9         0.020      3892        3829  1.00
        source

        General statistics

        PosteriorStats.hdi — Function
        hdi(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper)

        Estimate the unimodal highest density interval (HDI) of samples for the probability prob.

        The HDI is the minimum width Bayesian credible interval (BCI). That is, it is the smallest possible interval containing (100*prob)% of the probability mass.[Hyndman1996]

        samples is an array of shape (draws[, chains[, params...]]). If multiple parameters are present, then lower and upper are arrays with the shape (params...,), computed separately for each marginal.

        This implementation uses the algorithm of [ChenShao1999].

        Note

        Any default value of prob is arbitrary. The default value of prob=0.94 instead of a more common default like prob=0.95 is chosen to reminder the user of this arbitrariness.

        Examples

        Here we calculate the 83% HDI for a normal random variable:

        julia> x = randn(2_000);
+
+julia> hdi(x; prob=0.83) |> pairs
+pairs(::NamedTuple) with 2 entries:
+  :lower => -1.38266
+  :upper => 1.25982

        We can also calculate the HDI for a 3-dimensional array of samples:

        julia> x = randn(1_000, 1, 1) .+ reshape(0:5:10, 1, 1, :);
+
+julia> hdi(x) |> pairs
+pairs(::NamedTuple) with 2 entries:
+  :lower => [-1.9674, 3.0326, 8.0326]
+  :upper => [1.90028, 6.90028, 11.9003]
        source
        PosteriorStats.hdi! — Function
        hdi!(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper)

        A version of hdi that sorts samples in-place while computing the HDI.

        source

        LOO and WAIC

        PosteriorStats.AbstractELPDResult — Type
        abstract type AbstractELPDResult

        An abstract type representing the result of an ELPD computation.

        Every subtype stores estimates of both the expected log predictive density (elpd) and the effective number of parameters p, as well as standard errors and pointwise estimates of each, from which other relevant estimates can be computed.

        Subtypes implement the following functions:

        source
        PosteriorStats.PSISLOOResult — Type

        Results of Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO).

        See also: loo, AbstractELPDResult

        • estimates: Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p)

        • pointwise: Pointwise estimates

        • psis_result: Pareto-smoothed importance sampling (PSIS) results

        source
        PosteriorStats.WAICResult — Type

        Results of computing the widely applicable information criterion (WAIC).

        See also: waic, AbstractELPDResult

        • estimates: Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p)

        • pointwise: Pointwise estimates

        source
        PosteriorStats.elpd_estimates — Function
        elpd_estimates(result::AbstractELPDResult; pointwise=false) -> (; elpd, elpd_mcse, lpd)

        Return the (E)LPD estimates from the result.

        source
        PosteriorStats.information_criterion — Function
        information_criterion(elpd, scale::Symbol)

        Compute the information criterion for the given scale from the elpd estimate.

        scale must be one of (:deviance, :log, :negative_log).

        See also: loo, waic

        source
        information_criterion(result::AbstractELPDResult, scale::Symbol; pointwise=false)

        Compute information criterion for the given scale from the existing ELPD result.

        scale must be one of (:deviance, :log, :negative_log).

        If pointwise=true, then pointwise estimates are returned.

        source
        PosteriorStats.loo — Function
        loo(log_likelihood; reff=nothing, kwargs...) -> PSISLOOResult{<:NamedTuple,<:NamedTuple}

        Compute the Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO). [Vehtari2017][LOOFAQ]

        log_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]).

        Keywords

        • reff::Union{Real,AbstractArray{<:Real}}: The relative effective sample size(s) of the likelihood values. If an array, it must have the same data dimensions as the corresponding log-likelihood variable. If not provided, then this is estimated using MCMCDiagnosticTools.ess.
        • kwargs: Remaining keywords are forwarded to [PSIS.psis].

        See also: PSISLOOResult, waic

        Examples

        Manually compute $R_\mathrm{eff}$ and calculate PSIS-LOO of a model:

        julia> using ArviZExampleData, MCMCDiagnosticTools
+
+julia> idata = load_example_data("centered_eight");
+
+julia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));
+
+julia> reff = ess(log_like; kind=:basic, split_chains=1, relative=true);
+
+julia> loo(log_like; reff)
+PSISLOOResult with estimates
+ elpd  elpd_mcse    p  p_mcse
+  -31        1.4  0.9    0.34
+
+and PSISResult with 500 draws, 4 chains, and 8 parameters
+Pareto shape (k) diagnostic values:
+                    Count      Min. ESS
+ (-Inf, 0.5]  good  7 (87.5%)  151
+  (0.5, 0.7]  okay  1 (12.5%)  446
        source
        PosteriorStats.waic — Function
        waic(log_likelihood::AbstractArray) -> WAICResult{<:NamedTuple,<:NamedTuple}

        Compute the widely applicable information criterion (WAIC).[Watanabe2010][Vehtari2017][LOOFAQ]

        log_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]).

        See also: WAICResult, loo

        Examples

        Calculate WAIC of a model:

        julia> using ArviZExampleData
+
+julia> idata = load_example_data("centered_eight");
+
+julia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));
+
+julia> waic(log_like)
+WAICResult with estimates
+ elpd  elpd_mcse    p  p_mcse
+  -31        1.4  0.9    0.33
        source

        Model comparison

        PosteriorStats.ModelComparisonResult — Type
        ModelComparisonResult

        Result of model comparison using ELPD.

        This struct implements the Tables and TableTraits interfaces.

        Each field returns a collection of the corresponding entry for each model:

        • name: Names of the models, if provided.

        • rank: Ranks of the models (ordered by decreasing ELPD)

        • elpd_diff: ELPD of a model subtracted from the largest ELPD of any model

        • elpd_diff_mcse: Monte Carlo standard error of the ELPD difference

        • weight: Model weights computed with weights_method

        • elpd_result: AbstactELPDResults for each model, which can be used to access useful stats like ELPD estimates, pointwise estimates, and Pareto shape values for PSIS-LOO

        • weights_method: Method used to compute model weights with model_weights

        source
        PosteriorStats.compare — Function
        compare(models; kwargs...) -> ModelComparisonResult

        Compare models based on their expected log pointwise predictive density (ELPD).

        The ELPD is estimated either by Pareto smoothed importance sampling leave-one-out cross-validation (LOO) or using the widely applicable information criterion (WAIC). We recommend loo. Read more theory here - in a paper by some of the leading authorities on model comparison dx.doi.org/10.1111/1467-9868.00353

        Arguments

        • models: a Tuple, NamedTuple, or AbstractVector whose values are either AbstractELPDResult entries or any argument to elpd_method.

        Keywords

        • weights_method::AbstractModelWeightsMethod=Stacking(): the method to be used to weight the models. See model_weights for details
        • elpd_method=loo: a method that computes an AbstractELPDResult from an argument in models.
        • sort::Bool=true: Whether to sort models by decreasing ELPD.

        Returns

        • ModelComparisonResult: A container for the model comparison results. The fields contain a similar collection to models.

        Examples

        Compare the centered and non centered models of the eight school problem using the defaults: loo and Stacking weights. A custom myloo method formates the inputs as expected by loo.

        julia> using ArviZExampleData
+
+julia> models = (
+           centered=load_example_data("centered_eight"),
+           non_centered=load_example_data("non_centered_eight"),
+       );
+
+julia> function myloo(idata)
+           log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1))
+           return loo(log_like)
+       end;
+
+julia> mc = compare(models; elpd_method=myloo)
+┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.
+└ @ PSIS ~/.julia/packages/PSIS/...
+ModelComparisonResult with Stacking weights
+               rank  elpd  elpd_mcse  elpd_diff  elpd_diff_mcse  weight    p   ⋯
+ non_centered     1   -31        1.4       0              0.0       1.0  0.9   ⋯
+ centered         2   -31        1.4       0.06           0.067     0.0  0.9   ⋯
+                                                                1 column omitted
+julia> mc.weight |> pairs
+pairs(::NamedTuple) with 2 entries:
+  :non_centered => 1.0
+  :centered     => 5.34175e-19

        Compare the same models from pre-computed PSIS-LOO results and computing BootstrappedPseudoBMA weights:

        julia> elpd_results = mc.elpd_result;
+
+julia> compare(elpd_results; weights_method=BootstrappedPseudoBMA())
+ModelComparisonResult with BootstrappedPseudoBMA weights
+               rank  elpd  elpd_mcse  elpd_diff  elpd_diff_mcse  weight    p   ⋯
+ non_centered     1   -31        1.4       0              0.0      0.52  0.9   ⋯
+ centered         2   -31        1.4       0.06           0.067    0.48  0.9   ⋯
+                                                                1 column omitted
        source
        PosteriorStats.model_weights — Function
        model_weights(elpd_results; method=Stacking())
+model_weights(method::AbstractModelWeightsMethod, elpd_results)

        Compute weights for each model in elpd_results using method.

        elpd_results is a Tuple, NamedTuple, or AbstractVector with AbstractELPDResult entries. The weights are returned in the same type of collection.

        Stacking is the recommended approach, as it performs well even when the true data generating process is not included among the candidate models. See [YaoVehtari2018] for details.

        See also: AbstractModelWeightsMethod, compare

        Examples

        Compute Stacking weights for two models:

        julia> using ArviZExampleData
+
+julia> models = (
+           centered=load_example_data("centered_eight"),
+           non_centered=load_example_data("non_centered_eight"),
+       );
+
+julia> elpd_results = map(models) do idata
+           log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1))
+           return loo(log_like)
+       end;
+┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.
+└ @ PSIS ~/.julia/packages/PSIS/...
+
+julia> model_weights(elpd_results; method=Stacking()) |> pairs
+pairs(::NamedTuple) with 2 entries:
+  :centered     => 5.34175e-19
+  :non_centered => 1.0

        Now we compute BootstrappedPseudoBMA weights for the same models:

        julia> model_weights(elpd_results; method=BootstrappedPseudoBMA()) |> pairs
+pairs(::NamedTuple) with 2 entries:
+  :centered     => 0.483723
+  :non_centered => 0.516277
        source

        The following model weighting methods are available

        PosteriorStats.BootstrappedPseudoBMA — Type
        struct BootstrappedPseudoBMA{R<:Random.AbstractRNG, T<:Real} <: AbstractModelWeightsMethod

        Model weighting method using pseudo Bayesian Model Averaging using Akaike-type weighting with the Bayesian bootstrap (pseudo-BMA+)[YaoVehtari2018].

        The Bayesian bootstrap stabilizes the model weights.

        BootstrappedPseudoBMA(; rng=Random.default_rng(), samples=1_000, alpha=1)
+BootstrappedPseudoBMA(rng, samples, alpha)

        Construct the method.

        • rng::Random.AbstractRNG: The random number generator to use for the Bayesian bootstrap

        • samples::Int64: The number of samples to draw for bootstrapping

        • alpha::Real: The shape parameter in the Dirichlet distribution used for the Bayesian bootstrap. The default (1) corresponds to a uniform distribution on the simplex.

        See also: Stacking

        source
        PosteriorStats.PseudoBMA — Type
        struct PseudoBMA <: AbstractModelWeightsMethod

        Model weighting method using pseudo Bayesian Model Averaging (pseudo-BMA) and Akaike-type weighting.

        PseudoBMA(; regularize=false)
+PseudoBMA(regularize)

        Construct the method with optional regularization of the weights using the standard error of the ELPD estimate.

        Note

        This approach is not recommended, as it produces unstable weight estimates. It is recommended to instead use BootstrappedPseudoBMA to stabilize the weights or Stacking. For details, see [YaoVehtari2018].

        See also: Stacking

        source
        PosteriorStats.Stacking — Type
        struct Stacking{O<:Optim.AbstractOptimizer} <: AbstractModelWeightsMethod

        Model weighting using stacking of predictive distributions[YaoVehtari2018].

        Stacking(; optimizer=Optim.LBFGS(), options=Optim.Options()
+Stacking(optimizer[, options])

        Construct the method, optionally customizing the optimization.

        • optimizer::Optim.AbstractOptimizer: The optimizer to use for the optimization of the weights. The optimizer must support projected gradient optimization via a manifold field.

        • options::Optim.Options: The Optim options to use for the optimization of the weights.

        See also: BootstrappedPseudoBMA

        source

        Predictive checks

        PosteriorStats.loo_pit — Function
        loo_pit(y, y_pred, log_weights; kwargs...) -> Union{Real,AbstractArray}

        Compute leave-one-out probability integral transform (LOO-PIT) checks.

        Arguments

        • y: array of observations with shape (params...,)
        • y_pred: array of posterior predictive samples with shape (draws, chains, params...).
        • log_weights: array of normalized log LOO importance weights with shape (draws, chains, params...).

        Keywords

        • is_discrete: If not provided, then it is set to true iff elements of y and y_pred are all integer-valued. If true, then data are smoothed using smooth_data to make them non-discrete before estimating LOO-PIT values.
        • kwargs: Remaining keywords are forwarded to smooth_data if data is discrete.

        Returns

        • pitvals: LOO-PIT values with same size as y. If y is a scalar, then pitvals is a scalar.

        LOO-PIT is a marginal posterior predictive check. If $y_{-i}$ is the array $y$ of observations with the $i$th observation left out, and $y_i^*$ is a posterior prediction of the $i$th observation, then the LOO-PIT value for the $i$th observation is defined as

        \[P(y_i^* \le y_i \mid y_{-i}) = \int_{-\infty}^{y_i} p(y_i^* \mid y_{-i}) \mathrm{d} y_i^*\]

        The LOO posterior predictions and the corresponding observations should have similar distributions, so if conditional predictive distributions are well-calibrated, then all LOO-PIT values should be approximately uniformly distributed on $[0, 1]$.[Gabry2019]

        Examples

        Calculate LOO-PIT values using as test quantity the observed values themselves.

        julia> using ArviZExampleData
+
+julia> idata = load_example_data("centered_eight");
+
+julia> y = idata.observed_data.obs;
+
+julia> y_pred = PermutedDimsArray(idata.posterior_predictive.obs, (:draw, :chain, :school));
+
+julia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));
+
+julia> log_weights = loo(log_like).psis_result.log_weights;
+
+julia> loo_pit(y, y_pred, log_weights)
+8-element DimArray{Float64,1} with dimensions:
+  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered
+ "Choate"            0.943511
+ "Deerfield"         0.63797
+ "Phillips Andover"  0.316697
+ "Phillips Exeter"   0.582252
+ "Hotchkiss"         0.295321
+ "Lawrenceville"     0.403318
+ "St. Paul's"        0.902508
+ "Mt. Hermon"        0.655275

        Calculate LOO-PIT values using as test quantity the square of the difference between each observation and mu.

        julia> using Statistics
+
+julia> mu = idata.posterior.mu;
+
+julia> T = y .- median(mu);
+
+julia> T_pred = y_pred .- mu;
+
+julia> loo_pit(T .^ 2, T_pred .^ 2, log_weights)
+8-element DimArray{Float64,1} with dimensions:
+  Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered
+ "Choate"            0.873577
+ "Deerfield"         0.243686
+ "Phillips Andover"  0.357563
+ "Phillips Exeter"   0.149908
+ "Hotchkiss"         0.435094
+ "Lawrenceville"     0.220627
+ "St. Paul's"        0.775086
+ "Mt. Hermon"        0.296706
        source
        PosteriorStats.r2_score — Function
        r2_score(y_true::AbstractVector, y_pred::AbstractArray) -> (; r2, r2_std)

        $R²$ for linear Bayesian regression models.[GelmanGoodrich2019]

        Arguments

        • y_true: Observed data of length noutputs
        • y_pred: Predicted data with size (ndraws[, nchains], noutputs)

        Examples

        julia> using ArviZExampleData
+
+julia> idata = load_example_data("regression1d");
+
+julia> y_true = idata.observed_data.y;
+
+julia> y_pred = PermutedDimsArray(idata.posterior_predictive.y, (:draw, :chain, :y_dim_0));
+
+julia> r2_score(y_true, y_pred) |> pairs
+pairs(::NamedTuple) with 2 entries:
+  :r2     => 0.683197
+  :r2_std => 0.0368838
        source

        Utilities

        PosteriorStats.smooth_data — Function
        smooth_data(y; dims=:, interp_method=CubicSpline, offset_frac=0.01)

        Smooth y along dims using interp_method.

        interp_method is a 2-argument callabale that takes the arguments y and x and returns a DataInterpolations.jl interpolation method, defaulting to a cubic spline interpolator.

        offset_frac is the fraction of the length of y to use as an offset when interpolating.

        source
        • Hyndman1996Rob J. Hyndman (1996) Computing and Graphing Highest Density Regions, Amer. Stat., 50(2): 120-6. DOI: 10.1080/00031305.1996.10474359jstor.
        • ChenShao1999Ming-Hui Chen & Qi-Man Shao (1999) Monte Carlo Estimation of Bayesian Credible and HPD Intervals, J Comput. Graph. Stat., 8:1, 69-92. DOI: 10.1080/10618600.1999.10474802jstor.
        • Vehtari2017Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544
        • LOOFAQAki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html
        • Watanabe2010Watanabe, S. Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory. 11(116):3571−3594, 2010. https://jmlr.csail.mit.edu/papers/v11/watanabe10a.html
        • Vehtari2017Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544
        • LOOFAQAki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html
        • YaoVehtari2018Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030
        • YaoVehtari2018Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030
        • YaoVehtari2018Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030
        • YaoVehtari2018Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030
        • Gabry2019Gabry, J., Simpson, D., Vehtari, A., Betancourt, M. & Gelman, A. Visualization in Bayesian Workflow. J. R. Stat. Soc. Ser. A Stat. Soc. 182, 389–402 (2019). doi: 10.1111/rssa.12378 arXiv: 1709.01449
        • GelmanGoodrich2019Andrew Gelman, Ben Goodrich, Jonah Gabry & Aki Vehtari (2019) R-squared for Bayesian Regression Models, The American Statistician, 73:3, 307-9, DOI: 10.1080/00031305.2018.1549100.
        \ No newline at end of file diff --git a/PosteriorStats/v0.2.0/assets/documenter.js b/PosteriorStats/v0.2.0/assets/documenter.js new file mode 100644 index 000000000..f5311607b --- /dev/null +++ b/PosteriorStats/v0.2.0/assets/documenter.js @@ -0,0 +1,889 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'minisearch': 'https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function () { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'minisearch'], function($, minisearch) { + +// In general, most search related things will have "search" as a prefix. +// To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +let results = []; +let timer = undefined; + +let data = documenterSearchIndex["docs"].map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; +}); + +// list below is the lunr 2.1.3 list minus the intersect with names(Base) +// (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) +// ideally we'd just filter the original list but it's not available as a variable +const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", +]); + +let index = new minisearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with search results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + boost: { title: 100 }, + fuzzy: 2, + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + tokenize: (string) => string.split(/[\s\-\.]+/), + }, +}); + +index.addAll(data); + +let filters = [...new Set(data.map((x) => x.category))]; +var modal_filters = make_modal_body_filters(filters); +var filter_results = []; + +$(document).on("keyup", ".documenter-search-input", function (event) { + // Adding a debounce to prevent disruptions from super-speed typing! + debounce(() => update_search(filter_results), 300); +}); + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + $(this).removeClass("search-filter-selected"); + } else { + $(this).addClass("search-filter-selected"); + } + + // Adding a debounce to prevent disruptions from crazy clicking! + debounce(() => get_filters(), 300); +}); + +/** + * A debounce function, takes a function and an optional timeout in milliseconds + * + * @function callback + * @param {number} timeout + */ +function debounce(callback, timeout = 300) { + clearTimeout(timer); + timer = setTimeout(callback, timeout); +} + +/** + * Make/Update the search component + * + * @param {string[]} selected_filters + */ +function update_search(selected_filters = []) { + let initial_search_body = ` +
        Type something to get started!
        + `; + + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + results = index.search(querystring, { + filter: (result) => { + // Filtering results + if (selected_filters.length === 0) { + return result.score >= 1; + } else { + return ( + result.score >= 1 && selected_filters.includes(result.category) + ); + } + }, + }); + + let search_result_container = ``; + let search_divider = `
        `; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + results.forEach(function (result) { + if (result.location) { + // Checking for duplication of results for the same page + if (!links.includes(result.location)) { + search_results += make_search_result(result, querystring); + count++; + } + + links.push(result.location); + } + }); + + let result_count = `
        ${count} result(s)
        `; + + search_result_container = ` +
        + ${modal_filters} + ${search_divider} + ${result_count} +
        + ${search_results} +
        +
        + `; + } else { + search_result_container = ` +
        + ${modal_filters} + ${search_divider} +
        0 result(s)
        +
        +
        No result found!
        + `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + filter_results = []; + modal_filters = make_modal_body_filters(filters, filter_results); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(initial_search_body); + } +} + +/** + * Make the modal filter html + * + * @param {string[]} filters + * @param {string[]} selected_filters + * @returns string + */ +function make_modal_body_filters(filters, selected_filters = []) { + let str = ``; + + filters.forEach((val) => { + if (selected_filters.includes(val)) { + str += `${val}`; + } else { + str += `${val}`; + } + }); + + let filter_html = ` +
        + Filters: + ${str} +
        + `; + + return filter_html; +} + +/** + * Make the result component given a minisearch result data object and the value of the search input as queryString. + * To view the result object structure, refer: https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ +function make_search_result(result, querystring) { + let search_divider = `
        `; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + + let textindex = new RegExp(`\\b${querystring}\\b`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`\\b${querystring}\\b`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
        +
        ${result.title}
        +
        ${result.category}
        +
        +

        + ${display_result} +

        +
        + ${display_link} +
        +         + ${search_divider} + `; + + return result_div; +} + +/** + * Get selected filters, remake the filter html and lastly update the search modal + */ +function get_filters() { + let ele = $(".search-filters .search-filter-selected").get(); + filter_results = ele.map((x) => $(x).text().toLowerCase()); + modal_filters = make_modal_body_filters(filters, filter_results); + update_search(filter_results); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let search_modal_header = ` +
        +
        +

        + + + + +

        +
        +
        + +
        +
        +`; + +let initial_search_body = ` +
        Type something to get started!
        +`; + +let search_modal_footer = ` + +`; + +$(document.body).append( + ` + + ` +); + +document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); +}); + +document.querySelector(".close-search-modal").addEventListener("click", () => { + closeModal(); +}); + +$(document).on("click", ".search-result-link", function () { + closeModal(); +}); + +document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; +}); + +// Functions to open and close a modal +function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); +} + +function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
        Type something to get started!
        + `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); +} + +document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/PosteriorStats/v0.2.0/assets/themes/documenter-dark.css b/PosteriorStats/v0.2.0/assets/themes/documenter-dark.css new file mode 100644 index 000000000..9f5449f4b --- /dev/null +++ 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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.button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#ad8100;box-shadow:none;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark 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.button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content 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html.theme--documenter-dark .navbar-dropdown,html.theme--documenter-dark .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--documenter-dark .navbar-dropdown.is-right{left:auto;right:0}html.theme--documenter-dark .navbar-divider{display:block}html.theme--documenter-dark .navbar>.container .navbar-brand,html.theme--documenter-dark .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--documenter-dark .navbar>.container .navbar-menu,html.theme--documenter-dark .container>.navbar .navbar-menu{margin-right:-.75rem}html.theme--documenter-dark .navbar.is-fixed-bottom-desktop,html.theme--documenter-dark .navbar.is-fixed-top-desktop{left:0;position:fixed;right:0;z-index:30}html.theme--documenter-dark 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a.navbar-item.is-active:not(:focus):not(:hover),html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--documenter-dark .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--documenter-dark .pagination{font-size:1rem;margin:-.25rem}html.theme--documenter-dark .pagination.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--documenter-dark .pagination.is-medium{font-size:1.25rem}html.theme--documenter-dark .pagination.is-large{font-size:1.5rem}html.theme--documenter-dark .pagination.is-rounded .pagination-previous,html.theme--documenter-dark #documenter .docs-sidebar 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+ Maintainer: @highlightjs/core-team + Website: https://highlightjs.org/ + License: see project LICENSE + Touched: 2021 +*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem} diff --git a/PosteriorStats/v0.2.0/assets/themeswap.js b/PosteriorStats/v0.2.0/assets/themeswap.js new file mode 100644 index 000000000..9f5eebe6a --- /dev/null +++ b/PosteriorStats/v0.2.0/assets/themeswap.js @@ -0,0 +1,84 @@ +// Small function to quickly swap out themes. Gets put into the tag.. +function set_theme_from_local_storage() { + // Initialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if (window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the users preference is for dark color scheme + var darkPreference = + window.matchMedia("(prefers-color-scheme: dark)").matches === true; + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; + var disabled = []; + var primaryLightTheme = null; + var primaryDarkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + if (ss.ownerNode.getAttribute("data-theme-primary") !== null) { + primaryLightTheme = themename; + } + // Check if the theme is primary dark theme so that we could store its name in darkTheme + if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) { + primaryDarkTheme = themename; + } + // If we find a matching theme (and it's not the default), we'll set active to non-null + if (themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if (themename !== theme) disabled.push(ss); + } + var activeTheme = null; + if (active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName("html")[0].className = "theme--" + theme; + activeTheme = theme; + } else { + // If we did _not_ find an active theme, then we need to fall back to the primary theme + // which can either be dark or light, depending on the user's OS preference. + var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme; + // In case it somehow happens that the relevant primary theme was not found in the + // preceding loop, we abort without doing anything. + if (activeTheme === null) { + console.error("Unable to determine primary theme."); + return; + } + // When switching to the primary light theme, then we must not have a class name + // for the tag. That's only for non-primary or the primary dark theme. + if (darkPreference) { + document.getElementsByTagName("html")[0].className = + "theme--" + activeTheme; + } else { + document.getElementsByTagName("html")[0].className = ""; + } + } + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // we'll disable all the stylesheets, except for the active one + ss.disabled = !(themename == activeTheme); + } +} +set_theme_from_local_storage(); diff --git a/PosteriorStats/v0.2.0/assets/warner.js b/PosteriorStats/v0.2.0/assets/warner.js new file mode 100644 index 000000000..3f6f5d008 --- /dev/null +++ b/PosteriorStats/v0.2.0/assets/warner.js @@ -0,0 +1,52 @@ +function maybeAddWarning() { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return; + } + + // Current version is not a version number, so we can't tell if it's the newest version. Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return; + } + + // Current version is newest version, so no need to add a warning. + if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { + return; + } + + // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. + if (document.body.querySelector('meta[name="robots"]') === null) { + const meta = document.createElement("meta"); + meta.name = "robots"; + meta.content = "noindex"; + + document.getElementsByTagName("head")[0].appendChild(meta); + } + + const div = document.createElement("div"); + div.classList.add("outdated-warning-overlay"); + const closer = document.createElement("button"); + closer.classList.add("outdated-warning-closer", "delete"); + closer.addEventListener("click", function () { + document.body.removeChild(div); + }); + const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE; + div.innerHTML = + 'This documentation is not for the latest stable release, but for either the development version or an older release.
        Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", maybeAddWarning); +} else { + maybeAddWarning(); +} diff --git a/PosteriorStats/v0.2.0/index.html b/PosteriorStats/v0.2.0/index.html new file mode 100644 index 000000000..31fd8855c --- /dev/null +++ b/PosteriorStats/v0.2.0/index.html @@ -0,0 +1 @@ +Home · PosteriorStats.jl
        GitHub

        PosteriorStats

        PosteriorStats implements widely-used and well-characterized statistical analyses for the Bayesian workflow. These functions generally estimate properties of posterior and/or posterior predictive distributions. The default implementations defined here operate on Monte Carlo samples.

        See the API for details.

        Extending this package

        The methods defined here are intended to be extended by two types of packages.

        • packages that implement data types for storing Monte Carlo samples
        • packages that implement other representations for posterior distributions than Monte Carlo draws
        \ No newline at end of file diff --git a/PosteriorStats/v0.2.0/search_index.js b/PosteriorStats/v0.2.0/search_index.js new file mode 100644 index 000000000..7a0063106 --- /dev/null +++ b/PosteriorStats/v0.2.0/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"api/#API","page":"API","title":"API","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"Pages = [\"stats.md\"]","category":"page"},{"location":"api/#Summary-statistics","page":"API","title":"Summary statistics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"SummaryStats\ndefault_diagnostics\ndefault_stats\ndefault_summary_stats\nsummarize","category":"page"},{"location":"api/#PosteriorStats.SummaryStats","page":"API","title":"PosteriorStats.SummaryStats","text":"struct SummaryStats{D, V<:(AbstractVector)}\n\nA container for a column table of values computed by summarize.\n\nThis object implements the Tables and TableTraits column table interfaces. It has a custom show method.\n\nSummaryStats behaves like an OrderedDict of columns, where the columns can be accessed using either Symbols or a 1-based integer index.\n\nname::String: The name of the collection of summary statistics, used as the table title in display.\ndata::Any: The summary statistics for each parameter. It must implement the Tables interface.\nparameter_names::AbstractVector: Names of the parameters\n\nSummaryStats([name::String,] data[, parameter_names])\nSummaryStats(data[, parameter_names]; name::String=\"SummaryStats\")\n\nConstruct a SummaryStats from tabular data with optional stats name and param_names.\n\ndata must not contain a column :parameter, as this is reserved for the parameter names, which are always in the first column.\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.default_diagnostics","page":"API","title":"PosteriorStats.default_diagnostics","text":"default_diagnostics(focus=Statistics.mean; kwargs...)\n\nDefault diagnostics to be computed with summarize.\n\nThe value of focus determines the diagnostics to be returned:\n\nStatistics.mean: mcse_mean, mcse_std, ess_tail, ess_bulk, rhat\nStatistics.median: mcse_median, ess_tail, ess_bulk, rhat\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.default_stats","page":"API","title":"PosteriorStats.default_stats","text":"default_stats(focus=Statistics.mean; prob_interval=0.94, kwargs...)\n\nDefault statistics to be computed with summarize.\n\nThe value of focus determines the statistics to be returned:\n\nStatistics.mean: mean, std, hdi_3%, hdi_97%\nStatistics.median: median, mad, eti_3%, eti_97%\n\nIf prob_interval is set to a different value than the default, then different HDI and ETI statistics are computed accordingly. hdi refers to the highest-density interval, while eti refers to the equal-tailed interval (i.e. the credible interval computed from symmetric quantiles).\n\nSee also: hdi\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.default_summary_stats","page":"API","title":"PosteriorStats.default_summary_stats","text":"default_summary_stats(focus=Statistics.mean; kwargs...)\n\nCombinatiton of default_stats and default_diagnostics to be used with summarize.\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.summarize","page":"API","title":"PosteriorStats.summarize","text":"summarize(data, stats_funs...; name=\"SummaryStats\", [var_names]) -> SummaryStats\n\nCompute the summary statistics in stats_funs on each param in data.\n\nstats_funs is a collection of functions that reduces a matrix with shape (draws, chains) to a scalar or a collection of scalars. Alternatively, an item in stats_funs may be a Pair of the form name => fun specifying the name to be used for the statistic or of the form (name1, ...) => fun when the function returns a collection. When the function returns a collection, the names in this latter format must be provided.\n\nIf no stats functions are provided, then those specified in default_summary_stats are computed.\n\nvar_names specifies the names of the parameters in data. If not provided, the names are inferred from data.\n\nTo support computing summary statistics from a custom object, overload this method specifying the type of data.\n\nSee also SummaryStats, default_summary_stats, default_stats, default_diagnostics.\n\nExamples\n\nCompute mean, std and the Monte Carlo standard error (MCSE) of the mean estimate:\n\njulia> using Statistics, StatsBase\n\njulia> x = randn(1000, 4, 3) .+ reshape(0:10:20, 1, 1, :);\n\njulia> summarize(x, mean, std, :mcse_mean => sem; name=\"Mean/Std\")\nMean/Std\n mean std mcse_mean\n 1 0.0003 0.990 0.016\n 2 10.02 0.988 0.016\n 3 19.98 0.988 0.016\n\nAvoid recomputing the mean by using mean_and_std, and provide parameter names:\n\njulia> summarize(x, (:mean, :std) => mean_and_std, mad; var_names=[:a, :b, :c])\nSummaryStats\n mean std mad\n a 0.000305 0.990 0.978\n b 10.0 0.988 0.995\n c 20.0 0.988 0.979\n\nNote that when an estimator and its MCSE are both computed, the MCSE is used to determine the number of significant digits that will be displayed.\n\njulia> summarize(x; var_names=[:a, :b, :c])\nSummaryStats\n mean std hdi_3% hdi_97% mcse_mean mcse_std ess_tail ess_bulk r ⋯\n a 0.0003 0.99 -1.92 1.78 0.016 0.012 3567 3663 1 ⋯\n b 10.02 0.99 8.17 11.9 0.016 0.011 3841 3906 1 ⋯\n c 19.98 0.99 18.1 21.9 0.016 0.012 3892 3749 1 ⋯\n 1 column omitted\n\nCompute just the statistics with an 89% HDI on all parameters, and provide the parameter names:\n\njulia> summarize(x, default_stats(; prob_interval=0.89)...; var_names=[:a, :b, :c])\nSummaryStats\n mean std hdi_5.5% hdi_94.5%\n a 0.000305 0.990 -1.63 1.52\n b 10.0 0.988 8.53 11.6\n c 20.0 0.988 18.5 21.6\n\nCompute the summary stats focusing on Statistics.median:\n\njulia> summarize(x, default_summary_stats(median)...; var_names=[:a, :b, :c])\nSummaryStats\n median mad eti_3% eti_97% mcse_median ess_tail ess_median rhat\n a 0.004 0.978 -1.83 1.89 0.020 3567 3336 1.00\n b 10.02 0.995 8.17 11.9 0.023 3841 3787 1.00\n c 19.99 0.979 18.1 21.9 0.020 3892 3829 1.00\n\n\n\n\n\n","category":"function"},{"location":"api/#General-statistics","page":"API","title":"General statistics","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"hdi\nhdi!","category":"page"},{"location":"api/#PosteriorStats.hdi","page":"API","title":"PosteriorStats.hdi","text":"hdi(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper)\n\nEstimate the unimodal highest density interval (HDI) of samples for the probability prob.\n\nThe HDI is the minimum width Bayesian credible interval (BCI). That is, it is the smallest possible interval containing (100*prob)% of the probability mass.[Hyndman1996]\n\nsamples is an array of shape (draws[, chains[, params...]]). If multiple parameters are present, then lower and upper are arrays with the shape (params...,), computed separately for each marginal.\n\nThis implementation uses the algorithm of [ChenShao1999].\n\nnote: Note\nAny default value of prob is arbitrary. The default value of prob=0.94 instead of a more common default like prob=0.95 is chosen to reminder the user of this arbitrariness.\n\n[Hyndman1996]: Rob J. Hyndman (1996) Computing and Graphing Highest Density Regions, Amer. Stat., 50(2): 120-6. DOI: 10.1080/00031305.1996.10474359 jstor.\n\n[ChenShao1999]: Ming-Hui Chen & Qi-Man Shao (1999) Monte Carlo Estimation of Bayesian Credible and HPD Intervals, J Comput. Graph. Stat., 8:1, 69-92. DOI: 10.1080/10618600.1999.10474802 jstor.\n\nExamples\n\nHere we calculate the 83% HDI for a normal random variable:\n\njulia> x = randn(2_000);\n\njulia> hdi(x; prob=0.83) |> pairs\npairs(::NamedTuple) with 2 entries:\n :lower => -1.38266\n :upper => 1.25982\n\nWe can also calculate the HDI for a 3-dimensional array of samples:\n\njulia> x = randn(1_000, 1, 1) .+ reshape(0:5:10, 1, 1, :);\n\njulia> hdi(x) |> pairs\npairs(::NamedTuple) with 2 entries:\n :lower => [-1.9674, 3.0326, 8.0326]\n :upper => [1.90028, 6.90028, 11.9003]\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.hdi!","page":"API","title":"PosteriorStats.hdi!","text":"hdi!(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper)\n\nA version of hdi that sorts samples in-place while computing the HDI.\n\n\n\n\n\n","category":"function"},{"location":"api/#LOO-and-WAIC","page":"API","title":"LOO and WAIC","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"AbstractELPDResult\nPSISLOOResult\nWAICResult\nelpd_estimates\ninformation_criterion\nloo\nwaic","category":"page"},{"location":"api/#PosteriorStats.AbstractELPDResult","page":"API","title":"PosteriorStats.AbstractELPDResult","text":"abstract type AbstractELPDResult\n\nAn abstract type representing the result of an ELPD computation.\n\nEvery subtype stores estimates of both the expected log predictive density (elpd) and the effective number of parameters p, as well as standard errors and pointwise estimates of each, from which other relevant estimates can be computed.\n\nSubtypes implement the following functions:\n\nelpd_estimates\ninformation_criterion\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.PSISLOOResult","page":"API","title":"PosteriorStats.PSISLOOResult","text":"Results of Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO).\n\nSee also: loo, AbstractELPDResult\n\nestimates: Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p)\npointwise: Pointwise estimates\npsis_result: Pareto-smoothed importance sampling (PSIS) results\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.WAICResult","page":"API","title":"PosteriorStats.WAICResult","text":"Results of computing the widely applicable information criterion (WAIC).\n\nSee also: waic, AbstractELPDResult\n\nestimates: Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p)\npointwise: Pointwise estimates\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.elpd_estimates","page":"API","title":"PosteriorStats.elpd_estimates","text":"elpd_estimates(result::AbstractELPDResult; pointwise=false) -> (; elpd, elpd_mcse, lpd)\n\nReturn the (E)LPD estimates from the result.\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.information_criterion","page":"API","title":"PosteriorStats.information_criterion","text":"information_criterion(elpd, scale::Symbol)\n\nCompute the information criterion for the given scale from the elpd estimate.\n\nscale must be one of (:deviance, :log, :negative_log).\n\nSee also: loo, waic\n\n\n\n\n\ninformation_criterion(result::AbstractELPDResult, scale::Symbol; pointwise=false)\n\nCompute information criterion for the given scale from the existing ELPD result.\n\nscale must be one of (:deviance, :log, :negative_log).\n\nIf pointwise=true, then pointwise estimates are returned.\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.loo","page":"API","title":"PosteriorStats.loo","text":"loo(log_likelihood; reff=nothing, kwargs...) -> PSISLOOResult{<:NamedTuple,<:NamedTuple}\n\nCompute the Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO). [Vehtari2017][LOOFAQ]\n\nlog_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]).\n\nKeywords\n\nreff::Union{Real,AbstractArray{<:Real}}: The relative effective sample size(s) of the likelihood values. If an array, it must have the same data dimensions as the corresponding log-likelihood variable. If not provided, then this is estimated using MCMCDiagnosticTools.ess.\nkwargs: Remaining keywords are forwarded to [PSIS.psis].\n\nSee also: PSISLOOResult, waic\n\n[Vehtari2017]: Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544\n\n[LOOFAQ]: Aki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html\n\nExamples\n\nManually compute R_mathrmeff and calculate PSIS-LOO of a model:\n\njulia> using ArviZExampleData, MCMCDiagnosticTools\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> reff = ess(log_like; kind=:basic, split_chains=1, relative=true);\n\njulia> loo(log_like; reff)\nPSISLOOResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.34\n\nand PSISResult with 500 draws, 4 chains, and 8 parameters\nPareto shape (k) diagnostic values:\n Count Min. ESS\n (-Inf, 0.5] good 7 (87.5%) 151\n (0.5, 0.7] okay 1 (12.5%) 446\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.waic","page":"API","title":"PosteriorStats.waic","text":"waic(log_likelihood::AbstractArray) -> WAICResult{<:NamedTuple,<:NamedTuple}\n\nCompute the widely applicable information criterion (WAIC).[Watanabe2010][Vehtari2017][LOOFAQ]\n\nlog_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]).\n\nSee also: WAICResult, loo\n\n[Watanabe2010]: Watanabe, S. Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory. 11(116):3571−3594, 2010. https://jmlr.csail.mit.edu/papers/v11/watanabe10a.html\n\n[Vehtari2017]: Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544\n\n[LOOFAQ]: Aki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html\n\nExamples\n\nCalculate WAIC of a model:\n\njulia> using ArviZExampleData\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> waic(log_like)\nWAICResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.33\n\n\n\n\n\n","category":"function"},{"location":"api/#Model-comparison","page":"API","title":"Model comparison","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"ModelComparisonResult\ncompare\nmodel_weights","category":"page"},{"location":"api/#PosteriorStats.ModelComparisonResult","page":"API","title":"PosteriorStats.ModelComparisonResult","text":"ModelComparisonResult\n\nResult of model comparison using ELPD.\n\nThis struct implements the Tables and TableTraits interfaces.\n\nEach field returns a collection of the corresponding entry for each model:\n\nname: Names of the models, if provided.\nrank: Ranks of the models (ordered by decreasing ELPD)\nelpd_diff: ELPD of a model subtracted from the largest ELPD of any model\nelpd_diff_mcse: Monte Carlo standard error of the ELPD difference\nweight: Model weights computed with weights_method\nelpd_result: AbstactELPDResults for each model, which can be used to access useful stats like ELPD estimates, pointwise estimates, and Pareto shape values for PSIS-LOO\nweights_method: Method used to compute model weights with model_weights\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.compare","page":"API","title":"PosteriorStats.compare","text":"compare(models; kwargs...) -> ModelComparisonResult\n\nCompare models based on their expected log pointwise predictive density (ELPD).\n\nThe ELPD is estimated either by Pareto smoothed importance sampling leave-one-out cross-validation (LOO) or using the widely applicable information criterion (WAIC). We recommend loo. Read more theory here - in a paper by some of the leading authorities on model comparison dx.doi.org/10.1111/1467-9868.00353\n\nArguments\n\nmodels: a Tuple, NamedTuple, or AbstractVector whose values are either AbstractELPDResult entries or any argument to elpd_method.\n\nKeywords\n\nweights_method::AbstractModelWeightsMethod=Stacking(): the method to be used to weight the models. See model_weights for details\nelpd_method=loo: a method that computes an AbstractELPDResult from an argument in models.\nsort::Bool=true: Whether to sort models by decreasing ELPD.\n\nReturns\n\nModelComparisonResult: A container for the model comparison results. The fields contain a similar collection to models.\n\nExamples\n\nCompare the centered and non centered models of the eight school problem using the defaults: loo and Stacking weights. A custom myloo method formates the inputs as expected by loo.\n\njulia> using ArviZExampleData\n\njulia> models = (\n centered=load_example_data(\"centered_eight\"),\n non_centered=load_example_data(\"non_centered_eight\"),\n );\n\njulia> function myloo(idata)\n log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1))\n return loo(log_like)\n end;\n\njulia> mc = compare(models; elpd_method=myloo)\n┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.\n└ @ PSIS ~/.julia/packages/PSIS/...\nModelComparisonResult with Stacking weights\n rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯\n non_centered 1 -31 1.4 0 0.0 1.0 0.9 ⋯\n centered 2 -31 1.4 0.06 0.067 0.0 0.9 ⋯\n 1 column omitted\njulia> mc.weight |> pairs\npairs(::NamedTuple) with 2 entries:\n :non_centered => 1.0\n :centered => 5.34175e-19\n\nCompare the same models from pre-computed PSIS-LOO results and computing BootstrappedPseudoBMA weights:\n\njulia> elpd_results = mc.elpd_result;\n\njulia> compare(elpd_results; weights_method=BootstrappedPseudoBMA())\nModelComparisonResult with BootstrappedPseudoBMA weights\n rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯\n non_centered 1 -31 1.4 0 0.0 0.52 0.9 ⋯\n centered 2 -31 1.4 0.06 0.067 0.48 0.9 ⋯\n 1 column omitted\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.model_weights","page":"API","title":"PosteriorStats.model_weights","text":"model_weights(elpd_results; method=Stacking())\nmodel_weights(method::AbstractModelWeightsMethod, elpd_results)\n\nCompute weights for each model in elpd_results using method.\n\nelpd_results is a Tuple, NamedTuple, or AbstractVector with AbstractELPDResult entries. The weights are returned in the same type of collection.\n\nStacking is the recommended approach, as it performs well even when the true data generating process is not included among the candidate models. See [YaoVehtari2018] for details.\n\nSee also: AbstractModelWeightsMethod, compare\n\n[YaoVehtari2018]: Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030\n\nExamples\n\nCompute Stacking weights for two models:\n\njulia> using ArviZExampleData\n\njulia> models = (\n centered=load_example_data(\"centered_eight\"),\n non_centered=load_example_data(\"non_centered_eight\"),\n );\n\njulia> elpd_results = map(models) do idata\n log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1))\n return loo(log_like)\n end;\n┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.\n└ @ PSIS ~/.julia/packages/PSIS/...\n\njulia> model_weights(elpd_results; method=Stacking()) |> pairs\npairs(::NamedTuple) with 2 entries:\n :centered => 5.34175e-19\n :non_centered => 1.0\n\nNow we compute BootstrappedPseudoBMA weights for the same models:\n\njulia> model_weights(elpd_results; method=BootstrappedPseudoBMA()) |> pairs\npairs(::NamedTuple) with 2 entries:\n :centered => 0.483723\n :non_centered => 0.516277\n\n\n\n\n\n","category":"function"},{"location":"api/","page":"API","title":"API","text":"The following model weighting methods are available","category":"page"},{"location":"api/","page":"API","title":"API","text":"AbstractModelWeightsMethod\nBootstrappedPseudoBMA\nPseudoBMA\nStacking","category":"page"},{"location":"api/#PosteriorStats.AbstractModelWeightsMethod","page":"API","title":"PosteriorStats.AbstractModelWeightsMethod","text":"abstract type AbstractModelWeightsMethod\n\nAn abstract type representing methods for computing model weights.\n\nSubtypes implement model_weights(method, elpd_results).\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.BootstrappedPseudoBMA","page":"API","title":"PosteriorStats.BootstrappedPseudoBMA","text":"struct BootstrappedPseudoBMA{R<:Random.AbstractRNG, T<:Real} <: AbstractModelWeightsMethod\n\nModel weighting method using pseudo Bayesian Model Averaging using Akaike-type weighting with the Bayesian bootstrap (pseudo-BMA+)[YaoVehtari2018].\n\nThe Bayesian bootstrap stabilizes the model weights.\n\nBootstrappedPseudoBMA(; rng=Random.default_rng(), samples=1_000, alpha=1)\nBootstrappedPseudoBMA(rng, samples, alpha)\n\nConstruct the method.\n\nrng::Random.AbstractRNG: The random number generator to use for the Bayesian bootstrap\nsamples::Int64: The number of samples to draw for bootstrapping\nalpha::Real: The shape parameter in the Dirichlet distribution used for the Bayesian bootstrap. The default (1) corresponds to a uniform distribution on the simplex.\n\nSee also: Stacking\n\n[YaoVehtari2018]: Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.PseudoBMA","page":"API","title":"PosteriorStats.PseudoBMA","text":"struct PseudoBMA <: AbstractModelWeightsMethod\n\nModel weighting method using pseudo Bayesian Model Averaging (pseudo-BMA) and Akaike-type weighting.\n\nPseudoBMA(; regularize=false)\nPseudoBMA(regularize)\n\nConstruct the method with optional regularization of the weights using the standard error of the ELPD estimate.\n\nnote: Note\nThis approach is not recommended, as it produces unstable weight estimates. It is recommended to instead use BootstrappedPseudoBMA to stabilize the weights or Stacking. For details, see [YaoVehtari2018].\n\n[YaoVehtari2018]: Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030\n\nSee also: Stacking\n\n\n\n\n\n","category":"type"},{"location":"api/#PosteriorStats.Stacking","page":"API","title":"PosteriorStats.Stacking","text":"struct Stacking{O<:Optim.AbstractOptimizer} <: AbstractModelWeightsMethod\n\nModel weighting using stacking of predictive distributions[YaoVehtari2018].\n\nStacking(; optimizer=Optim.LBFGS(), options=Optim.Options()\nStacking(optimizer[, options])\n\nConstruct the method, optionally customizing the optimization.\n\noptimizer::Optim.AbstractOptimizer: The optimizer to use for the optimization of the weights. The optimizer must support projected gradient optimization via a manifold field.\noptions::Optim.Options: The Optim options to use for the optimization of the weights.\n\nSee also: BootstrappedPseudoBMA\n\n[YaoVehtari2018]: Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030\n\n\n\n\n\n","category":"type"},{"location":"api/#Predictive-checks","page":"API","title":"Predictive checks","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"loo_pit\nr2_score","category":"page"},{"location":"api/#PosteriorStats.loo_pit","page":"API","title":"PosteriorStats.loo_pit","text":"loo_pit(y, y_pred, log_weights; kwargs...) -> Union{Real,AbstractArray}\n\nCompute leave-one-out probability integral transform (LOO-PIT) checks.\n\nArguments\n\ny: array of observations with shape (params...,)\ny_pred: array of posterior predictive samples with shape (draws, chains, params...).\nlog_weights: array of normalized log LOO importance weights with shape (draws, chains, params...).\n\nKeywords\n\nis_discrete: If not provided, then it is set to true iff elements of y and y_pred are all integer-valued. If true, then data are smoothed using smooth_data to make them non-discrete before estimating LOO-PIT values.\nkwargs: Remaining keywords are forwarded to smooth_data if data is discrete.\n\nReturns\n\npitvals: LOO-PIT values with same size as y. If y is a scalar, then pitvals is a scalar.\n\nLOO-PIT is a marginal posterior predictive check. If y_-i is the array y of observations with the ith observation left out, and y_i^* is a posterior prediction of the ith observation, then the LOO-PIT value for the ith observation is defined as\n\nP(y_i^* le y_i mid y_-i) = int_-infty^y_i p(y_i^* mid y_-i) mathrmd y_i^*\n\nThe LOO posterior predictions and the corresponding observations should have similar distributions, so if conditional predictive distributions are well-calibrated, then all LOO-PIT values should be approximately uniformly distributed on 0 1.[Gabry2019]\n\n[Gabry2019]: Gabry, J., Simpson, D., Vehtari, A., Betancourt, M. & Gelman, A. Visualization in Bayesian Workflow. J. R. Stat. Soc. Ser. A Stat. Soc. 182, 389–402 (2019). doi: 10.1111/rssa.12378 arXiv: 1709.01449\n\nExamples\n\nCalculate LOO-PIT values using as test quantity the observed values themselves.\n\njulia> using ArviZExampleData\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> y = idata.observed_data.obs;\n\njulia> y_pred = PermutedDimsArray(idata.posterior_predictive.obs, (:draw, :chain, :school));\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> log_weights = loo(log_like).psis_result.log_weights;\n\njulia> loo_pit(y, y_pred, log_weights)\n8-element DimArray{Float64,1} with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.943511\n \"Deerfield\" 0.63797\n \"Phillips Andover\" 0.316697\n \"Phillips Exeter\" 0.582252\n \"Hotchkiss\" 0.295321\n \"Lawrenceville\" 0.403318\n \"St. Paul's\" 0.902508\n \"Mt. Hermon\" 0.655275\n\nCalculate LOO-PIT values using as test quantity the square of the difference between each observation and mu.\n\njulia> using Statistics\n\njulia> mu = idata.posterior.mu;\n\njulia> T = y .- median(mu);\n\njulia> T_pred = y_pred .- mu;\n\njulia> loo_pit(T .^ 2, T_pred .^ 2, log_weights)\n8-element DimArray{Float64,1} with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.873577\n \"Deerfield\" 0.243686\n \"Phillips Andover\" 0.357563\n \"Phillips Exeter\" 0.149908\n \"Hotchkiss\" 0.435094\n \"Lawrenceville\" 0.220627\n \"St. Paul's\" 0.775086\n \"Mt. Hermon\" 0.296706\n\n\n\n\n\n","category":"function"},{"location":"api/#PosteriorStats.r2_score","page":"API","title":"PosteriorStats.r2_score","text":"r2_score(y_true::AbstractVector, y_pred::AbstractArray) -> (; r2, r2_std)\n\nR² for linear Bayesian regression models.[GelmanGoodrich2019]\n\nArguments\n\ny_true: Observed data of length noutputs\ny_pred: Predicted data with size (ndraws[, nchains], noutputs)\n\n[GelmanGoodrich2019]: Andrew Gelman, Ben Goodrich, Jonah Gabry & Aki Vehtari (2019) R-squared for Bayesian Regression Models, The American Statistician, 73:3, 307-9, DOI: 10.1080/00031305.2018.1549100.\n\nExamples\n\njulia> using ArviZExampleData\n\njulia> idata = load_example_data(\"regression1d\");\n\njulia> y_true = idata.observed_data.y;\n\njulia> y_pred = PermutedDimsArray(idata.posterior_predictive.y, (:draw, :chain, :y_dim_0));\n\njulia> r2_score(y_true, y_pred) |> pairs\npairs(::NamedTuple) with 2 entries:\n :r2 => 0.683197\n :r2_std => 0.0368838\n\n\n\n\n\n","category":"function"},{"location":"api/#Utilities","page":"API","title":"Utilities","text":"","category":"section"},{"location":"api/","page":"API","title":"API","text":"PosteriorStats.smooth_data","category":"page"},{"location":"api/#PosteriorStats.smooth_data","page":"API","title":"PosteriorStats.smooth_data","text":"smooth_data(y; dims=:, interp_method=CubicSpline, offset_frac=0.01)\n\nSmooth y along dims using interp_method.\n\ninterp_method is a 2-argument callabale that takes the arguments y and x and returns a DataInterpolations.jl interpolation method, defaulting to a cubic spline interpolator.\n\noffset_frac is the fraction of the length of y to use as an offset when interpolating.\n\n\n\n\n\n","category":"function"},{"location":"","page":"Home","title":"Home","text":"CurrentModule = PosteriorStats","category":"page"},{"location":"#PosteriorStats","page":"Home","title":"PosteriorStats","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"PosteriorStats implements widely-used and well-characterized statistical analyses for the Bayesian workflow. These functions generally estimate properties of posterior and/or posterior predictive distributions. The default implementations defined here operate on Monte Carlo samples.","category":"page"},{"location":"","page":"Home","title":"Home","text":"See the API for details.","category":"page"},{"location":"#Extending-this-package","page":"Home","title":"Extending this package","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"The methods defined here are intended to be extended by two types of packages.","category":"page"},{"location":"","page":"Home","title":"Home","text":"packages that implement data types for storing Monte Carlo samples\npackages that implement other representations for posterior distributions than Monte Carlo draws","category":"page"}] +} diff --git a/PosteriorStats/v0.2.0/siteinfo.js b/PosteriorStats/v0.2.0/siteinfo.js new file mode 100644 index 000000000..057c824fd --- /dev/null +++ b/PosteriorStats/v0.2.0/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v0.2.0"; diff --git a/PosteriorStats/versions.js b/PosteriorStats/versions.js index 268b25c80..46870d7be 100644 --- a/PosteriorStats/versions.js +++ b/PosteriorStats/versions.js @@ -1,7 +1,8 @@ var DOC_VERSIONS = [ "stable", + "v0.2", "v0.1", "dev", ]; -var DOCUMENTER_NEWEST = "v0.1.4"; +var DOCUMENTER_NEWEST = "v0.2.0"; var DOCUMENTER_STABLE = "stable"; diff --git a/index.json b/index.json index c0f271c70..dd78e7dc4 100644 --- a/index.json +++ b/index.json @@ -1 +1 @@ -[{"id":3,"pagetitle":"Home","title":"ArviZ.jl: Exploratory analysis of Bayesian models in Julia","ref":"/ArviZ/stable/#arvizjl","content":" ArviZ.jl: Exploratory analysis of Bayesian models in Julia ArviZ.jl is a Julia meta-package for exploratory analysis of Bayesian models. It is part of the ArviZ project , which also includes a related Python package . ArviZ consists of and re-exports the following subpackages, along with extensions integrating them with InferenceObjects: InferenceObjects.jl : a base package implementing the InferenceData type with utilities for building, saving, and working with it MCMCDiagnosticTools.jl : diagnostics for Markov Chain Monte Carlo methods PSIS.jl : Pareto-smoothed importance sampling PosteriorStats.jl : common statistical analyses for the Bayesian workflow Additional functionality can be loaded with the following packages: ArviZExampleData.jl : example InferenceData objects, useful for demonstration and testing ArviZPythonPlots.jl : Python ArviZ's library of plotting functions for Julia types See the navigation bar for more useful packages."},{"id":4,"pagetitle":"Home","title":"Installation","ref":"/ArviZ/stable/#installation","content":" Installation From the Julia REPL, type ] to enter the Pkg REPL mode and run pkg> add ArviZ"},{"id":5,"pagetitle":"Home","title":"Usage","ref":"/ArviZ/stable/#usage","content":" Usage See the Quickstart for example usage and the API Overview for description of functions."},{"id":6,"pagetitle":"Home","title":"Extending ArviZ.jl","ref":"/ArviZ/stable/#extendingarviz","content":" Extending ArviZ.jl To use a custom data type with ArviZ.jl, simply overload InferenceObjects.convert_to_inference_data to convert your input(s) to an InferenceObjects.InferenceData ."},{"id":9,"pagetitle":"API Overview","title":"API Overview","ref":"/ArviZ/stable/api/#api","content":" API Overview Data Dataset Diagnostics InferenceData Stats"},{"id":12,"pagetitle":"Data","title":"Data","ref":"/ArviZ/stable/api/data/#data-api","content":" Data ArviZ.from_mcmcchains ArviZ.from_samplechains InferenceObjects.from_netcdf InferenceObjects.to_netcdf"},{"id":13,"pagetitle":"Data","title":"Inference library converters","ref":"/ArviZ/stable/api/data/#Inference-library-converters","content":" Inference library converters"},{"id":14,"pagetitle":"Data","title":"ArviZ.from_mcmcchains","ref":"/ArviZ/stable/api/data/#ArviZ.from_mcmcchains","content":" ArviZ.from_mcmcchains — Function from_mcmcchains(posterior::MCMCChains.Chains; kwargs...) -> InferenceData\nfrom_mcmcchains(; kwargs...) -> InferenceData\nfrom_mcmcchains(\n posterior::MCMCChains.Chains,\n posterior_predictive,\n predictions,\n log_likelihood;\n kwargs...\n) -> InferenceData Convert data in an MCMCChains.Chains format into an InferenceData . Any keyword argument below without an an explicitly annotated type above is allowed, so long as it can be passed to convert_to_inference_data . Arguments posterior::MCMCChains.Chains : Draws from the posterior Keywords posterior_predictive::Any=nothing : Draws from the posterior predictive distribution or name(s) of predictive variables in posterior predictions : Out-of-sample predictions for the posterior. prior : Draws from the prior prior_predictive : Draws from the prior predictive distribution or name(s) of predictive variables in prior observed_data : Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values. constant_data : Model constants, data included in the model that are not modeled as random variables. Keys are parameter names. predictions_constant_data : Constants relevant to the model predictions (i.e. new x values in a linear regression). log_likelihood : Pointwise log-likelihood for the data. It is recommended to use this argument as a named tuple whose keys are observed variable names and whose values are log likelihood arrays. Alternatively, provide the name of variable in posterior containing log likelihoods. library=MCMCChains : Name of library that generated the chains coords : Map from named dimension to named indices dims : Map from variable name to names of its dimensions eltypes : Map from variable names to eltypes. This is primarily used to assign discrete eltypes to discrete variables that were stored in Chains as floats. Returns InferenceData : The data with groups corresponding to the provided data source"},{"id":15,"pagetitle":"Data","title":"ArviZ.from_samplechains","ref":"/ArviZ/stable/api/data/#ArviZ.from_samplechains","content":" ArviZ.from_samplechains — Function from_samplechains(\n posterior=nothing;\n prior=nothing,\n library=SampleChains,\n kwargs...,\n) -> InferenceData Convert SampleChains samples to an InferenceData . Either posterior or prior may be a SampleChains.AbstractChain or SampleChains.MultiChain object. For descriptions of remaining kwargs , see from_namedtuple . source"},{"id":16,"pagetitle":"Data","title":"IO / Conversion","ref":"/ArviZ/stable/api/data/#IO-/-Conversion","content":" IO / Conversion"},{"id":17,"pagetitle":"Data","title":"InferenceObjects.from_netcdf","ref":"/ArviZ/stable/api/data/#InferenceObjects.from_netcdf","content":" InferenceObjects.from_netcdf — Function from_netcdf(path::AbstractString; kwargs...) -> InferenceData Load an InferenceData from an unopened NetCDF file. Remaining kwargs are passed to NCDatasets.NCDataset . This method loads data eagerly. To instead load data lazily, pass an opened NCDataset to from_netcdf . Note This method requires that NCDatasets is loaded before it can be used. Examples julia> using InferenceObjects, NCDatasets\n\njulia> idata = from_netcdf(\"centered_eight.nc\")\nInferenceData with groups:\n > posterior\n > posterior_predictive\n > sample_stats\n > prior\n > observed_data from_netcdf(ds::NCDatasets.NCDataset; load_mode) -> InferenceData Load an InferenceData from an opened NetCDF file. load_mode defaults to :lazy , which avoids reading variables into memory. Operations on these arrays will be slow. load_mode can also be :eager , which copies all variables into memory. It is then safe to close ds . If load_mode is :lazy and ds is closed after constructing InferenceData , using the variable arrays will have undefined behavior. Examples Here is how we might load an InferenceData from an InferenceData lazily from a web-hosted NetCDF file. julia> using HTTP, InferenceObjects, NCDatasets\n\njulia> resp = HTTP.get(\"https://github.com/arviz-devs/arviz_example_data/blob/main/data/centered_eight.nc?raw=true\");\n\njulia> ds = NCDataset(\"centered_eight\", \"r\"; memory = resp.body);\n\njulia> idata = from_netcdf(ds)\nInferenceData with groups:\n > posterior\n > posterior_predictive\n > sample_stats\n > prior\n > observed_data\n\njulia> idata_copy = copy(idata); # disconnect from the loaded dataset\n\njulia> close(ds); source"},{"id":18,"pagetitle":"Data","title":"InferenceObjects.to_netcdf","ref":"/ArviZ/stable/api/data/#InferenceObjects.to_netcdf","content":" InferenceObjects.to_netcdf — Function to_netcdf(data, dest::AbstractString; group::Symbol=:posterior, kwargs...)\nto_netcdf(data, dest::NCDatasets.NCDataset; group::Symbol=:posterior) Write data to a NetCDF file. data is any type that can be converted to an InferenceData using convert_to_inference_data . If not an InferenceData , then group specifies which group the data represents. dest specifies either the path to the NetCDF file or an opened NetCDF file. If dest is a path, remaining kwargs are passed to NCDatasets.NCDataset . Note This method requires that NCDatasets is loaded before it can be used. Examples julia> using InferenceObjects, NCDatasets\n\njulia> idata = from_namedtuple((; x = randn(4, 100, 3), z = randn(4, 100)))\nInferenceData with groups:\n > posterior\n\njulia> to_netcdf(idata, \"data.nc\")\n\"data.nc\" source"},{"id":21,"pagetitle":"Dataset","title":"Dataset","ref":"/ArviZ/stable/api/dataset/#dataset-api","content":" Dataset InferenceObjects.Dataset InferenceObjects.convert_to_dataset InferenceObjects.namedtuple_to_dataset"},{"id":22,"pagetitle":"Dataset","title":"Type definition","ref":"/ArviZ/stable/api/dataset/#Type-definition","content":" Type definition"},{"id":23,"pagetitle":"Dataset","title":"InferenceObjects.Dataset","ref":"/ArviZ/stable/api/dataset/#InferenceObjects.Dataset","content":" InferenceObjects.Dataset — Type Dataset{L} <: DimensionalData.AbstractDimStack{L} Container of dimensional arrays sharing some dimensions. This type is an DimensionalData.AbstractDimStack that implements the same interface as DimensionalData.DimStack and has identical usage. When a Dataset is passed to Python, it is converted to an xarray.Dataset without copying the data. That is, the Python object shares the same memory as the Julia object. However, if an xarray.Dataset is passed to Julia, its data must be copied. Constructors Dataset(data::DimensionalData.AbstractDimArray...)\nDataset(data::Tuple{Vararg{<:DimensionalData.AbstractDimArray}})\nDataset(data::NamedTuple{Keys,Vararg{<:DimensionalData.AbstractDimArray}})\nDataset(\n data::NamedTuple,\n dims::Tuple{Vararg{DimensionalData.Dimension}};\n metadata=DimensionalData.NoMetadata(),\n) In most cases, use convert_to_dataset to create a Dataset instead of directly using a constructor. source"},{"id":24,"pagetitle":"Dataset","title":"General conversion","ref":"/ArviZ/stable/api/dataset/#General-conversion","content":" General conversion"},{"id":25,"pagetitle":"Dataset","title":"InferenceObjects.convert_to_dataset","ref":"/ArviZ/stable/api/dataset/#InferenceObjects.convert_to_dataset","content":" InferenceObjects.convert_to_dataset — Function convert_to_dataset(obj; group = :posterior, kwargs...) -> Dataset Convert a supported object to a Dataset . In most cases, this function calls convert_to_inference_data and returns the corresponding group . source"},{"id":26,"pagetitle":"Dataset","title":"InferenceObjects.namedtuple_to_dataset","ref":"/ArviZ/stable/api/dataset/#InferenceObjects.namedtuple_to_dataset","content":" InferenceObjects.namedtuple_to_dataset — Function namedtuple_to_dataset(data; kwargs...) -> Dataset Convert NamedTuple mapping variable names to arrays to a Dataset . Any non-array values will be converted to a 0-dimensional array. Keywords attrs::AbstractDict{<:AbstractString} : a collection of metadata to attach to the dataset, in addition to defaults. Values should be JSON serializable. library::Union{String,Module} : library used for performing inference. Will be attached to the attrs metadata. dims : a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are: Symbol : dimension name Type{<:DimensionsionalData.Dimension} : dimension type DimensionsionalData.Dimension : dimension, potentially with indices Nothing : no dimension name provided, dimension name is automatically generated coords : a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated. source"},{"id":27,"pagetitle":"Dataset","title":"DimensionalData","ref":"/ArviZ/stable/api/dataset/#DimensionalData","content":" DimensionalData As a DimensionalData.AbstractDimStack , Dataset also implements the AbstractDimStack API and can be used like a DimStack . See DimensionalData's documentation for example usage."},{"id":28,"pagetitle":"Dataset","title":"Tables inteface","ref":"/ArviZ/stable/api/dataset/#Tables-inteface","content":" Tables inteface Dataset implements the Tables interface. This allows Dataset s to be used as sources for any function that can accept a table. For example, it's straightforward to: write to CSV with CSV.jl flatten to a DataFrame with DataFrames.jl plot with StatsPlots.jl plot with AlgebraOfGraphics.jl"},{"id":31,"pagetitle":"Diagnostics","title":"Diagnostics","ref":"/ArviZ/stable/api/diagnostics/#diagnostics-api","content":" Diagnostics MCMCDiagnosticTools.AutocovMethod MCMCDiagnosticTools.BDAAutocovMethod MCMCDiagnosticTools.FFTAutocovMethod MCMCDiagnosticTools.bfmi MCMCDiagnosticTools.ess MCMCDiagnosticTools.ess_rhat MCMCDiagnosticTools.mcse MCMCDiagnosticTools.rhat MCMCDiagnosticTools.rstar"},{"id":32,"pagetitle":"Diagnostics","title":"Bayesian fraction of missing information","ref":"/ArviZ/stable/api/diagnostics/#bfmi","content":" Bayesian fraction of missing information"},{"id":33,"pagetitle":"Diagnostics","title":"MCMCDiagnosticTools.bfmi","ref":"/ArviZ/stable/api/diagnostics/#MCMCDiagnosticTools.bfmi","content":" MCMCDiagnosticTools.bfmi — Function bfmi(energy::AbstractVector{<:Real}) -> Real\nbfmi(energy::AbstractMatrix{<:Real}; dims::Int=1) -> AbstractVector{<:Real} Calculate the estimated Bayesian fraction of missing information (BFMI). When sampling with Hamiltonian Monte Carlo (HMC), BFMI quantifies how well momentum resampling matches the marginal energy distribution. The current advice is that values smaller than 0.3 indicate poor sampling. However, this threshold is provisional and may change. A BFMI value below the threshold often indicates poor adaptation of sampling parameters or that the target distribution has heavy tails that were not well explored by the Markov chain. For more information, see Section 6.1 of [Betancourt2018] or [Betancourt2016] for a complete account. energy is either a vector of Hamiltonian energies of draws or a matrix of energies of draws for multiple chains. dims indicates the dimension in energy that contains the draws. The default dims=1 assumes energy has the shape draws or (draws, chains) . If a different shape is provided, dims must be set accordingly. If energy is a vector, a single BFMI value is returned. Otherwise, a vector of BFMI values for each chain is returned. source"},{"id":34,"pagetitle":"Diagnostics","title":"Effective sample size and $\\widehat{R}$ diagnostic","ref":"/ArviZ/stable/api/diagnostics/#ess_rhat","content":" Effective sample size and $\\widehat{R}$ diagnostic"},{"id":35,"pagetitle":"Diagnostics","title":"MCMCDiagnosticTools.ess","ref":"/ArviZ/stable/api/diagnostics/#MCMCDiagnosticTools.ess","content":" MCMCDiagnosticTools.ess — Function ess(\n samples::AbstractArray{<:Union{Missing,Real}};\n kind=:bulk,\n relative::Bool=false,\n autocov_method=AutocovMethod(),\n split_chains::Int=2,\n maxlag::Int=250,\n kwargs...\n) Estimate the effective sample size (ESS) of the samples of shape (draws, [chains[, parameters...]]) with the autocov_method . Optionally, the kind of ESS estimate to be computed can be specified (see below). Some kind s accept additional kwargs . If relative is true , the relative ESS is returned, i.e. ess / (draws * chains) . split_chains indicates the number of chains each chain is split into. When split_chains > 1 , then the diagnostics check for within-chain convergence. When d = mod(draws, split_chains) > 0 , i.e. the chains cannot be evenly split, then 1 draw is discarded after each of the first d splits within each chain. There must be at least 3 draws in each chain after splitting. maxlag indicates the maximum lag for which autocovariance is computed and must be greater than 0. For a given estimand, it is recommended that the ESS is at least 100 * chains and that $\\widehat{R} < 1.01$ . [VehtariGelman2021] See also: AutocovMethod , FFTAutocovMethod , BDAAutocovMethod , rhat , ess_rhat , mcse Kinds of ESS estimates If kind isa a Symbol , it may take one of the following values: :bulk : basic ESS computed on rank-normalized draws. This kind diagnoses poor convergence in the bulk of the distribution due to trends or different locations of the chains. :tail : minimum of the quantile-ESS for the symmetric quantiles where tail_prob=0.1 is the probability in the tails. This kind diagnoses poor convergence in the tails of the distribution. If this kind is chosen, kwargs may contain a tail_prob keyword. :basic : basic ESS, equivalent to specifying kind=Statistics.mean . Note While Bulk-ESS is conceptually related to basic ESS, it is well-defined even if the chains do not have finite variance. [VehtariGelman2021] For each parameter, rank-normalization proceeds by first ranking the inputs using \"tied ranking\" and then transforming the ranks to normal quantiles so that the result is standard normally distributed. This transform is monotonic. Otherwise, kind specifies one of the following estimators, whose ESS is to be estimated: Statistics.mean Statistics.median Statistics.std StatsBase.mad Base.Fix2(Statistics.quantile, p::Real) source ess(data::InferenceData; kwargs...) -> Dataset\ness(data::Dataset; kwargs...) -> Dataset Calculate the effective sample size (ESS) for each parameter in the data. source"},{"id":36,"pagetitle":"Diagnostics","title":"MCMCDiagnosticTools.rhat","ref":"/ArviZ/stable/api/diagnostics/#MCMCDiagnosticTools.rhat","content":" MCMCDiagnosticTools.rhat — Function rhat(samples::AbstractArray{Union{Real,Missing}}; kind::Symbol=:rank, split_chains=2) Compute the $\\widehat{R}$ diagnostics for each parameter in samples of shape (draws, [chains[, parameters...]]) . [VehtariGelman2021] kind indicates the kind of $\\widehat{R}$ to compute (see below). split_chains indicates the number of chains each chain is split into. When split_chains > 1 , then the diagnostics check for within-chain convergence. When d = mod(draws, split_chains) > 0 , i.e. the chains cannot be evenly split, then 1 draw is discarded after each of the first d splits within each chain. See also ess , ess_rhat , rstar Kinds of $\\widehat{R}$ The following kind s are supported: :rank : maximum of $\\widehat{R}$ with kind=:bulk and kind=:tail . :bulk : basic $\\widehat{R}$ computed on rank-normalized draws. This kind diagnoses poor convergence in the bulk of the distribution due to trends or different locations of the chains. :tail : $\\widehat{R}$ computed on draws folded around the median and then rank-normalized. This kind diagnoses poor convergence in the tails of the distribution due to different scales of the chains. :basic : Classic $\\widehat{R}$ . source rhat(data::InferenceData; kwargs...) -> Dataset\nrhat(data::Dataset; kwargs...) -> Dataset Calculate the $\\widehat{R}$ diagnostic for each parameter in the data. source"},{"id":37,"pagetitle":"Diagnostics","title":"MCMCDiagnosticTools.ess_rhat","ref":"/ArviZ/stable/api/diagnostics/#MCMCDiagnosticTools.ess_rhat","content":" MCMCDiagnosticTools.ess_rhat — Function ess_rhat(\n samples::AbstractArray{<:Union{Missing,Real}};\n kind::Symbol=:rank,\n kwargs...,\n) -> NamedTuple{(:ess, :rhat)} Estimate the effective sample size and $\\widehat{R}$ of the samples of shape (draws, [chains[, parameters...]]) . When both ESS and $\\widehat{R}$ are needed, this method is often more efficient than calling ess and rhat separately. See rhat for a description of supported kind s and ess for a description of kwargs . source ess_rhat(data::InferenceData; kwargs...) -> Dataset\ness_rhat(data::Dataset; kwargs...) -> Dataset Calculate the effective sample size (ESS) and $\\widehat{R}$ diagnostic for each parameter in the data. source The following autocovariance methods are supported:"},{"id":38,"pagetitle":"Diagnostics","title":"MCMCDiagnosticTools.AutocovMethod","ref":"/ArviZ/stable/api/diagnostics/#MCMCDiagnosticTools.AutocovMethod","content":" MCMCDiagnosticTools.AutocovMethod — Type AutocovMethod <: AbstractAutocovMethod The AutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains. It is is based on the discussion by [VehtariGelman2021] and uses the biased estimator of the autocovariance, as discussed by [Geyer1992] . source"},{"id":39,"pagetitle":"Diagnostics","title":"MCMCDiagnosticTools.FFTAutocovMethod","ref":"/ArviZ/stable/api/diagnostics/#MCMCDiagnosticTools.FFTAutocovMethod","content":" MCMCDiagnosticTools.FFTAutocovMethod — Type FFTAutocovMethod <: AbstractAutocovMethod The FFTAutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains. The algorithm is the same as the one of AutocovMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation. Info To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl . source"},{"id":40,"pagetitle":"Diagnostics","title":"MCMCDiagnosticTools.BDAAutocovMethod","ref":"/ArviZ/stable/api/diagnostics/#MCMCDiagnosticTools.BDAAutocovMethod","content":" MCMCDiagnosticTools.BDAAutocovMethod — Type BDAAutocovMethod <: AbstractAutocovMethod The BDAAutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains. It is is based on the discussion by [VehtariGelman2021] . and uses the variogram estimator of the autocorrelation function discussed by [BDA3] . source"},{"id":41,"pagetitle":"Diagnostics","title":"Monte Carlo standard error","ref":"/ArviZ/stable/api/diagnostics/#mcse","content":" Monte Carlo standard error"},{"id":42,"pagetitle":"Diagnostics","title":"MCMCDiagnosticTools.mcse","ref":"/ArviZ/stable/api/diagnostics/#MCMCDiagnosticTools.mcse","content":" MCMCDiagnosticTools.mcse — Function mcse(samples::AbstractArray{<:Union{Missing,Real}}; kind=Statistics.mean, kwargs...) Estimate the Monte Carlo standard errors (MCSE) of the estimator kind applied to samples of shape (draws, [chains[, parameters...]]) . See also: ess Kinds of MCSE estimates The estimator whose MCSE should be estimated is specified with kind . kind must accept a vector of the same eltype as samples and return a real estimate. For the following estimators, the effective sample size ess and an estimate of the asymptotic variance are used to compute the MCSE, and kwargs are forwarded to ess : Statistics.mean Statistics.median Statistics.std Base.Fix2(Statistics.quantile, p::Real) For other estimators, the subsampling bootstrap method (SBM) [FlegalJones2011] [Flegal2012] is used as a fallback, and the only accepted kwargs are batch_size , which indicates the size of the overlapping batches used to estimate the MCSE, defaulting to floor(Int, sqrt(draws * chains)) . Note that SBM tends to underestimate the MCSE, especially for highly autocorrelated chains. One should verify that autocorrelation is low by checking the bulk- and tail-ESS values. source mcse(data::InferenceData; kwargs...) -> Dataset\nmcse(data::Dataset; kwargs...) -> Dataset Calculate the Monte Carlo standard error (MCSE) for each parameter in the data. source"},{"id":43,"pagetitle":"Diagnostics","title":"$R^*$ diagnostic","ref":"/ArviZ/stable/api/diagnostics/#rstar","content":" $R^*$ diagnostic"},{"id":44,"pagetitle":"Diagnostics","title":"MCMCDiagnosticTools.rstar","ref":"/ArviZ/stable/api/diagnostics/#MCMCDiagnosticTools.rstar","content":" MCMCDiagnosticTools.rstar — Function rstar(\n rng::Random.AbstractRNG=Random.default_rng(),\n classifier,\n samples,\n chain_indices::AbstractVector{Int};\n subset::Real=0.7,\n split_chains::Int=2,\n verbosity::Int=0,\n) Compute the $R^*$ convergence statistic of the table samples with the classifier . samples must be either an AbstractMatrix , an AbstractVector , or a table (i.e. implements the Tables.jl interface) whose rows are draws and whose columns are parameters. chain_indices indicates the chain ids of each row of samples . This method supports ragged chains, i.e. chains of nonequal lengths. source rstar(\n rng::Random.AbstractRNG=Random.default_rng(),\n classifier,\n samples::AbstractArray{<:Real};\n subset::Real=0.7,\n split_chains::Int=2,\n verbosity::Int=0,\n) Compute the $R^*$ convergence statistic of the samples with the classifier . samples is an array of draws with the shape (draws, [chains[, parameters...]]) .` This implementation is an adaption of algorithms 1 and 2 described by Lambert and Vehtari. The classifier has to be a supervised classifier of the MLJ framework (see the MLJ documentation for a list of supported models). It is trained with a subset of the samples from each chain. Each chain is split into split_chains separate chains to additionally check for within-chain convergence. The training of the classifier can be inspected by adjusting the verbosity level. If the classifier is deterministic, i.e., if it predicts a class, the value of the $R^*$ statistic is returned (algorithm 1). If the classifier is probabilistic, i.e., if it outputs probabilities of classes, the scaled Poisson-binomial distribution of the $R^*$ statistic is returned (algorithm 2). Note The correctness of the statistic depends on the convergence of the classifier used internally in the statistic. Examples julia> using MLJBase, MLJIteration, EvoTrees, Statistics, StatisticalMeasures\n\njulia> samples = fill(4.0, 100, 3, 2); One can compute the distribution of the $R^*$ statistic (algorithm 2) with a probabilistic classifier. For instance, we can use a gradient-boosted trees model with nrounds = 100 sequentially stacked trees and learning rate eta = 0.05 : julia> model = EvoTreeClassifier(; nrounds=100, eta=0.05);\n\njulia> distribution = rstar(model, samples);\n\njulia> round(mean(distribution); digits=2)\n1.0f0 Note, however, that it is recommended to determine nrounds based on early-stopping. With the MLJ framework, this can be achieved in the following way (see the MLJ documentation for additional explanations): julia> model = IteratedModel(;\n model=EvoTreeClassifier(; eta=0.05),\n iteration_parameter=:nrounds,\n resampling=Holdout(),\n measures=log_loss,\n controls=[Step(5), Patience(2), NumberLimit(100)],\n retrain=true,\n );\n\njulia> distribution = rstar(model, samples);\n\njulia> round(mean(distribution); digits=2)\n1.0f0 For deterministic classifiers, a single $R^*$ statistic (algorithm 1) is returned. Deterministic classifiers can also be derived from probabilistic classifiers by e.g. predicting the mode. In MLJ this corresponds to a pipeline of models. julia> evotree_deterministic = Pipeline(model; operation=predict_mode);\n\njulia> value = rstar(evotree_deterministic, samples);\n\njulia> round(value; digits=2)\n1.0 References Lambert, B., & Vehtari, A. (2020). $R^*$ : A robust MCMC convergence diagnostic with uncertainty using decision tree classifiers. source rstar(\n rng::Random.AbstractRNG=Random.default_rng(),\n classifier,\n data::Union{InferenceData,Dataset};\n kwargs...,\n) Calculate the $R^*$ diagnostic for the data. source Betancourt2018 Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME] Betancourt2016 Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME] VehtariGelman2021 Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008 VehtariGelman2021 Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008 VehtariGelman2021 Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008 Geyer1992 Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483. VehtariGelman2021 Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008 BDA3 Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press. FlegalJones2011 Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf Flegal2012 Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18"},{"id":47,"pagetitle":"InferenceData","title":"InferenceData","ref":"/ArviZ/stable/api/inference_data/#inferencedata-api","content":" InferenceData InferenceObjects.InferenceData Base.cat Base.getindex Base.getproperty Base.merge Base.propertynames Base.setindex InferenceObjects.convert_to_inference_data InferenceObjects.from_dict InferenceObjects.from_namedtuple"},{"id":48,"pagetitle":"InferenceData","title":"Type definition","ref":"/ArviZ/stable/api/inference_data/#Type-definition","content":" Type definition"},{"id":49,"pagetitle":"InferenceData","title":"InferenceObjects.InferenceData","ref":"/ArviZ/stable/api/inference_data/#InferenceObjects.InferenceData","content":" InferenceObjects.InferenceData — Type InferenceData{group_names,group_types} Container for inference data storage using DimensionalData. This object implements the InferenceData schema . Internally, groups are stored in a NamedTuple , which can be accessed using parent(::InferenceData) . Constructors InferenceData(groups::NamedTuple)\nInferenceData(; groups...) Construct an inference data from either a NamedTuple or keyword arguments of groups. Groups must be Dataset objects. Instead of directly creating an InferenceData , use the exported from_xyz functions or convert_to_inference_data . source"},{"id":50,"pagetitle":"InferenceData","title":"Property interface","ref":"/ArviZ/stable/api/inference_data/#Property-interface","content":" Property interface"},{"id":51,"pagetitle":"InferenceData","title":"Base.getproperty","ref":"/ArviZ/stable/api/inference_data/#Base.getproperty","content":" Base.getproperty — Function getproperty(data::InferenceData, name::Symbol) -> Dataset Get group with the specified name . source"},{"id":52,"pagetitle":"InferenceData","title":"Base.propertynames","ref":"/ArviZ/stable/api/inference_data/#Base.propertynames","content":" Base.propertynames — Function propertynames(data::InferenceData) -> Tuple{Symbol} Get names of groups source"},{"id":53,"pagetitle":"InferenceData","title":"Indexing interface","ref":"/ArviZ/stable/api/inference_data/#Indexing-interface","content":" Indexing interface"},{"id":54,"pagetitle":"InferenceData","title":"Base.getindex","ref":"/ArviZ/stable/api/inference_data/#Base.getindex","content":" Base.getindex — Function Base.getindex(data::InferenceData, groups::Symbol; coords...) -> Dataset\nBase.getindex(data::InferenceData, groups; coords...) -> InferenceData Return a new InferenceData containing the specified groups sliced to the specified coords. coords specifies a dimension name mapping to an index, a DimensionalData.Selector , or an IntervalSets.AbstractInterval . If one or more groups lack the specified dimension, a warning is raised but can be ignored. All groups that contain the dimension must also contain the specified indices, or an exception will be raised. Examples Select data from all groups for just the specified id values. julia> using InferenceObjects, DimensionalData\n\njulia> idata = from_namedtuple(\n (θ=randn(4, 100, 4), τ=randn(4, 100));\n prior=(θ=randn(4, 100, 4), τ=randn(4, 100)),\n observed_data=(y=randn(4),),\n dims=(θ=[:id], y=[:id]),\n coords=(id=[\"a\", \"b\", \"c\", \"d\"],),\n )\nInferenceData with groups:\n > posterior\n > prior\n > observed_data\n\njulia> idata.posterior\nDataset with dimensions:\n Dim{:chain} Sampled 1:4 ForwardOrdered Regular Points,\n Dim{:draw} Sampled 1:100 ForwardOrdered Regular Points,\n Dim{:id} Categorical String[a, b, c, d] ForwardOrdered\nand 2 layers:\n :θ Float64 dims: Dim{:chain}, Dim{:draw}, Dim{:id} (4×100×4)\n :τ Float64 dims: Dim{:chain}, Dim{:draw} (4×100)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2022-08-11T11:15:21.4\"\n\njulia> idata_sel = idata[id=At([\"a\", \"b\"])]\nInferenceData with groups:\n > posterior\n > prior\n > observed_data\n\njulia> idata_sel.posterior\nDataset with dimensions:\n Dim{:chain} Sampled 1:4 ForwardOrdered Regular Points,\n Dim{:draw} Sampled 1:100 ForwardOrdered Regular Points,\n Dim{:id} Categorical String[a, b] ForwardOrdered\nand 2 layers:\n :θ Float64 dims: Dim{:chain}, Dim{:draw}, Dim{:id} (4×100×2)\n :τ Float64 dims: Dim{:chain}, Dim{:draw} (4×100)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2022-08-11T11:15:21.4\" Select data from just the posterior, returning a Dataset if the indices index more than one element from any of the variables: julia> idata[:observed_data, id=At([\"a\"])]\nDataset with dimensions:\n Dim{:id} Categorical String[a] ForwardOrdered\nand 1 layer:\n :y Float64 dims: Dim{:id} (1)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2022-08-11T11:19:25.982\" Note that if a single index is provided, the behavior is still to slice so that the dimension is preserved. source"},{"id":55,"pagetitle":"InferenceData","title":"Base.setindex","ref":"/ArviZ/stable/api/inference_data/#Base.setindex","content":" Base.setindex — Function Base.setindex(data::InferenceData, group::Dataset, name::Symbol) -> InferenceData Create a new InferenceData containing the group with the specified name . If a group with name is already in data , it is replaced. source"},{"id":56,"pagetitle":"InferenceData","title":"Iteration interface","ref":"/ArviZ/stable/api/inference_data/#Iteration-interface","content":" Iteration interface InferenceData also implements the same iteration interface as its underlying NamedTuple . That is, iterating over an InferenceData iterates over its groups."},{"id":57,"pagetitle":"InferenceData","title":"General conversion","ref":"/ArviZ/stable/api/inference_data/#General-conversion","content":" General conversion"},{"id":58,"pagetitle":"InferenceData","title":"InferenceObjects.convert_to_inference_data","ref":"/ArviZ/stable/api/inference_data/#InferenceObjects.convert_to_inference_data","content":" InferenceObjects.convert_to_inference_data — Function convert_to_inference_data(obj; group, kwargs...) -> InferenceData Convert a supported object to an InferenceData object. If obj converts to a single dataset, group specifies which dataset in the resulting InferenceData that is. See convert_to_dataset Arguments obj can be many objects. Basic supported types are: InferenceData : return unchanged Dataset / DimensionalData.AbstractDimStack : add to InferenceData as the only group NamedTuple / AbstractDict : create a Dataset as the only group AbstractArray{<:Real} : create a Dataset as the only group, given an arbitrary name, if the name is not set More specific types may be documented separately. Keywords group::Symbol = :posterior : If obj converts to a single dataset, assign the resulting dataset to this group. dims : a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are: Symbol : dimension name Type{<:DimensionsionalData.Dimension} : dimension type DimensionsionalData.Dimension : dimension, potentially with indices Nothing : no dimension name provided, dimension name is automatically generated coords : a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated. kwargs : remaining keywords forwarded to converter functions source"},{"id":59,"pagetitle":"InferenceData","title":"InferenceObjects.from_dict","ref":"/ArviZ/stable/api/inference_data/#InferenceObjects.from_dict","content":" InferenceObjects.from_dict — Function from_dict(posterior::AbstractDict; kwargs...) -> InferenceData Convert a Dict to an InferenceData . Arguments posterior : The data to be converted. Its strings must be Symbol or AbstractString , and its values must be arrays. Keywords posterior_predictive::Any=nothing : Draws from the posterior predictive distribution sample_stats::Any=nothing : Statistics of the posterior sampling process predictions::Any=nothing : Out-of-sample predictions for the posterior. prior::Dict=nothing : Draws from the prior prior_predictive::Any=nothing : Draws from the prior predictive distribution sample_stats_prior::Any=nothing : Statistics of the prior sampling process observed_data::NamedTuple : Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values. constant_data::NamedTuple : Model constants, data included in the model which is not modeled as a random variable. Keys are parameter names and values. predictions_constant_data::NamedTuple : Constants relevant to the model predictions (i.e. new x values in a linear regression). log_likelihood : Pointwise log-likelihood for the data. It is recommended to use this argument as a NamedTuple whose keys are observed variable names and whose values are log likelihood arrays. library : Name of library that generated the draws coords : Map from named dimension to named indices dims : Map from variable name to names of its dimensions Returns InferenceData : The data with groups corresponding to the provided data Examples using InferenceObjects\nnchains = 2\nndraws = 100\n\ndata = Dict(\n :x => rand(ndraws, nchains),\n :y => randn(2, ndraws, nchains),\n :z => randn(3, 2, ndraws, nchains),\n)\nidata = from_dict(data) source"},{"id":60,"pagetitle":"InferenceData","title":"InferenceObjects.from_namedtuple","ref":"/ArviZ/stable/api/inference_data/#InferenceObjects.from_namedtuple","content":" InferenceObjects.from_namedtuple — Function from_namedtuple(posterior::NamedTuple; kwargs...) -> InferenceData\nfrom_namedtuple(posterior::Vector{Vector{<:NamedTuple}}; kwargs...) -> InferenceData\nfrom_namedtuple(\n posterior::NamedTuple,\n sample_stats::Any,\n posterior_predictive::Any,\n predictions::Any,\n log_likelihood::Any;\n kwargs...\n) -> InferenceData Convert a NamedTuple or container of NamedTuple s to an InferenceData . If containers are passed, they are flattened into a single NamedTuple with array elements whose first dimensions correspond to the dimensions of the containers. Arguments posterior : The data to be converted. It may be of the following types: ::NamedTuple : The keys are the variable names and the values are arrays with dimensions (ndraws, nchains[, sizes...]) . ::Vector{Vector{<:NamedTuple}} : A vector of length nchains whose elements have length ndraws . Keywords posterior_predictive::Any=nothing : Draws from the posterior predictive distribution sample_stats::Any=nothing : Statistics of the posterior sampling process predictions::Any=nothing : Out-of-sample predictions for the posterior. prior=nothing : Draws from the prior. Accepts the same types as posterior . prior_predictive::Any=nothing : Draws from the prior predictive distribution sample_stats_prior::Any=nothing : Statistics of the prior sampling process observed_data::NamedTuple : Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values. constant_data::NamedTuple : Model constants, data included in the model which is not modeled as a random variable. Keys are parameter names and values. predictions_constant_data::NamedTuple : Constants relevant to the model predictions (i.e. new x values in a linear regression). log_likelihood : Pointwise log-likelihood for the data. It is recommended to use this argument as a NamedTuple whose keys are observed variable names and whose values are log likelihood arrays. library : Name of library that generated the draws coords : Map from named dimension to named indices dims : Map from variable name to names of its dimensions Returns InferenceData : The data with groups corresponding to the provided data Note If a NamedTuple is provided for observed_data , constant_data , or predictions constant data`, any non-array values (e.g. integers) are converted to 0-dimensional arrays. Examples using InferenceObjects\nnchains = 2\nndraws = 100\n\ndata1 = (\n x=rand(ndraws, nchains), y=randn(ndraws, nchains, 2), z=randn(ndraws, nchains, 3, 2)\n)\nidata1 = from_namedtuple(data1)\n\ndata2 = [[(x=rand(), y=randn(2), z=randn(3, 2)) for _ in 1:ndraws] for _ in 1:nchains];\nidata2 = from_namedtuple(data2) source"},{"id":61,"pagetitle":"InferenceData","title":"General functions","ref":"/ArviZ/stable/api/inference_data/#General-functions","content":" General functions"},{"id":62,"pagetitle":"InferenceData","title":"Base.cat","ref":"/ArviZ/stable/api/inference_data/#Base.cat","content":" Base.cat — Function cat(data::InferenceData...; [groups=keys(data[1]),] dims) -> InferenceData Concatenate InferenceData objects along the specified dimension dims . Only the groups in groups are concatenated. Remaining groups are merge d into the new InferenceData object. Examples Here is how we can concatenate all groups of two InferenceData objects along the existing chain dimension: julia> coords = (; a_dim=[\"x\", \"y\", \"z\"]);\n\njulia> dims = dims=(; a=[:a_dim]);\n\njulia> data = Dict(:a => randn(100, 4, 3), :b => randn(100, 4));\n\njulia> idata = from_dict(data; coords=coords, dims=dims)\nInferenceData with groups:\n > posterior\n\njulia> idata_cat1 = cat(idata, idata; dims=:chain)\nInferenceData with groups:\n > posterior\n\njulia> idata_cat1.posterior\nDataset with dimensions:\n Dim{:draw},\n Dim{:chain},\n Dim{:a_dim} Categorical{String} String[\"x\", \"y\", \"z\"] ForwardOrdered\nand 2 layers:\n :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim} (100×8×3)\n :b Float64 dims: Dim{:draw}, Dim{:chain} (100×8)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-04-03T18:41:35.779\" Alternatively, we can concatenate along a new run dimension, which will be created. julia> idata_cat2 = cat(idata, idata; dims=:run)\nInferenceData with groups:\n > posterior\n\njulia> idata_cat2.posterior\nDataset with dimensions:\n Dim{:draw},\n Dim{:chain},\n Dim{:a_dim} Categorical{String} String[\"x\", \"y\", \"z\"] ForwardOrdered,\n Dim{:run}\nand 2 layers:\n :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim}, Dim{:run} (100×4×3×2)\n :b Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:run} (100×4×2)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-04-03T18:41:35.779\" We can also concatenate only a subset of groups and merge the rest, which is useful when some groups are present only in some of the InferenceData objects or will be identical in all of them: julia> observed_data = Dict(:y => randn(10));\n\njulia> idata2 = from_dict(data; observed_data=observed_data, coords=coords, dims=dims)\nInferenceData with groups:\n > posterior\n > observed_data\n\njulia> idata_cat3 = cat(idata, idata2; groups=(:posterior,), dims=:run)\nInferenceData with groups:\n > posterior\n > observed_data\n\njulia> idata_cat3.posterior\nDataset with dimensions:\n Dim{:draw},\n Dim{:chain},\n Dim{:a_dim} Categorical{String} String[\"x\", \"y\", \"z\"] ForwardOrdered,\n Dim{:run}\nand 2 layers:\n :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim}, Dim{:run} (100×4×3×2)\n :b Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:run} (100×4×2)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-04-03T18:41:35.779\"\n\njulia> idata_cat3.observed_data\nDataset with dimensions: Dim{:y_dim_1}\nand 1 layer:\n :y Float64 dims: Dim{:y_dim_1} (10)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-02-17T15:11:00.59\" source"},{"id":63,"pagetitle":"InferenceData","title":"Base.merge","ref":"/ArviZ/stable/api/inference_data/#Base.merge","content":" Base.merge — Function merge(data::InferenceData...) -> InferenceData Merge InferenceData objects. The result contains all groups in data and others . If a group appears more than once, the one that occurs last is kept. See also: cat Examples Here we merge an InferenceData containing only a posterior group with one containing only a prior group to create a new one containing both groups. julia> idata1 = from_dict(Dict(:a => randn(100, 4, 3), :b => randn(100, 4)))\nInferenceData with groups:\n > posterior\n\njulia> idata2 = from_dict(; prior=Dict(:a => randn(100, 1, 3), :c => randn(100, 1)))\nInferenceData with groups:\n > prior\n\njulia> idata_merged = merge(idata1, idata2)\nInferenceData with groups:\n > posterior\n > prior source"},{"id":66,"pagetitle":"Stats","title":"Stats","ref":"/ArviZ/stable/api/stats/#stats-api","content":" Stats PSIS.PSISResult PosteriorStats.AbstractELPDResult PosteriorStats.AbstractModelWeightsMethod PosteriorStats.BootstrappedPseudoBMA PosteriorStats.ModelComparisonResult PosteriorStats.PSISLOOResult PosteriorStats.PseudoBMA PosteriorStats.Stacking PosteriorStats.SummaryStats PosteriorStats.WAICResult PSIS.PSISPlots.paretoshapeplot PSIS.ess_is PSIS.psis PSIS.psis! PosteriorStats.compare PosteriorStats.default_diagnostics PosteriorStats.default_stats PosteriorStats.default_summary_stats PosteriorStats.elpd_estimates PosteriorStats.hdi PosteriorStats.hdi! PosteriorStats.information_criterion PosteriorStats.loo PosteriorStats.loo_pit PosteriorStats.model_weights PosteriorStats.r2_score PosteriorStats.smooth_data PosteriorStats.summarize PosteriorStats.waic StatsBase.summarystats"},{"id":67,"pagetitle":"Stats","title":"Summary statistics","ref":"/ArviZ/stable/api/stats/#Summary-statistics","content":" Summary statistics"},{"id":68,"pagetitle":"Stats","title":"PosteriorStats.SummaryStats","ref":"/ArviZ/stable/api/stats/#PosteriorStats.SummaryStats","content":" PosteriorStats.SummaryStats — Type A container for a column table of values computed by summarize . This object implements the Tables and TableTraits interfaces and has a custom show method. name : The name of the collection of summary statistics, used as the table title in display. data : The summary statistics for each parameter, with an optional first column parameter containing the parameter names. source"},{"id":69,"pagetitle":"Stats","title":"PosteriorStats.default_summary_stats","ref":"/ArviZ/stable/api/stats/#PosteriorStats.default_summary_stats","content":" PosteriorStats.default_summary_stats — Function default_summary_stats(focus=Statistics.mean; kwargs...) Combinatiton of default_stats and default_diagnostics to be used with summarize . source"},{"id":70,"pagetitle":"Stats","title":"PosteriorStats.default_stats","ref":"/ArviZ/stable/api/stats/#PosteriorStats.default_stats","content":" PosteriorStats.default_stats — Function default_stats(focus=Statistics.mean; prob_interval=0.94, kwargs...) Default statistics to be computed with summarize . The value of focus determines the statistics to be returned: Statistics.mean : mean , std , hdi_3% , hdi_97% Statistics.median : median , mad , eti_3% , eti_97% If prob_interval is set to a different value than the default, then different HDI and ETI statistics are computed accordingly. hdi refers to the highest-density interval, while eti refers to the equal-tailed interval (i.e. the credible interval computed from symmetric quantiles). See also: hdi source"},{"id":71,"pagetitle":"Stats","title":"PosteriorStats.default_diagnostics","ref":"/ArviZ/stable/api/stats/#PosteriorStats.default_diagnostics","content":" PosteriorStats.default_diagnostics — Function default_diagnostics(focus=Statistics.mean; kwargs...) Default diagnostics to be computed with summarize . The value of focus determines the diagnostics to be returned: Statistics.mean : mcse_mean , mcse_std , ess_tail , ess_bulk , rhat Statistics.median : mcse_median , ess_tail , ess_bulk , rhat source"},{"id":72,"pagetitle":"Stats","title":"PosteriorStats.summarize","ref":"/ArviZ/stable/api/stats/#PosteriorStats.summarize","content":" PosteriorStats.summarize — Function summarize(data, stats_funs...; name=\"SummaryStats\", [var_names]) -> SummaryStats Compute the summary statistics in stats_funs on each param in data . stats_funs is a collection of functions that reduces a matrix with shape (draws, chains) to a scalar or a collection of scalars. Alternatively, an item in stats_funs may be a Pair of the form name => fun specifying the name to be used for the statistic or of the form (name1, ...) => fun when the function returns a collection. When the function returns a collection, the names in this latter format must be provided. If no stats functions are provided, then those specified in default_summary_stats are computed. var_names specifies the names of the parameters in data . If not provided, the names are inferred from data . To support computing summary statistics from a custom object, overload this method specifying the type of data . See also SummaryStats , default_summary_stats , default_stats , default_diagnostics . Examples Compute mean , std and the Monte Carlo standard error (MCSE) of the mean estimate: julia> using Statistics, StatsBase\n\njulia> x = randn(1000, 4, 3) .+ reshape(0:10:20, 1, 1, :);\n\njulia> summarize(x, mean, std, :mcse_mean => sem; name=\"Mean/Std\")\nMean/Std\n mean std mcse_mean\n 1 0.0003 0.990 0.016\n 2 10.02 0.988 0.016\n 3 19.98 0.988 0.016 Avoid recomputing the mean by using mean_and_std , and provide parameter names: julia> summarize(x, (:mean, :std) => mean_and_std, mad; var_names=[:a, :b, :c])\nSummaryStats\n mean std mad\n a 0.000305 0.990 0.978\n b 10.0 0.988 0.995\n c 20.0 0.988 0.979 Note that when an estimator and its MCSE are both computed, the MCSE is used to determine the number of significant digits that will be displayed. julia> summarize(x; var_names=[:a, :b, :c])\nSummaryStats\n mean std hdi_3% hdi_97% mcse_mean mcse_std ess_tail ess_bulk r ⋯\n a 0.0003 0.99 -1.92 1.78 0.016 0.012 3567 3663 1 ⋯\n b 10.02 0.99 8.17 11.9 0.016 0.011 3841 3906 1 ⋯\n c 19.98 0.99 18.1 21.9 0.016 0.012 3892 3749 1 ⋯\n 1 column omitted Compute just the statistics with an 89% HDI on all parameters, and provide the parameter names: julia> summarize(x, default_stats(; prob_interval=0.89)...; var_names=[:a, :b, :c])\nSummaryStats\n mean std hdi_5.5% hdi_94.5%\n a 0.000305 0.990 -1.63 1.52\n b 10.0 0.988 8.53 11.6\n c 20.0 0.988 18.5 21.6 Compute the summary stats focusing on Statistics.median : julia> summarize(x, default_summary_stats(median)...; var_names=[:a, :b, :c])\nSummaryStats\n median mad eti_3% eti_97% mcse_median ess_tail ess_median rhat\n a 0.004 0.978 -1.83 1.89 0.020 3567 3336 1.00\n b 10.02 0.995 8.17 11.9 0.023 3841 3787 1.00\n c 19.99 0.979 18.1 21.9 0.020 3892 3829 1.00 source"},{"id":73,"pagetitle":"Stats","title":"StatsBase.summarystats","ref":"/ArviZ/stable/api/stats/#StatsBase.summarystats","content":" StatsBase.summarystats — Function summarystats(data::InferenceData; group=:posterior, kwargs...) -> SummaryStats\nsummarystats(data::Dataset; kwargs...) -> SummaryStats Compute default summary statistics for the data using summarize . source"},{"id":74,"pagetitle":"Stats","title":"General statistics","ref":"/ArviZ/stable/api/stats/#General-statistics","content":" General statistics"},{"id":75,"pagetitle":"Stats","title":"PosteriorStats.hdi","ref":"/ArviZ/stable/api/stats/#PosteriorStats.hdi","content":" PosteriorStats.hdi — Function hdi(data::InferenceData; kwargs...) -> Dataset\nhdi(data::Dataset; kwargs...) -> Dataset Calculate the highest density interval (HDI) for each parameter in the data. source hdi(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper) Estimate the unimodal highest density interval (HDI) of samples for the probability prob . The HDI is the minimum width Bayesian credible interval (BCI). That is, it is the smallest possible interval containing (100*prob) % of the probability mass. [Hyndman1996] samples is an array of shape (draws[, chains[, params...]]) . If multiple parameters are present, then lower and upper are arrays with the shape (params...,) , computed separately for each marginal. This implementation uses the algorithm of [ChenShao1999] . Note Any default value of prob is arbitrary. The default value of prob=0.94 instead of a more common default like prob=0.95 is chosen to reminder the user of this arbitrariness. Examples Here we calculate the 83% HDI for a normal random variable: julia> x = randn(2_000);\n\njulia> hdi(x; prob=0.83) |> pairs\npairs(::NamedTuple) with 2 entries:\n :lower => -1.38266\n :upper => 1.25982 We can also calculate the HDI for a 3-dimensional array of samples: julia> x = randn(1_000, 1, 1) .+ reshape(0:5:10, 1, 1, :);\n\njulia> hdi(x) |> pairs\npairs(::NamedTuple) with 2 entries:\n :lower => [-1.9674, 3.0326, 8.0326]\n :upper => [1.90028, 6.90028, 11.9003] source"},{"id":76,"pagetitle":"Stats","title":"PosteriorStats.hdi!","ref":"/ArviZ/stable/api/stats/#PosteriorStats.hdi!","content":" PosteriorStats.hdi! — Function hdi!(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper) A version of hdi that sorts samples in-place while computing the HDI. source"},{"id":77,"pagetitle":"Stats","title":"PosteriorStats.r2_score","ref":"/ArviZ/stable/api/stats/#PosteriorStats.r2_score","content":" PosteriorStats.r2_score — Function r2_score(idata::InferenceData; y_name, y_pred_name) -> (; r2, r2_std) Compute $R²$ from idata , automatically formatting the predictions to the correct shape. Keywords y_name : Name of observed data variable in idata.observed_data . If not provided, then the only observed data variable is used. y_pred_name : Name of posterior predictive variable in idata.posterior_predictive . If not provided, then y_name is used. Examples julia> using ArviZExampleData, PosteriorStats\n\njulia> idata = load_example_data(\"regression10d\");\n\njulia> r2_score(idata) |> pairs\npairs(::NamedTuple) with 2 entries:\n :r2 => 0.998385\n :r2_std => 0.000100621 source r2_score(y_true::AbstractVector, y_pred::AbstractVecOrMat) -> (; r2, r2_std) $R²$ for linear Bayesian regression models. [GelmanGoodrich2019] Arguments y_true : Observed data of length noutputs y_pred : Predicted data with size (ndraws[, nchains], noutputs) Examples julia> using ArviZExampleData\n\njulia> idata = load_example_data(\"regression1d\");\n\njulia> y_true = idata.observed_data.y;\n\njulia> y_pred = PermutedDimsArray(idata.posterior_predictive.y, (:draw, :chain, :y_dim_0));\n\njulia> r2_score(y_true, y_pred) |> pairs\npairs(::NamedTuple) with 2 entries:\n :r2 => 0.683197\n :r2_std => 0.0368838 source"},{"id":78,"pagetitle":"Stats","title":"Pareto-smoothed importance sampling","ref":"/ArviZ/stable/api/stats/#Pareto-smoothed-importance-sampling","content":" Pareto-smoothed importance sampling"},{"id":79,"pagetitle":"Stats","title":"PSIS.PSISResult","ref":"/ArviZ/stable/api/stats/#PSIS.PSISResult","content":" PSIS.PSISResult — Type PSISResult Result of Pareto-smoothed importance sampling (PSIS) using psis . Properties log_weights : un-normalized Pareto-smoothed log weights weights : normalized Pareto-smoothed weights (allocates a copy) pareto_shape : Pareto $k=ξ$ shape parameter nparams : number of parameters in log_weights ndraws : number of draws in log_weights nchains : number of chains in log_weights reff : the ratio of the effective sample size of the unsmoothed importance ratios and the actual sample size. ess : estimated effective sample size of estimate of mean using smoothed importance samples (see ess_is ) tail_length : length of the upper tail of log_weights that was smoothed tail_dist : the generalized Pareto distribution that was fit to the tail of log_weights . Note that the tail weights are scaled to have a maximum of 1, so tail_dist * exp(maximum(log_ratios)) is the corresponding fit directly to the tail of log_ratios . normalized::Bool :indicates whether log_weights are log-normalized along the sample dimensions. Diagnostic The pareto_shape parameter $k=ξ$ of the generalized Pareto distribution tail_dist can be used to diagnose reliability and convergence of estimates using the importance weights [VehtariSimpson2021] . if $k < \\frac{1}{3}$ , importance sampling is stable, and importance sampling (IS) and PSIS both are reliable. if $k ≤ \\frac{1}{2}$ , then the importance ratio distributon has finite variance, and the central limit theorem holds. As $k$ approaches the upper bound, IS becomes less reliable, while PSIS still works well but with a higher RMSE. if $\\frac{1}{2} < k ≤ 0.7$ , then the variance is infinite, and IS can behave quite poorly. However, PSIS works well in this regime. if $0.7 < k ≤ 1$ , then it quickly becomes impractical to collect enough importance weights to reliably compute estimates, and importance sampling is not recommended. if $k > 1$ , then neither the variance nor the mean of the raw importance ratios exists. The convergence rate is close to zero, and bias can be large with practical sample sizes. See PSISPlots.paretoshapeplot for a diagnostic plot. source"},{"id":80,"pagetitle":"Stats","title":"PSIS.ess_is","ref":"/ArviZ/stable/api/stats/#PSIS.ess_is","content":" PSIS.ess_is — Function ess_is(weights; reff=1) Estimate effective sample size (ESS) for importance sampling over the sample dimensions. Given normalized weights $w_{1:n}$ , the ESS is estimated using the L2-norm of the weights: \\[\\mathrm{ESS}(w_{1:n}) = \\frac{r_{\\mathrm{eff}}}{\\sum_{i=1}^n w_i^2}\\] where $r_{\\mathrm{eff}}$ is the relative efficiency of the log_weights . ess_is(result::PSISResult; bad_shape_nan=true) Estimate ESS for Pareto-smoothed importance sampling. Note ESS estimates for Pareto shape values $k > 0.7$ , which are unreliable and misleadingly high, are set to NaN . To avoid this, set bad_shape_nan=false . source"},{"id":81,"pagetitle":"Stats","title":"PSIS.PSISPlots.paretoshapeplot","ref":"/ArviZ/stable/api/stats/#PSIS.PSISPlots.paretoshapeplot","content":" PSIS.PSISPlots.paretoshapeplot — Function paretoshapeplot(values; showlines=false, ...)\nparetoshapeplot!(values; showlines=false, kwargs...) Plot shape parameters of fitted Pareto tail distributions for diagnosing convergence. values may be either a vector of Pareto shape parameters or a PSIS.PSISResult . If showlines==true , horizontal lines indicating relevant Pareto shape thresholds are drawn. See PSIS.PSISResult for an explanation of the thresholds. All remaining kwargs are forwarded to the plotting function. See psis , PSISResult . Examples using PSIS, Distributions, Plots\nproposal = Normal()\ntarget = TDist(7)\nx = rand(proposal, 1_000, 100)\nlog_ratios = logpdf.(target, x) .- logpdf.(proposal, x)\nresult = psis(log_ratios)\nparetoshapeplot(result) We can also plot the Pareto shape parameters directly: paretoshapeplot(result.pareto_shape) We can also use plot directly: plot(result.pareto_shape; showlines=true) source"},{"id":82,"pagetitle":"Stats","title":"PSIS.psis","ref":"/ArviZ/stable/api/stats/#PSIS.psis","content":" PSIS.psis — Function psis(log_ratios, reff = 1.0; kwargs...) -> PSISResult\npsis!(log_ratios, reff = 1.0; kwargs...) -> PSISResult Compute Pareto smoothed importance sampling (PSIS) log weights [VehtariSimpson2021] . While psis computes smoothed log weights out-of-place, psis! smooths them in-place. Arguments log_ratios : an array of logarithms of importance ratios, with size (draws, [chains, [parameters...]]) , where chains>1 would be used when chains are generated using Markov chain Monte Carlo. reff::Union{Real,AbstractArray} : the ratio(s) of effective sample size of log_ratios and the actual sample size reff = ess/(draws * chains) , used to account for autocorrelation, e.g. due to Markov chain Monte Carlo. If an array, it must have the size (parameters...,) to match log_ratios . Keywords warn=true : If true , warning messages are delivered normalize=true : If true , the log-weights will be log-normalized so that exp.(log_weights) sums to 1 along the sample dimensions. Returns result : a PSISResult object containing the results of the Pareto-smoothing. A warning is raised if the Pareto shape parameter $k ≥ 0.7$ . See PSISResult for details and PSISPlots.paretoshapeplot for a diagnostic plot. source"},{"id":83,"pagetitle":"Stats","title":"PSIS.psis!","ref":"/ArviZ/stable/api/stats/#PSIS.psis!","content":" PSIS.psis! — Function psis(log_ratios, reff = 1.0; kwargs...) -> PSISResult\npsis!(log_ratios, reff = 1.0; kwargs...) -> PSISResult Compute Pareto smoothed importance sampling (PSIS) log weights [VehtariSimpson2021] . While psis computes smoothed log weights out-of-place, psis! smooths them in-place. Arguments log_ratios : an array of logarithms of importance ratios, with size (draws, [chains, [parameters...]]) , where chains>1 would be used when chains are generated using Markov chain Monte Carlo. reff::Union{Real,AbstractArray} : the ratio(s) of effective sample size of log_ratios and the actual sample size reff = ess/(draws * chains) , used to account for autocorrelation, e.g. due to Markov chain Monte Carlo. If an array, it must have the size (parameters...,) to match log_ratios . Keywords warn=true : If true , warning messages are delivered normalize=true : If true , the log-weights will be log-normalized so that exp.(log_weights) sums to 1 along the sample dimensions. Returns result : a PSISResult object containing the results of the Pareto-smoothing. A warning is raised if the Pareto shape parameter $k ≥ 0.7$ . See PSISResult for details and PSISPlots.paretoshapeplot for a diagnostic plot. source"},{"id":84,"pagetitle":"Stats","title":"LOO and WAIC","ref":"/ArviZ/stable/api/stats/#LOO-and-WAIC","content":" LOO and WAIC"},{"id":85,"pagetitle":"Stats","title":"PosteriorStats.AbstractELPDResult","ref":"/ArviZ/stable/api/stats/#PosteriorStats.AbstractELPDResult","content":" PosteriorStats.AbstractELPDResult — Type abstract type AbstractELPDResult An abstract type representing the result of an ELPD computation. Every subtype stores estimates of both the expected log predictive density ( elpd ) and the effective number of parameters p , as well as standard errors and pointwise estimates of each, from which other relevant estimates can be computed. Subtypes implement the following functions: elpd_estimates information_criterion source"},{"id":86,"pagetitle":"Stats","title":"PosteriorStats.PSISLOOResult","ref":"/ArviZ/stable/api/stats/#PosteriorStats.PSISLOOResult","content":" PosteriorStats.PSISLOOResult — Type Results of Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO). See also: loo , AbstractELPDResult estimates : Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p) pointwise : Pointwise estimates psis_result : Pareto-smoothed importance sampling (PSIS) results source"},{"id":87,"pagetitle":"Stats","title":"PosteriorStats.WAICResult","ref":"/ArviZ/stable/api/stats/#PosteriorStats.WAICResult","content":" PosteriorStats.WAICResult — Type Results of computing the widely applicable information criterion (WAIC). See also: waic , AbstractELPDResult estimates : Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p) pointwise : Pointwise estimates source"},{"id":88,"pagetitle":"Stats","title":"PosteriorStats.elpd_estimates","ref":"/ArviZ/stable/api/stats/#PosteriorStats.elpd_estimates","content":" PosteriorStats.elpd_estimates — Function elpd_estimates(result::AbstractELPDResult; pointwise=false) -> (; elpd, elpd_mcse, lpd) Return the (E)LPD estimates from the result . source"},{"id":89,"pagetitle":"Stats","title":"PosteriorStats.information_criterion","ref":"/ArviZ/stable/api/stats/#PosteriorStats.information_criterion","content":" PosteriorStats.information_criterion — Function information_criterion(elpd, scale::Symbol) Compute the information criterion for the given scale from the elpd estimate. scale must be one of (:deviance, :log, :negative_log) . See also: loo , waic source information_criterion(result::AbstractELPDResult, scale::Symbol; pointwise=false) Compute information criterion for the given scale from the existing ELPD result . scale must be one of (:deviance, :log, :negative_log) . If pointwise=true , then pointwise estimates are returned. source"},{"id":90,"pagetitle":"Stats","title":"PosteriorStats.loo","ref":"/ArviZ/stable/api/stats/#PosteriorStats.loo","content":" PosteriorStats.loo — Function loo(data::Dataset; [var_name::Symbol,] kwargs...) -> PSISLOOResult{<:NamedTuple,<:Dataset}\nloo(data::InferenceData; [var_name::Symbol,] kwargs...) -> PSISLOOResult{<:NamedTuple,<:Dataset} Compute PSIS-LOO from log-likelihood values in data . If more than one log-likelihood variable is present, then var_name must be provided. Examples Calculate PSIS-LOO of a model: julia> using ArviZExampleData, PosteriorStats\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> loo(idata)\nPSISLOOResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.34\n\nand PSISResult with 500 draws, 4 chains, and 8 parameters\nPareto shape (k) diagnostic values:\n Count Min. ESS\n (-Inf, 0.5] good 6 (75.0%) 135\n (0.5, 0.7] okay 2 (25.0%) 421 source loo(log_likelihood; reff=nothing, kwargs...) -> PSISLOOResult{<:NamedTuple,<:NamedTuple} Compute the Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO). [Vehtari2017] [LOOFAQ] log_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]) . Keywords reff::Union{Real,AbstractArray{<:Real}} : The relative effective sample size(s) of the likelihood values. If an array, it must have the same data dimensions as the corresponding log-likelihood variable. If not provided, then this is estimated using MCMCDiagnosticTools.ess . kwargs : Remaining keywords are forwarded to [ PSIS.psis ]. See also: PSISLOOResult , waic Examples Manually compute $R_\\mathrm{eff}$ and calculate PSIS-LOO of a model: julia> using ArviZExampleData, MCMCDiagnosticTools\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> reff = ess(log_like; kind=:basic, split_chains=1, relative=true);\n\njulia> loo(log_like; reff)\nPSISLOOResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.34\n\nand PSISResult with 500 draws, 4 chains, and 8 parameters\nPareto shape (k) diagnostic values:\n Count Min. ESS\n (-Inf, 0.5] good 7 (87.5%) 151\n (0.5, 0.7] okay 1 (12.5%) 446 source"},{"id":91,"pagetitle":"Stats","title":"PosteriorStats.waic","ref":"/ArviZ/stable/api/stats/#PosteriorStats.waic","content":" PosteriorStats.waic — Function waic(data::Dataset; [var_name::Symbol]) -> WAICResult{<:NamedTuple,<:Dataset}\nwaic(data::InferenceData; [var_name::Symbol]) -> WAICResult{<:NamedTuple,<:Dataset} Compute WAIC from log-likelihood values in data . If more than one log-likelihood variable is present, then var_name must be provided. Examples Calculate WAIC of a model: julia> using ArviZExampleData, PosteriorStats\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> waic(idata)\nWAICResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.33 source waic(log_likelihood::AbstractArray) -> WAICResult{<:NamedTuple,<:NamedTuple} Compute the widely applicable information criterion (WAIC). [Watanabe2010] [Vehtari2017] [LOOFAQ] log_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]) . See also: WAICResult , loo Examples Calculate WAIC of a model: julia> using ArviZExampleData\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> waic(log_like)\nWAICResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.33 source"},{"id":92,"pagetitle":"Stats","title":"Model comparison","ref":"/ArviZ/stable/api/stats/#Model-comparison","content":" Model comparison"},{"id":93,"pagetitle":"Stats","title":"PosteriorStats.ModelComparisonResult","ref":"/ArviZ/stable/api/stats/#PosteriorStats.ModelComparisonResult","content":" PosteriorStats.ModelComparisonResult — Type ModelComparisonResult Result of model comparison using ELPD. This struct implements the Tables and TableTraits interfaces. Each field returns a collection of the corresponding entry for each model: name : Names of the models, if provided. rank : Ranks of the models (ordered by decreasing ELPD) elpd_diff : ELPD of a model subtracted from the largest ELPD of any model elpd_diff_mcse : Monte Carlo standard error of the ELPD difference weight : Model weights computed with weights_method elpd_result : AbstactELPDResult s for each model, which can be used to access useful stats like ELPD estimates, pointwise estimates, and Pareto shape values for PSIS-LOO weights_method : Method used to compute model weights with model_weights source"},{"id":94,"pagetitle":"Stats","title":"PosteriorStats.compare","ref":"/ArviZ/stable/api/stats/#PosteriorStats.compare","content":" PosteriorStats.compare — Function compare(models; kwargs...) -> ModelComparisonResult Compare models based on their expected log pointwise predictive density (ELPD). The ELPD is estimated either by Pareto smoothed importance sampling leave-one-out cross-validation (LOO) or using the widely applicable information criterion (WAIC). We recommend loo. Read more theory here - in a paper by some of the leading authorities on model comparison dx.doi.org/10.1111/1467-9868.00353 Arguments models : a Tuple , NamedTuple , or AbstractVector whose values are either AbstractELPDResult entries or any argument to elpd_method . Keywords weights_method::AbstractModelWeightsMethod=Stacking() : the method to be used to weight the models. See model_weights for details elpd_method=loo : a method that computes an AbstractELPDResult from an argument in models . sort::Bool=true : Whether to sort models by decreasing ELPD. Returns ModelComparisonResult : A container for the model comparison results. The fields contain a similar collection to models . Examples Compare the centered and non centered models of the eight school problem using the defaults: loo and Stacking weights. A custom myloo method formates the inputs as expected by loo . julia> using ArviZExampleData\n\njulia> models = (\n centered=load_example_data(\"centered_eight\"),\n non_centered=load_example_data(\"non_centered_eight\"),\n );\n\njulia> function myloo(idata)\n log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1))\n return loo(log_like)\n end;\n\njulia> mc = compare(models; elpd_method=myloo)\n┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.\n└ @ PSIS ~/.julia/packages/PSIS/...\nModelComparisonResult with Stacking weights\n rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯\n non_centered 1 -31 1.4 0 0.0 1.0 0.9 ⋯\n centered 2 -31 1.4 0.06 0.067 0.0 0.9 ⋯\n 1 column omitted\njulia> mc.weight |> pairs\npairs(::NamedTuple) with 2 entries:\n :non_centered => 1.0\n :centered => 5.34175e-19 Compare the same models from pre-computed PSIS-LOO results and computing BootstrappedPseudoBMA weights: julia> elpd_results = mc.elpd_result;\n\njulia> compare(elpd_results; weights_method=BootstrappedPseudoBMA())\nModelComparisonResult with BootstrappedPseudoBMA weights\n rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯\n non_centered 1 -31 1.4 0 0.0 0.52 0.9 ⋯\n centered 2 -31 1.4 0.06 0.067 0.48 0.9 ⋯\n 1 column omitted source"},{"id":95,"pagetitle":"Stats","title":"PosteriorStats.model_weights","ref":"/ArviZ/stable/api/stats/#PosteriorStats.model_weights","content":" PosteriorStats.model_weights — Function model_weights(elpd_results; method=Stacking())\nmodel_weights(method::AbstractModelWeightsMethod, elpd_results) Compute weights for each model in elpd_results using method . elpd_results is a Tuple , NamedTuple , or AbstractVector with AbstractELPDResult entries. The weights are returned in the same type of collection. Stacking is the recommended approach, as it performs well even when the true data generating process is not included among the candidate models. See [YaoVehtari2018] for details. See also: AbstractModelWeightsMethod , compare Examples Compute Stacking weights for two models: julia> using ArviZExampleData\n\njulia> models = (\n centered=load_example_data(\"centered_eight\"),\n non_centered=load_example_data(\"non_centered_eight\"),\n );\n\njulia> elpd_results = map(models) do idata\n log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1))\n return loo(log_like)\n end;\n┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.\n└ @ PSIS ~/.julia/packages/PSIS/...\n\njulia> model_weights(elpd_results; method=Stacking()) |> pairs\npairs(::NamedTuple) with 2 entries:\n :centered => 5.34175e-19\n :non_centered => 1.0 Now we compute BootstrappedPseudoBMA weights for the same models: julia> model_weights(elpd_results; method=BootstrappedPseudoBMA()) |> pairs\npairs(::NamedTuple) with 2 entries:\n :centered => 0.483723\n :non_centered => 0.516277 source The following model weighting methods are available"},{"id":96,"pagetitle":"Stats","title":"PosteriorStats.AbstractModelWeightsMethod","ref":"/ArviZ/stable/api/stats/#PosteriorStats.AbstractModelWeightsMethod","content":" PosteriorStats.AbstractModelWeightsMethod — Type abstract type AbstractModelWeightsMethod An abstract type representing methods for computing model weights. Subtypes implement model_weights (method, elpd_results) . source"},{"id":97,"pagetitle":"Stats","title":"PosteriorStats.BootstrappedPseudoBMA","ref":"/ArviZ/stable/api/stats/#PosteriorStats.BootstrappedPseudoBMA","content":" PosteriorStats.BootstrappedPseudoBMA — Type struct BootstrappedPseudoBMA{R<:Random.AbstractRNG, T<:Real} <: AbstractModelWeightsMethod Model weighting method using pseudo Bayesian Model Averaging using Akaike-type weighting with the Bayesian bootstrap (pseudo-BMA+) [YaoVehtari2018] . The Bayesian bootstrap stabilizes the model weights. BootstrappedPseudoBMA(; rng=Random.default_rng(), samples=1_000, alpha=1)\nBootstrappedPseudoBMA(rng, samples, alpha) Construct the method. rng::Random.AbstractRNG : The random number generator to use for the Bayesian bootstrap samples::Int64 : The number of samples to draw for bootstrapping alpha::Real : The shape parameter in the Dirichlet distribution used for the Bayesian bootstrap. The default (1) corresponds to a uniform distribution on the simplex. See also: Stacking source"},{"id":98,"pagetitle":"Stats","title":"PosteriorStats.PseudoBMA","ref":"/ArviZ/stable/api/stats/#PosteriorStats.PseudoBMA","content":" PosteriorStats.PseudoBMA — Type struct PseudoBMA <: AbstractModelWeightsMethod Model weighting method using pseudo Bayesian Model Averaging (pseudo-BMA) and Akaike-type weighting. PseudoBMA(; regularize=false)\nPseudoBMA(regularize) Construct the method with optional regularization of the weights using the standard error of the ELPD estimate. Note This approach is not recommended, as it produces unstable weight estimates. It is recommended to instead use BootstrappedPseudoBMA to stabilize the weights or Stacking . For details, see [YaoVehtari2018] . See also: Stacking source"},{"id":99,"pagetitle":"Stats","title":"PosteriorStats.Stacking","ref":"/ArviZ/stable/api/stats/#PosteriorStats.Stacking","content":" PosteriorStats.Stacking — Type struct Stacking{O<:Optim.AbstractOptimizer} <: AbstractModelWeightsMethod Model weighting using stacking of predictive distributions [YaoVehtari2018] . Stacking(; optimizer=Optim.LBFGS(), options=Optim.Options()\nStacking(optimizer[, options]) Construct the method, optionally customizing the optimization. optimizer::Optim.AbstractOptimizer : The optimizer to use for the optimization of the weights. The optimizer must support projected gradient optimization via a manifold field. options::Optim.Options : The Optim options to use for the optimization of the weights. See also: BootstrappedPseudoBMA source"},{"id":100,"pagetitle":"Stats","title":"Predictive checks","ref":"/ArviZ/stable/api/stats/#Predictive-checks","content":" Predictive checks"},{"id":101,"pagetitle":"Stats","title":"PosteriorStats.loo_pit","ref":"/ArviZ/stable/api/stats/#PosteriorStats.loo_pit","content":" PosteriorStats.loo_pit — Function loo_pit(idata::InferenceData, log_weights; kwargs...) -> DimArray Compute LOO-PIT values using existing normalized log LOO importance weights. Keywords y_name : Name of observed data variable in idata.observed_data . If not provided, then the only observed data variable is used. y_pred_name : Name of posterior predictive variable in idata.posterior_predictive . If not provided, then y_name is used. kwargs : Remaining keywords are forwarded to the base method of loo_pit . Examples Calculate LOO-PIT values using already computed log weights. julia> using ArviZExampleData, PosteriorStats\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> loo_result = loo(idata; var_name=:obs);\n\njulia> loo_pit(idata, loo_result.psis_result.log_weights; y_name=:obs)\n8-element DimArray{Float64,1} loo_pit_obs with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.943511\n \"Deerfield\" 0.63797\n \"Phillips Andover\" 0.316697\n \"Phillips Exeter\" 0.582252\n \"Hotchkiss\" 0.295321\n \"Lawrenceville\" 0.403318\n \"St. Paul's\" 0.902508\n \"Mt. Hermon\" 0.655275 source loo_pit(idata::InferenceData; kwargs...) -> DimArray Compute LOO-PIT from groups in idata using PSIS-LOO. Keywords y_name : Name of observed data variable in idata.observed_data . If not provided, then the only observed data variable is used. y_pred_name : Name of posterior predictive variable in idata.posterior_predictive . If not provided, then y_name is used. log_likelihood_name : Name of log-likelihood variable in idata.log_likelihood . If not provided, then y_name is used if idata has a log_likelihood group, otherwise the only variable is used. reff::Union{Real,AbstractArray{<:Real}} : The relative effective sample size(s) of the likelihood values. If an array, it must have the same data dimensions as the corresponding log-likelihood variable. If not provided, then this is estimated using ess . kwargs : Remaining keywords are forwarded to the base method of loo_pit . Examples Calculate LOO-PIT values using as test quantity the observed values themselves. julia> using ArviZExampleData, PosteriorStats\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> loo_pit(idata; y_name=:obs)\n8-element DimArray{Float64,1} loo_pit_obs with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.943511\n \"Deerfield\" 0.63797\n \"Phillips Andover\" 0.316697\n \"Phillips Exeter\" 0.582252\n \"Hotchkiss\" 0.295321\n \"Lawrenceville\" 0.403318\n \"St. Paul's\" 0.902508\n \"Mt. Hermon\" 0.655275 source loo_pit(y, y_pred, log_weights; kwargs...) -> Union{Real,AbstractArray} Compute leave-one-out probability integral transform (LOO-PIT) checks. Arguments y : array of observations with shape (params...,) y_pred : array of posterior predictive samples with shape (draws, chains, params...) . log_weights : array of normalized log LOO importance weights with shape (draws, chains, params...) . Keywords is_discrete : If not provided, then it is set to true iff elements of y and y_pred are all integer-valued. If true , then data are smoothed using smooth_data to make them non-discrete before estimating LOO-PIT values. kwargs : Remaining keywords are forwarded to smooth_data if data is discrete. Returns pitvals : LOO-PIT values with same size as y . If y is a scalar, then pitvals is a scalar. LOO-PIT is a marginal posterior predictive check. If $y_{-i}$ is the array $y$ of observations with the $i$ th observation left out, and $y_i^*$ is a posterior prediction of the $i$ th observation, then the LOO-PIT value for the $i$ th observation is defined as \\[P(y_i^* \\le y_i \\mid y_{-i}) = \\int_{-\\infty}^{y_i} p(y_i^* \\mid y_{-i}) \\mathrm{d} y_i^*\\] The LOO posterior predictions and the corresponding observations should have similar distributions, so if conditional predictive distributions are well-calibrated, then all LOO-PIT values should be approximately uniformly distributed on $[0, 1]$ . [Gabry2019] Examples Calculate LOO-PIT values using as test quantity the observed values themselves. julia> using ArviZExampleData\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> y = idata.observed_data.obs;\n\njulia> y_pred = PermutedDimsArray(idata.posterior_predictive.obs, (:draw, :chain, :school));\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> log_weights = loo(log_like).psis_result.log_weights;\n\njulia> loo_pit(y, y_pred, log_weights)\n8-element DimArray{Float64,1} with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.943511\n \"Deerfield\" 0.63797\n \"Phillips Andover\" 0.316697\n \"Phillips Exeter\" 0.582252\n \"Hotchkiss\" 0.295321\n \"Lawrenceville\" 0.403318\n \"St. Paul's\" 0.902508\n \"Mt. Hermon\" 0.655275 Calculate LOO-PIT values using as test quantity the square of the difference between each observation and mu . julia> using Statistics\n\njulia> mu = idata.posterior.mu;\n\njulia> T = y .- median(mu);\n\njulia> T_pred = y_pred .- mu;\n\njulia> loo_pit(T .^ 2, T_pred .^ 2, log_weights)\n8-element DimArray{Float64,1} with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.873577\n \"Deerfield\" 0.243686\n \"Phillips Andover\" 0.357563\n \"Phillips Exeter\" 0.149908\n \"Hotchkiss\" 0.435094\n \"Lawrenceville\" 0.220627\n \"St. Paul's\" 0.775086\n \"Mt. Hermon\" 0.296706 source"},{"id":102,"pagetitle":"Stats","title":"Utilities","ref":"/ArviZ/stable/api/stats/#Utilities","content":" Utilities"},{"id":103,"pagetitle":"Stats","title":"PosteriorStats.smooth_data","ref":"/ArviZ/stable/api/stats/#PosteriorStats.smooth_data","content":" PosteriorStats.smooth_data — Function smooth_data(y; dims=:, interp_method=CubicSpline, offset_frac=0.01) Smooth y along dims using interp_method . interp_method is a 2-argument callabale that takes the arguments y and x and returns a DataInterpolations.jl interpolation method, defaulting to a cubic spline interpolator. offset_frac is the fraction of the length of y to use as an offset when interpolating. source Hyndman1996 Rob J. Hyndman (1996) Computing and Graphing Highest Density Regions, Amer. Stat., 50(2): 120-6. DOI: 10.1080/00031305.1996.10474359 jstor . ChenShao1999 Ming-Hui Chen & Qi-Man Shao (1999) Monte Carlo Estimation of Bayesian Credible and HPD Intervals, J Comput. Graph. Stat., 8:1, 69-92. DOI: 10.1080/10618600.1999.10474802 jstor . GelmanGoodrich2019 Andrew Gelman, Ben Goodrich, Jonah Gabry & Aki Vehtari (2019) R-squared for Bayesian Regression Models, The American Statistician, 73:3, 307-9, DOI: 10.1080/00031305.2018.1549100 . VehtariSimpson2021 Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO] VehtariSimpson2021 Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO] VehtariSimpson2021 Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO] Vehtari2017 Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544 LOOFAQ Aki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html Watanabe2010 Watanabe, S. Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory. 11(116):3571−3594, 2010. https://jmlr.csail.mit.edu/papers/v11/watanabe10a.html Vehtari2017 Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544 LOOFAQ Aki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html YaoVehtari2018 Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030 YaoVehtari2018 Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030 YaoVehtari2018 Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030 YaoVehtari2018 Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030 Gabry2019 Gabry, J., Simpson, D., Vehtari, A., Betancourt, M. & Gelman, A. Visualization in Bayesian Workflow. J. R. Stat. Soc. Ser. A Stat. Soc. 182, 389–402 (2019). doi: 10.1111/rssa.12378 arXiv: 1709.01449"},{"id":106,"pagetitle":"Creating custom plots","title":"Environment","ref":"/ArviZ/stable/creating_custom_plots/#Environment","content":" Environment using Pkg, InteractiveUtils using PlutoUI with_terminal(Pkg.status; color=false) Status `~/work/ArviZ.jl/ArviZ.jl/docs/Project.toml`\n [cbdf2221] AlgebraOfGraphics v0.6.17\n [131c737c] ArviZ v0.10.3 `~/work/ArviZ.jl/ArviZ.jl`\n [2f96bb34] ArviZExampleData v0.1.8\n [4a6e88f0] ArviZPythonPlots v0.1.3\n [13f3f980] CairoMakie v0.11.4\n [a93c6f00] DataFrames v1.6.1\n⌃ [0703355e] DimensionalData v0.24.13\n [31c24e10] Distributions v0.25.104\n [e30172f5] Documenter v1.2.1\n [f6006082] EvoTrees v0.16.5\n [b5cf5a8d] InferenceObjects v0.3.14\n [be115224] MCMCDiagnosticTools v0.3.8\n [a7f614a8] MLJBase v1.0.1\n [614be32b] MLJIteration v0.6.0\n [ce719bf2] PSIS v0.9.4\n [359b1769] PlutoStaticHTML v6.0.18\n [7f904dfe] PlutoUI v0.7.54\n [7f36be82] PosteriorStats v0.1.4\n [c1514b29] StanSample v7.6.0\n [a19d573c] StatisticalMeasures v0.1.3\n [2913bbd2] StatsBase v0.34.2\n⌅ [fce5fe82] Turing v0.29.3\n [f43a241f] Downloads v1.6.0\n [37e2e46d] LinearAlgebra\n [10745b16] Statistics v1.9.0\nInfo Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated`\n with_terminal(versioninfo) Julia Version 1.9.4\nCommit 8e5136fa297 (2023-11-14 08:46 UTC)\nBuild Info:\n Official https://julialang.org/ release\nPlatform Info:\n OS: Linux (x86_64-linux-gnu)\n CPU: 4 × AMD EPYC 7763 64-Core Processor\n WORD_SIZE: 64\n LIBM: libopenlibm\n LLVM: libLLVM-14.0.6 (ORCJIT, znver3)\n Threads: 2 on 4 virtual cores\nEnvironment:\n JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager\n JULIA_PROJECT = /home/runner/work/ArviZ.jl/ArviZ.jl/docs/\n JULIA_DEPOT_PATH = /home/runner/.julia:/opt/hostedtoolcache/julia/1.9.4/x64/local/share/julia:/opt/hostedtoolcache/julia/1.9.4/x64/share/julia\n JULIA_NUM_THREADS = 2\n JULIA_LOAD_PATH = @:@v#.#:@stdlib\n JULIA_CMDSTAN_HOME = /home/runner/work/ArviZ.jl/ArviZ.jl/.cmdstan//cmdstan-2.33.1/\n JULIA_REVISE_WORKER_ONLY = 1\n"},{"id":111,"pagetitle":"Working with InferenceData","title":"Working with InferenceData","ref":"/ArviZ/stable/working_with_inference_data/#working-with-inference-data","content":" Working with InferenceData using ArviZ, ArviZExampleData, DimensionalData, Statistics Here we present a collection of common manipulations you can use while working with InferenceData . Let's load one of ArviZ's example datasets. posterior , posterior_predictive , etc are the groups stored in idata , and they are stored as Dataset s. In this HTML view, you can click a group name to expand a summary of the group. idata = load_example_data(\"centered_eight\") InferenceData posterior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" posterior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:41.460544\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" log_likelihood Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:37.487399\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" sample_stats Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 16 layers:\n :max_energy_error Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :energy_error Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :lp Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :index_in_trajectory Int64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :acceptance_rate Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :diverging Bool dims: Dim{:draw}, Dim{:chain} (500×4)\n :process_time_diff Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :n_steps Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :perf_counter_start Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :largest_eigval Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (500×4)\n :smallest_eigval Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (500×4)\n :step_size_bar Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :step_size Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :energy Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :tree_depth Int64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :perf_counter_diff Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.324929\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.602116\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.604969\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" observed_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :obs Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.606375\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" constant_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :scores Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.607471\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" Info Dataset s are DimensionalData.AbstractDimStack s and can be used identically. The variables a Dataset contains are called \"layers\", and dimensions of the same name that appear in more than one layer within a Dataset must have the same indices. InferenceData behaves like a NamedTuple and can be used similarly. Note that unlike a NamedTuple , the groups always appear in a specific order. length(idata) # number of groups 8 keys(idata) # group names (:posterior, :posterior_predictive, :log_likelihood, :sample_stats, :prior, :prior_predictive, :observed_data, :constant_data)"},{"id":112,"pagetitle":"Working with InferenceData","title":"Get the dataset corresponding to a single group","ref":"/ArviZ/stable/working_with_inference_data/#Get-the-dataset-corresponding-to-a-single-group","content":" Get the dataset corresponding to a single group Group datasets can be accessed both as properties or as indexed items. post = idata.posterior Dataset with dimensions: \n Dim{ :draw } Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{ :chain } Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{ :school } Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n and 3 layers:\n :mu Float64 dims: Dim{ :draw } , Dim{ :chain } (500×4)\n :theta Float64 dims: Dim{ :school } , Dim{ :draw } , Dim{ :chain } (8×500×4)\n :tau Float64 dims: Dim{ :draw } , Dim{ :chain } (500×4)\n\n with metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" post is the dataset itself, so this is a non-allocating operation. idata[:posterior] === post true InferenceData supports a more advanced indexing syntax, which we'll see later."},{"id":113,"pagetitle":"Working with InferenceData","title":"Getting a new InferenceData with a subset of groups","ref":"/ArviZ/stable/working_with_inference_data/#Getting-a-new-InferenceData-with-a-subset-of-groups","content":" Getting a new InferenceData with a subset of groups We can index by a collection of group names to get a new InferenceData with just those groups. This is also non-allocating. idata_sub = idata[(:posterior, :posterior_predictive)] InferenceData posterior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" posterior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:41.460544\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\""},{"id":114,"pagetitle":"Working with InferenceData","title":"Adding groups to an InferenceData","ref":"/ArviZ/stable/working_with_inference_data/#Adding-groups-to-an-InferenceData","content":" Adding groups to an InferenceData InferenceData is immutable, so to add or replace groups we use merge to create a new object. merge(idata_sub, idata[(:observed_data, :prior)]) InferenceData posterior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" posterior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:41.460544\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.602116\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" observed_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :obs Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.606375\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" We can also use Base.setindex to out-of-place add or replace a single group. Base.setindex(idata_sub, idata.prior, :prior) InferenceData posterior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" posterior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:41.460544\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.602116\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\""},{"id":115,"pagetitle":"Working with InferenceData","title":"Add a new variable","ref":"/ArviZ/stable/working_with_inference_data/#Add-a-new-variable","content":" Add a new variable Dataset is also immutable. So while the values within the underlying data arrays can be mutated, layers cannot be added or removed from Dataset s, and groups cannot be added/removed from InferenceData . Instead, we do this out-of-place also using merge . merge(post, (log_tau=log.(post[:tau]),)) Dataset with dimensions: \n Dim{ :draw } Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{ :chain } Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{ :school } Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n and 4 layers:\n :mu Float64 dims: Dim{ :draw } , Dim{ :chain } (500×4)\n :theta Float64 dims: Dim{ :school } , Dim{ :draw } , Dim{ :chain } (8×500×4)\n :tau Float64 dims: Dim{ :draw } , Dim{ :chain } (500×4)\n :log_tau Float64 dims: Dim{ :draw } , Dim{ :chain } (500×4)\n\n with metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\""},{"id":116,"pagetitle":"Working with InferenceData","title":"Obtain an array for a given parameter","ref":"/ArviZ/stable/working_with_inference_data/#Obtain-an-array-for-a-given-parameter","content":" Obtain an array for a given parameter Let’s say we want to get the values for mu as an array. Parameters can be accessed with either property or index syntax. post.tau 500×4 DimArray{Float64,2} tau with dimensions: \n Dim{ :draw } Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{ :chain } Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\n 0 1 2 3 \n 0 4.72574 1.97083 3.50128 6.07326\n 1 3.90899 2.04903 2.89324 3.77187\n 2 4.84403 2.12376 4.27329 3.17054\n 3 1.8567 3.39183 11.8965 6.00193\n 4 4.74841 4.84368 7.11325 3.28632\n ⋮ \n 494 8.15827 1.61268 4.96249 3.13966\n 495 7.56498 1.61268 3.56495 2.78607\n 496 2.24702 1.84816 2.55959 4.28196\n 497 1.89384 2.17459 4.08978 2.74061\n 498 5.92006 1.32755 2.72017 2.93238\n 499 4.3259 1.21199 1.91701 4.46125 post[:tau] === post.tau true To remove the dimensions, just use parent to retrieve the underlying array. parent(post.tau) 500×4 Matrix{Float64}:\n 4.72574 1.97083 3.50128 6.07326\n 3.90899 2.04903 2.89324 3.77187\n 4.84403 2.12376 4.27329 3.17054\n 1.8567 3.39183 11.8965 6.00193\n 4.74841 4.84368 7.11325 3.28632\n 3.51387 10.8872 7.18892 2.16314\n 4.20898 4.01889 9.0977 7.68505\n 2.6834 4.28584 7.84286 4.08612\n 1.16889 3.70403 17.1548 5.1157\n 1.21052 3.15829 16.7573 4.86939\n ⋮ \n 2.05742 1.09087 10.8168 5.08507\n 2.72536 1.09087 2.16788 6.1552\n 5.97049 1.67101 5.19169 8.23756\n 8.15827 1.61268 4.96249 3.13966\n 7.56498 1.61268 3.56495 2.78607\n 2.24702 1.84816 2.55959 4.28196\n 1.89384 2.17459 4.08978 2.74061\n 5.92006 1.32755 2.72017 2.93238\n 4.3259 1.21199 1.91701 4.46125"},{"id":117,"pagetitle":"Working with InferenceData","title":"Get the dimension lengths","ref":"/ArviZ/stable/working_with_inference_data/#Get-the-dimension-lengths","content":" Get the dimension lengths Let’s check how many groups are in our hierarchical model. size(idata.observed_data, :school) 8"},{"id":118,"pagetitle":"Working with InferenceData","title":"Get coordinate/index values","ref":"/ArviZ/stable/working_with_inference_data/#Get-coordinate/index-values","content":" Get coordinate/index values What are the names of the groups in our hierarchical model? You can access them from the coordinate name school in this case. DimensionalData.index(idata.observed_data, :school) 8-element Vector{String}:\n \"Choate\"\n \"Deerfield\"\n \"Phillips Andover\"\n \"Phillips Exeter\"\n \"Hotchkiss\"\n \"Lawrenceville\"\n \"St. Paul's\"\n \"Mt. Hermon\""},{"id":119,"pagetitle":"Working with InferenceData","title":"Get a subset of chains","ref":"/ArviZ/stable/working_with_inference_data/#Get-a-subset-of-chains","content":" Get a subset of chains Let’s keep only chain 0 here. For the subset to take effect on all relevant InferenceData groups – posterior , sample_stats , log_likelihood , and posterior_predictive – we will index InferenceData instead of Dataset . Here we use DimensionalData's At selector. Its other selectors are also supported. idata[chain=At(0)] InferenceData posterior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" posterior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:41.460544\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" log_likelihood Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:37.487399\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" sample_stats Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points\nand 16 layers:\n :max_energy_error Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :energy_error Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :lp Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :index_in_trajectory Int64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :acceptance_rate Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :diverging Bool dims: Dim{:draw}, Dim{:chain} (500×1)\n :process_time_diff Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :n_steps Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :perf_counter_start Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :largest_eigval Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (500×1)\n :smallest_eigval Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (500×1)\n :step_size_bar Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :step_size Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :energy Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :tree_depth Int64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :perf_counter_diff Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.324929\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.602116\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.604969\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" observed_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :obs Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.606375\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" constant_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :scores Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.607471\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" Note that in this case, prior only has a chain of 0. If it also had the other chains, we could have passed chain=At([0, 2]) to subset by chains 0 and 2. Warning If we used idata[chain=[0, 2]] without the At selector, this is equivalent to idata[chain=DimensionalData.index(idata.posterior, :chain)[0, 2]] , that is, [0, 2] indexes an array of dimension indices, which here would error. But if we had requested idata[chain=[1, 2]] we would not hit an error, but we would index the wrong chains. So it's important to always use a selector to index by values of dimension indices."},{"id":120,"pagetitle":"Working with InferenceData","title":"Remove the first $n$ draws (burn-in)","ref":"/ArviZ/stable/working_with_inference_data/#Remove-the-first-n-draws-(burn-in)","content":" Remove the first $n$ draws (burn-in) Let’s say we want to remove the first 100 draws from all the chains and all InferenceData groups with draws. To do this we use the .. syntax from IntervalSets.jl, which is exported by DimensionalData. idata[draw=100 .. Inf] InferenceData posterior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[100, 101, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×400×4)\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" posterior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[100, 101, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×400×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:41.460544\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" log_likelihood Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[100, 101, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×400×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:37.487399\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" sample_stats Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[100, 101, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 16 layers:\n :max_energy_error Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :energy_error Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :lp Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :index_in_trajectory Int64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :acceptance_rate Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :diverging Bool dims: Dim{:draw}, Dim{:chain} (400×4)\n :process_time_diff Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :n_steps Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :perf_counter_start Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :largest_eigval Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (400×4)\n :smallest_eigval Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (400×4)\n :step_size_bar Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :step_size Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :energy Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :tree_depth Int64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :perf_counter_diff Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.324929\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[100, 101, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (400×1)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×400×1)\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (400×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.602116\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[100, 101, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×400×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.604969\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" observed_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :obs Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.606375\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" constant_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :scores Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.607471\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" If you check the object you will see that the groups posterior , posterior_predictive , prior , and sample_stats have 400 draws compared to idata , which has 500. The group observed_data has not been affected because it does not have the draw dimension. Alternatively, you can change a subset of groups by combining indexing styles with merge . Here we use this to build a new InferenceData where we have discarded the first 100 draws only from posterior . merge(idata, idata[(:posterior,), draw=100 .. Inf]) InferenceData posterior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[100, 101, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×400×4)\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" posterior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:41.460544\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" log_likelihood Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:37.487399\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" sample_stats Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 16 layers:\n :max_energy_error Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :energy_error Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :lp Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :index_in_trajectory Int64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :acceptance_rate Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :diverging Bool dims: Dim{:draw}, Dim{:chain} (500×4)\n :process_time_diff Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :n_steps Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :perf_counter_start Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :largest_eigval Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (500×4)\n :smallest_eigval Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (500×4)\n :step_size_bar Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :step_size Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :energy Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :tree_depth Int64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :perf_counter_diff Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.324929\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.602116\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.604969\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" observed_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :obs Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.606375\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" constant_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :scores Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.607471\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\""},{"id":121,"pagetitle":"Working with InferenceData","title":"Compute posterior mean values along draw and chain dimensions","ref":"/ArviZ/stable/working_with_inference_data/#Compute-posterior-mean-values-along-draw-and-chain-dimensions","content":" Compute posterior mean values along draw and chain dimensions To compute the mean value of the posterior samples, do the following: mean(post) (mu = 4.485933103402338,\n theta = 4.911515591394205,\n tau = 4.124222787491913,) This computes the mean along all dimensions, discarding all dimensions and returning the result as a NamedTuple . This may be what you wanted for mu and tau , which have only two dimensions ( chain and draw ), but maybe not what you expected for theta , which has one more dimension school . You can specify along which dimension you want to compute the mean (or other functions), which instead returns a Dataset . mean(post; dims=(:chain, :draw)) Dataset with dimensions: \n Dim{ :draw } Sampled{Float64} Float64[249.5] ForwardOrdered Irregular Points,\n Dim{ :chain } Sampled{Float64} Float64[1.5] ForwardOrdered Irregular Points,\n Dim{ :school } Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n and 3 layers:\n :mu Float64 dims: Dim{ :draw } , Dim{ :chain } (1×1)\n :theta Float64 dims: Dim{ :school } , Dim{ :draw } , Dim{ :chain } (8×1×1)\n :tau Float64 dims: Dim{ :draw } , Dim{ :chain } (1×1)\n\n with metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" The singleton dimensions of chain and draw now contain meaningless indices, so you may want to discard them, which you can do with dropdims . dropdims(mean(post; dims=(:chain, :draw)); dims=(:chain, :draw)) Dataset with dimensions: \n Dim{ :school } Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n and 3 layers:\n :mu Float64 dims: \n :theta Float64 dims: Dim{ :school } (8)\n :tau Float64 dims: \n\n with metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\""},{"id":122,"pagetitle":"Working with InferenceData","title":"Renaming a dimension","ref":"/ArviZ/stable/working_with_inference_data/#Renaming-a-dimension","content":" Renaming a dimension We can rename a dimension in a Dataset using DimensionalData's set method: theta_bis = set(post.theta; school=:school_bis) 8×500×4 DimArray{Float64,3} theta with dimensions: \n Dim{ :school_bis } Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{ :draw } Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{ :chain } Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\n[:, :, 1]\n 0 … 497 498 499 \n \"Choate\" 12.3207 -0.213828 10.4025 6.66131\n \"Deerfield\" 9.90537 1.35515 6.90741 7.41377\n \"Phillips Andover\" 14.9516 6.98269 -4.96414 -9.3226\n \"Phillips Exeter\" 11.0115 3.71681 3.13584 2.69192\n \"Hotchkiss\" 5.5796 … 5.32446 -2.2243 -0.502331\n \"Lawrenceville\" 16.9018 6.96589 -2.83504 -4.25487\n \"St. Paul's\" 13.1981 4.9302 5.39106 7.56657\n \"Mt. Hermon\" 15.0614 3.0586 6.38124 9.98762\n [and 3 more slices...] We can use this, for example, to broadcast functions across multiple arrays, automatically matching up shared dimensions, using DimensionalData.broadcast_dims . theta_school_diff = broadcast_dims(-, post.theta, theta_bis) 8×500×4×8 DimArray{Float64,4} theta with dimensions: \n Dim{ :school } Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{ :draw } Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{ :chain } Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{ :school_bis } Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n[:, :, 1, 1]\n 0 … 497 498 499 \n \"Choate\" 0.0 0.0 0.0 0.0\n \"Deerfield\" -2.41532 1.56898 -3.49509 0.752459\n \"Phillips Andover\" 2.63093 7.19652 -15.3666 -15.9839\n \"Phillips Exeter\" -1.3092 3.93064 -7.26666 -3.96939\n \"Hotchkiss\" -6.74108 … 5.53829 -12.6268 -7.16364\n \"Lawrenceville\" 4.58111 7.17972 -13.2375 -10.9162\n \"St. Paul's\" 0.877374 5.14403 -5.01144 0.905263\n \"Mt. Hermon\" 2.74068 3.27243 -4.02126 3.32631\n [and 31 more slices...]"},{"id":123,"pagetitle":"Working with InferenceData","title":"Compute and store posterior pushforward quantities","ref":"/ArviZ/stable/working_with_inference_data/#Compute-and-store-posterior-pushforward-quantities","content":" Compute and store posterior pushforward quantities We use “posterior pushfoward quantities” to refer to quantities that are not variables in the posterior but deterministic computations using posterior variables. You can compute these pushforward operations and store them as a new variable in a copy of the posterior group. Here we'll create a new InferenceData with theta_school_diff in the posterior: idata_new = Base.setindex(idata, merge(post, (; theta_school_diff)), :posterior) InferenceData posterior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:school_bis} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 4 layers:\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :theta_school_diff Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain}, Dim{:school_bis} (8×500×4×8)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" posterior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:41.460544\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" log_likelihood Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:37.487399\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" sample_stats Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 16 layers:\n :max_energy_error Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :energy_error Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :lp Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :index_in_trajectory Int64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :acceptance_rate Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :diverging Bool dims: Dim{:draw}, Dim{:chain} (500×4)\n :process_time_diff Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :n_steps Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :perf_counter_start Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :largest_eigval Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (500×4)\n :smallest_eigval Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (500×4)\n :step_size_bar Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :step_size Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :energy Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :tree_depth Int64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :perf_counter_diff Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.324929\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.602116\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.604969\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" observed_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :obs Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.606375\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" constant_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :scores Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.607471\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" Once you have these pushforward quantities in an InferenceData , you’ll then be able to plot them with ArviZ functions, calculate stats and diagnostics on them, or save and share the InferenceData object with the pushforward quantities included. Here we compute the mcse of theta_school_diff : mcse(idata_new.posterior).theta_school_diff 8×8 DimArray{Float64,2} theta_school_diff with dimensions: \n Dim{ :school } Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{ :school_bis } Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" … \"St. Paul's\" \"Mt. Hermon\" \n \"Choate\" NaN 0.117476 0.219695\n \"Deerfield\" 0.191463 0.16484 0.189386\n \"Phillips Andover\" 0.255636 0.258001 0.160477\n \"Phillips Exeter\" 0.162782 0.156724 0.144923\n \"Hotchkiss\" 0.282881 … 0.283969 0.189015\n \"Lawrenceville\" 0.259065 0.251988 0.178094\n \"St. Paul's\" 0.117476 NaN 0.222054\n \"Mt. Hermon\" 0.219695 0.222054 NaN"},{"id":124,"pagetitle":"Working with InferenceData","title":"Advanced subsetting","ref":"/ArviZ/stable/working_with_inference_data/#Advanced-subsetting","content":" Advanced subsetting To select the value corresponding to the difference between the Choate and Deerfield schools do: school_idx = [\"Choate\", \"Hotchkiss\", \"Mt. Hermon\"]\nschool_bis_idx = [\"Deerfield\", \"Choate\", \"Lawrenceville\"]\ntheta_school_diff[school=At(school_idx), school_bis=At(school_bis_idx)] 3×500×4×3 DimArray{Float64,4} theta with dimensions: \n Dim{ :school } Categorical{String} String[\"Choate\", \"Hotchkiss\", \"Mt. Hermon\"] Unordered,\n Dim{ :draw } Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{ :chain } Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{ :school_bis } Categorical{String} String[\"Deerfield\", \"Choate\", \"Lawrenceville\"] Unordered\n[:, :, 1, 1]\n 0 1 … 497 498 499 \n \"Choate\" 2.41532 2.1563 -1.56898 3.49509 -0.752459\n \"Hotchkiss\" -4.32577 -1.31781 3.96931 -9.13171 -7.9161\n \"Mt. Hermon\" 5.156 -2.9526 1.70345 -0.526168 2.57385\n [and 11 more slices...]"},{"id":125,"pagetitle":"Working with InferenceData","title":"Add new chains using cat","ref":"/ArviZ/stable/working_with_inference_data/#Add-new-chains-using-cat","content":" Add new chains using cat Suppose after checking the mcse and realizing you need more samples, you rerun the model with two chains and obtain an idata_rerun object. idata_rerun = InferenceData(; posterior=set(post[chain=At([0, 1])]; chain=[4, 5])) InferenceData posterior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[4, 5] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×2)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×2)\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×2)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" You can combine the two using cat . cat(idata[[:posterior]], idata_rerun; dims=:chain) InferenceData posterior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, …, 4, 5] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×6)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×6)\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×6)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\""},{"id":128,"pagetitle":"Home","title":"ArviZPythonPlots.jl","ref":"/ArviZPythonPlots/stable/#ArviZPythonPlots.jl","content":" ArviZPythonPlots.jl ArviZPythonPlots.jl provides PyPlot-compatible plotting functions for exploratory analysis of Bayesian models using ArviZ.jl . It uses PythonCall.jl to provide an interface for using the plotting functions in Python ArviZ with Julia types. It also re-exports all methods exported by PythonPlot.jl . For details, see the Example Gallery or the API ."},{"id":129,"pagetitle":"Home","title":"Installation","ref":"/ArviZPythonPlots/stable/#installation","content":" Installation To install ArviZPythonPlots.jl, we first need to install Python ArviZ. From the Julia REPL, type ] to enter the Pkg REPL mode and run pkg> add ArviZPythonPlots"},{"id":132,"pagetitle":"API Overview","title":"API Overview","ref":"/ArviZPythonPlots/stable/api/#api","content":" API Overview Plotting styles rcParams Plotting functions"},{"id":135,"pagetitle":"Plotting functions","title":"Plotting functions","ref":"/ArviZPythonPlots/stable/api/plots/#plots-api","content":" Plotting functions ArviZPythonPlots.plot_autocorr ArviZPythonPlots.plot_bf ArviZPythonPlots.plot_bpv ArviZPythonPlots.plot_compare ArviZPythonPlots.plot_density ArviZPythonPlots.plot_dist ArviZPythonPlots.plot_dist_comparison ArviZPythonPlots.plot_dot ArviZPythonPlots.plot_ecdf ArviZPythonPlots.plot_elpd ArviZPythonPlots.plot_energy ArviZPythonPlots.plot_ess ArviZPythonPlots.plot_forest ArviZPythonPlots.plot_hdi ArviZPythonPlots.plot_kde ArviZPythonPlots.plot_khat ArviZPythonPlots.plot_lm ArviZPythonPlots.plot_loo_pit ArviZPythonPlots.plot_mcse ArviZPythonPlots.plot_pair ArviZPythonPlots.plot_parallel ArviZPythonPlots.plot_posterior ArviZPythonPlots.plot_ppc ArviZPythonPlots.plot_rank ArviZPythonPlots.plot_separation ArviZPythonPlots.plot_trace ArviZPythonPlots.plot_violin"},{"id":136,"pagetitle":"Plotting functions","title":"Reference","ref":"/ArviZPythonPlots/stable/api/plots/#Reference","content":" Reference"},{"id":137,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_autocorr","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_autocorr-Tuple","content":" ArviZPythonPlots.plot_autocorr — Method Bar plot of the autocorrelation function (ACF) for a sequence of data.\n\n The ACF plots are helpful as a convergence diagnostic for posteriors from MCMC\n samples which display autocorrelation.\n\n Parameters\n ----------\n data : InferenceData\n Any object that can be converted to an :class:`arviz.InferenceData` object\n refer to documentation of :func:`arviz.convert_to_dataset` for details\n var_names : list of str, optional\n Variables to be plotted. Prefix the variables by ``~`` when you want to exclude\n them from the plot. See :ref:`this section ` for usage examples.\n filter_vars : {None, \"like\", \"regex\"}, default None\n If `None` (default), interpret `var_names` as the real variables names. If \"like\",\n interpret `var_names` as substrings of the real variables names. If \"regex\",\n interpret `var_names` as regular expressions on the real variables names. See\n :ref:`this section ` for usage examples.\n max_lag : int, optional\n Maximum lag to calculate autocorrelation. By Default, the plot displays the\n first 100 lag or the total number of draws, whichever is smaller.\n combined : bool, default False\n Flag for combining multiple chains into a single chain. If False, chains will be\n plotted separately.\n grid : tuple, optional\n Number of rows and columns. Defaults to None, the rows and columns are\n automatically inferred. See :ref:`this section ` for usage examples.\n figsize : (float, float), optional\n Figure size. If None it will be defined automatically.\n Note this is not used if `ax` is supplied.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If None it will be autoscaled based\n on `figsize`.\n labeller : Labeller, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n ax : 2D array-like of matplotlib_axes or bokeh_figure, optional\n A 2D array of locations into which to plot the densities. If not supplied, ArviZ will create\n its own array of plot areas (and return it).\n backend : {\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_config : dict, optional\n Currently specifies the bounds to use for bokeh axes. Defaults to value set in ``rcParams``.\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : matplotlib_axes or bokeh_figures\n\n See Also\n --------\n autocov : Compute autocovariance estimates for every lag for the input array.\n autocorr : Compute autocorrelation using FFT for every lag for the input array.\n\n Examples\n --------\n Plot default autocorrelation\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data('centered_eight')\n >>> az.plot_autocorr(data)\n\n Plot subset variables by specifying variable name exactly\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_autocorr(data, var_names=['mu', 'tau'] )\n\n\n Combine chains by variable and select variables by excluding some with partial naming\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_autocorr(data, var_names=['~thet'], filter_vars=\"like\", combined=True)\n\n\n Specify maximum lag (x axis bound)\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_autocorr(data, var_names=['mu', 'tau'], max_lag=200, combined=True)\n \n source"},{"id":138,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_bf","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_bf-Tuple","content":" ArviZPythonPlots.plot_bf — Method Approximated Bayes Factor for comparing hypothesis of two nested models.\n\n The Bayes factor is estimated by comparing a model (H1) against a model in which the\n parameter of interest has been restricted to be a point-null (H0). This computation\n assumes the models are nested and thus H0 is a special case of H1.\n\n Notes\n -----\n The bayes Factor is approximated pproximated as the Savage-Dickey density ratio\n algorithm presented in [1]_.\n\n Parameters\n -----------\n idata : InferenceData\n Any object that can be converted to an :class:`arviz.InferenceData` object\n Refer to documentation of :func:`arviz.convert_to_dataset` for details.\n var_name : str, optional\n Name of variable we want to test.\n prior : numpy.array, optional\n In case we want to use different prior, for example for sensitivity analysis.\n ref_val : int, default 0\n Point-null for Bayes factor estimation.\n xlim : tuple, optional\n Set the x limits, which might be used for visualization purposes.\n colors : tuple, default ('C0', 'C1')\n Tuple of valid Matplotlib colors. First element for the prior, second for the posterior.\n figsize : (float, float), optional\n Figure size. If `None` it will be defined automatically.\n textsize: float, optional\n Text size scaling factor for labels, titles and lines. If `None` it will be autoscaled based\n on `figsize`.\n plot_kwargs : dicts, optional\n Additional keywords passed to :func:`matplotlib.pyplot.plot`.\n hist_kwargs : dicts, optional\n Additional keywords passed to :func:`arviz.plot_dist`. Only works for discrete variables.\n ax : axes, optional\n :class:`matplotlib.axes.Axes` or :class:`bokeh.plotting.Figure`.\n backend :{\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n dict : A dictionary with BF10 (Bayes Factor 10 (H1/H0 ratio), and BF01 (H0/H1 ratio).\n axes : matplotlib_axes or bokeh_figure\n\n References\n ----------\n .. [1] Heck, D., 2019. A caveat on the avage-Dickey density ratio:\n The case of computing Bayes factors for regression parameters.\n\n Examples\n --------\n Moderate evidence indicating that the parameter \"a\" is different from zero.\n\n .. plot::\n :context: close-figs\n\n >>> import numpy as np\n >>> import arviz as az\n >>> idata = az.from_dict(posterior={\"a\":np.random.normal(1, 0.5, 5000)},\n ... prior={\"a\":np.random.normal(0, 1, 5000)})\n >>> az.plot_bf(idata, var_name=\"a\", ref_val=0)\n \n source"},{"id":139,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_bpv","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_bpv-Tuple","content":" ArviZPythonPlots.plot_bpv — Method Plot Bayesian p-value for observed data and Posterior/Prior predictive.\n\n Parameters\n ----------\n data : InferenceData\n :class:`arviz.InferenceData` object containing the observed and\n posterior/prior predictive data.\n kind : {\"u_value\", \"p_value\", \"t_stat\"}, default \"u_value\"\n Specify the kind of plot:\n\n * The ``kind=\"p_value\"`` computes :math:`p := p(y* \\leq y | y)`.\n This is the probability of the data y being larger or equal than the predicted data y*.\n The ideal value is 0.5 (half the predictions below and half above the data).\n * The ``kind=\"u_value\"`` argument computes :math:`p_i := p(y_i* \\leq y_i | y)`.\n i.e. like a p_value but per observation :math:`y_i`. This is also known as marginal\n p_value. The ideal distribution is uniform. This is similar to the LOO-PIT\n calculation/plot, the difference is than in LOO-pit plot we compute\n :math:`pi = p(y_i* r \\leq y_i | y_{-i} )`, where :math:`y_{-i}`,\n is all other data except :math:`y_i`.\n * The ``kind=\"t_stat\"`` argument computes :math:`:= p(T(y)* \\leq T(y) | y)`\n where T is any test statistic. See ``t_stat`` argument below for details\n of available options.\n\n t_stat : str, float, or callable, default \"median\"\n Test statistics to compute from the observations and predictive distributions.\n Allowed strings are “mean”, “median” or “std”. Alternative a quantile can be passed\n as a float (or str) in the interval (0, 1). Finally a user defined function is also\n acepted, see examples section for details.\n bpv : bool, default True\n If True add the Bayesian p_value to the legend when ``kind = t_stat``.\n plot_mean : bool, default True\n Whether or not to plot the mean test statistic.\n reference : {\"analytical\", \"samples\", None}, default \"analytical\"\n How to compute the distributions used as reference for ``kind=u_values``\n or ``kind=p_values``. Use `None` to not plot any reference.\n mse : bool, default False\n Show scaled mean square error between uniform distribution and marginal p_value\n distribution.\n n_ref : int, default 100\n Number of reference distributions to sample when ``reference=samples``.\n hdi_prob : float, optional\n Probability for the highest density interval for the analytical reference distribution when\n ``kind=u_values``. Should be in the interval (0, 1]. Defaults to the\n rcParam ``stats.hdi_prob``. See :ref:`this section ` for usage examples.\n color : str, optional\n Matplotlib color\n grid : tuple, optional\n Number of rows and columns. By default, the rows and columns are\n automatically inferred. See :ref:`this section ` for usage examples.\n figsize : (float, float), optional\n Figure size. If None it will be defined automatically.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If None it will be autoscaled based\n on `figsize`.\n data_pairs : dict, optional\n Dictionary containing relations between observed data and posterior/prior predictive data.\n Dictionary structure:\n\n - key = data var_name\n - value = posterior/prior predictive var_name\n\n For example, ``data_pairs = {'y' : 'y_hat'}``\n If None, it will assume that the observed data and the posterior/prior\n predictive data have the same variable name.\n Labeller : Labeller, optional\n Class providing the method ``make_pp_label`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n var_names : list of str, optional\n Variables to be plotted. If `None` all variable are plotted. Prefix the variables by ``~``\n when you want to exclude them from the plot. See the :ref:`this section `\n for usage examples. See :ref:`this section ` for usage examples.\n filter_vars : {None, \"like\", \"regex\"}, default None\n If `None` (default), interpret `var_names` as the real variables names. If \"like\",\n interpret `var_names` as substrings of the real variables names. If \"regex\",\n interpret `var_names` as regular expressions on the real variables names. See\n :ref:`this section ` for usage examples.\n coords : dict, optional\n Dictionary mapping dimensions to selected coordinates to be plotted.\n Dimensions without a mapping specified will include all coordinates for\n that dimension. Defaults to including all coordinates for all\n dimensions if None. See :ref:`this section ` for usage examples.\n flatten : list, optional\n List of dimensions to flatten in observed_data. Only flattens across the coordinates\n specified in the coords argument. Defaults to flattening all of the dimensions.\n flatten_pp : list, optional\n List of dimensions to flatten in posterior_predictive/prior_predictive. Only flattens\n across the coordinates specified in the coords argument. Defaults to flattening all\n of the dimensions. Dimensions should match flatten excluding dimensions for data_pairs\n parameters. If `flatten` is defined and `flatten_pp` is None, then ``flatten_pp=flatten``.\n legend : bool, default True\n Add legend to figure.\n ax : 2D array-like of matplotlib_axes or bokeh_figure, optional\n A 2D array of locations into which to plot the densities. If not supplied, ArviZ will create\n its own array of plot areas (and return it).\n backend : str, optional\n Select plotting backend {\"matplotlib\", \"bokeh\"}. Default \"matplotlib\".\n plot_ref_kwargs : dict, optional\n Extra keyword arguments to control how reference is represented.\n Passed to :meth:`matplotlib.axes.Axes.plot` or\n :meth:`matplotlib.axes.Axes.axhspan` (when ``kind=u_value``\n and ``reference=analytical``).\n backend_kwargs : bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n group : {\"posterior\", \"prior\"}, default \"posterior\"\n Specifies which InferenceData group should be plotted. If \"posterior\", then the values\n in `posterior_predictive` group are compared to the ones in `observed_data`, if \"prior\" then\n the same comparison happens, but with the values in `prior_predictive` group.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : 2D ndarray of matplotlib_axes or bokeh_figure\n\n See Also\n --------\n plot_ppc : Plot for posterior/prior predictive checks.\n plot_loo_pit : Plot Leave-One-Out probability integral transformation (PIT) predictive checks.\n plot_dist_comparison : Plot to compare fitted and unfitted distributions.\n\n References\n ----------\n * Gelman et al. (2013) see http://www.stat.columbia.edu/~gelman/book/ pages 151-153 for details\n\n Examples\n --------\n Plot Bayesian p_values.\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data(\"regression1d\")\n >>> az.plot_bpv(data, kind=\"p_value\")\n\n Plot custom test statistic comparison.\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data(\"regression1d\")\n >>> az.plot_bpv(data, kind=\"t_stat\", t_stat=lambda x:np.percentile(x, q=50, axis=-1))\n \n source"},{"id":140,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_compare","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_compare-Tuple","content":" ArviZPythonPlots.plot_compare — Method Summary plot for model comparison.\n\n Models are compared based on their expected log pointwise predictive density (ELPD).\n This plot is in the style of the one used in [2]_. Chapter 6 in the first edition\n or 7 in the second.\n\n Notes\n -----\n The ELPD is estimated either by Pareto smoothed importance sampling leave-one-out\n cross-validation (LOO) or using the widely applicable information criterion (WAIC).\n We recommend LOO in line with the work presented by [1]_.\n\n Parameters\n ----------\n comp_df : pandas.DataFrame\n Result of the :func:`arviz.compare` method.\n insample_dev : bool, default False\n Plot in-sample ELPD, that is the value of the information criteria without the\n penalization given by the effective number of parameters (p_loo or p_waic).\n plot_standard_error : bool, default True\n Plot the standard error of the ELPD.\n plot_ic_diff : bool, default True\n Plot standard error of the difference in ELPD between each model\n and the top-ranked model.\n order_by_rank : bool, default True\n If True ensure the best model is used as reference.\n legend : bool, default True\n Add legend to figure.\n figsize : (float, float), optional\n If `None`, size is (6, num of models) inches.\n title : bool, default True\n Show a tittle with a description of how to interpret the plot.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If `None` it will be autoscaled based\n on `figsize`.\n labeller : Labeller, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n plot_kwargs : dict, optional\n Optional arguments for plot elements. Currently accepts 'color_ic',\n 'marker_ic', 'color_insample_dev', 'marker_insample_dev', 'color_dse',\n 'marker_dse', 'ls_min_ic' 'color_ls_min_ic', 'fontsize'\n ax : matplotlib_axes or bokeh_figure, optional\n Matplotlib axes or bokeh figure.\n backend : {\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_kwargs : bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : matplotlib_axes or bokeh_figure\n\n See Also\n --------\n plot_elpd : Plot pointwise elpd differences between two or more models.\n compare : Compare models based on PSIS-LOO loo or WAIC waic cross-validation.\n loo : Compute Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO-CV).\n waic : Compute the widely applicable information criterion.\n\n References\n ----------\n .. [1] Vehtari et al. (2016). Practical Bayesian model evaluation using leave-one-out\n cross-validation and WAIC https://arxiv.org/abs/1507.04544\n\n .. [2] McElreath R. (2022). Statistical Rethinking A Bayesian Course with Examples in\n R and Stan, Second edition, CRC Press.\n\n Examples\n --------\n Show default compare plot\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> model_compare = az.compare({'Centered 8 schools': az.load_arviz_data('centered_eight'),\n >>> 'Non-centered 8 schools': az.load_arviz_data('non_centered_eight')})\n >>> az.plot_compare(model_compare)\n\n Include the in-sample ELDP\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_compare(model_compare, insample_dev=True)\n\n \n source"},{"id":141,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_density","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_density-Tuple","content":" ArviZPythonPlots.plot_density — Method Generate KDE plots for continuous variables and histograms for discrete ones.\n\n Plots are truncated at their 100*(1-alpha)% highest density intervals. Plots are grouped per\n variable and colors assigned to models.\n\n Parameters\n ----------\n data : InferenceData or iterable of InferenceData\n Any object that can be converted to an :class:`arviz.InferenceData` object, or an Iterator\n returning a sequence of such objects.\n Refer to documentation of :func:`arviz.convert_to_dataset` for details.\n group : {\"posterior\", \"prior\"}, default \"posterior\"\n Specifies which InferenceData group should be plotted. If \"posterior\", then the values\n in `posterior_predictive` group are compared to the ones in `observed_data`, if \"prior\" then\n the same comparison happens, but with the values in `prior_predictive` group.\n data_labels : list of str, default None\n List with names for the datasets passed as \"data.\" Useful when plotting more than one\n dataset. Must be the same shape as the data parameter.\n var_names : list of str, optional\n List of variables to plot. If multiple datasets are supplied and `var_names` is not None,\n will print the same set of variables for each dataset. Defaults to None, which results in\n all the variables being plotted.\n filter_vars : {None, \"like\", \"regex\"}, default None\n If `None` (default), interpret `var_names` as the real variables names. If \"like\",\n interpret `var_names` as substrings of the real variables names. If \"regex\",\n interpret `var_names` as regular expressions on the real variables names. See\n :ref:`this section ` for usage examples.\n combine_dims : set_like of str, optional\n List of dimensions to reduce. Defaults to reducing only the \"chain\" and \"draw\" dimensions.\n See :ref:`this section ` for usage examples.\n transform : callable\n Function to transform data (defaults to `None` i.e. the identity function).\n hdi_prob : float, default 0.94\n Probability for the highest density interval. Should be in the interval (0, 1].\n See :ref:`this section ` for usage examples.\n point_estimate : str, optional\n Plot point estimate per variable. Values should be 'mean', 'median', 'mode' or None.\n Defaults to 'auto' i.e. it falls back to default set in ``rcParams``.\n colors : str or list of str, optional\n List with valid matplotlib colors, one color per model. Alternative a string can be passed.\n If the string is `cycle`, it will automatically choose a color per model from matplotlib's\n cycle. If a single color is passed, e.g. 'k', 'C2' or 'red' this color will be used for all\n models. Defaults to `cycle`.\n outline : bool, default True\n Use a line to draw KDEs and histograms.\n hdi_markers : str\n A valid `matplotlib.markers` like 'v', used to indicate the limits of the highest density\n interval. Defaults to empty string (no marker).\n shade : float, default 0\n Alpha blending value for the shaded area under the curve, between 0 (no shade) and 1\n (opaque).\n bw : float or str, optional\n If numeric, indicates the bandwidth and must be positive.\n If str, indicates the method to estimate the bandwidth and must be\n one of \"scott\", \"silverman\", \"isj\" or \"experimental\" when `circular` is False\n and \"taylor\" (for now) when `circular` is True.\n Defaults to \"default\" which means \"experimental\" when variable is not circular\n and \"taylor\" when it is.\n circular : bool, default False\n If True, it interprets the values passed are from a circular variable measured in radians\n and a circular KDE is used. Only valid for 1D KDE.\n grid : tuple, optional\n Number of rows and columns. Defaults to ``None``, the rows and columns are\n automatically inferred. See :ref:`this section ` for usage examples.\n figsize : (float, float), optional\n Figure size. If `None` it will be defined automatically.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If `None` it will be autoscaled based\n on `figsize`.\n labeller : Labeller, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n ax : 2D array-like of matplotlib_axes or bokeh_figure, optional\n A 2D array of locations into which to plot the densities. If not supplied, ArviZ will create\n its own array of plot areas (and return it).\n backend : {\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : 2D ndarray of matplotlib_axes or bokeh_figure\n\n See Also\n --------\n plot_dist : Plot distribution as histogram or kernel density estimates.\n plot_posterior : Plot Posterior densities in the style of John K. Kruschke's book.\n\n Examples\n --------\n Plot default density plot\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> centered = az.load_arviz_data('centered_eight')\n >>> non_centered = az.load_arviz_data('non_centered_eight')\n >>> az.plot_density([centered, non_centered])\n\n Plot variables in a 4x5 grid\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_density([centered, non_centered], grid=(4, 5))\n\n Plot subset variables by specifying variable name exactly\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_density([centered, non_centered], var_names=[\"mu\"])\n\n Plot a specific `az.InferenceData` group\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_density([centered, non_centered], var_names=[\"mu\"], group=\"prior\")\n\n Specify highest density interval\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_density([centered, non_centered], var_names=[\"mu\"], hdi_prob=.5)\n\n Shade plots and/or remove outlines\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_density([centered, non_centered], var_names=[\"mu\"], outline=False, shade=.8)\n\n Specify binwidth for kernel density estimation\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_density([centered, non_centered], var_names=[\"mu\"], bw=.9)\n \n source"},{"id":142,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_dist","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_dist-Tuple","content":" ArviZPythonPlots.plot_dist — Method Plot distribution as histogram or kernel density estimates.\n\n By default continuous variables are plotted using KDEs and discrete ones using histograms\n\n Parameters\n ----------\n values : array-like\n Values to plot from an unknown continuous or discrete distribution.\n values2 : array-like, optional\n Values to plot. If present, a 2D KDE or a hexbin will be estimated.\n color : string\n valid matplotlib color.\n kind : string, default \"auto\"\n By default (\"auto\") continuous variables will use the kind defined by rcParam\n ``plot.density_kind`` and discrete ones will use histograms.\n To override this use \"hist\" to plot histograms and \"kde\" for KDEs.\n cumulative : bool, default False\n If true plot the estimated cumulative distribution function. Defaults to False.\n Ignored for 2D KDE.\n label : string\n Text to include as part of the legend.\n rotated : bool, default False\n Whether to rotate the 1D KDE plot 90 degrees.\n rug : bool, default False\n Add a `rug plot `_ for a specific subset\n of values. Ignored for 2D KDE.\n bw : float or str, optional\n If numeric, indicates the bandwidth and must be positive.\n If str, indicates the method to estimate the bandwidth and must be\n one of \"scott\", \"silverman\", \"isj\" or \"experimental\" when ``is_circular`` is False\n and \"taylor\" (for now) when ``is_circular`` is True.\n Defaults to \"experimental\" when variable is not circular and \"taylor\" when it is.\n quantiles : list, optional\n Quantiles in ascending order used to segment the KDE. Use [.25, .5, .75] for quartiles.\n contour : bool, default True\n If True plot the 2D KDE using contours, otherwise plot a smooth 2D KDE.\n fill_last : bool, default True\n If True fill the last contour of the 2D KDE plot.\n figsize : (float, float), optional\n Figure size. If `None` it will be defined automatically.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If `None` it will be autoscaled based\n on `figsize`. Not implemented for bokeh backend.\n plot_kwargs : dict\n Keywords passed to the pdf line of a 1D KDE. Passed to :func:`arviz.plot_kde` as\n ``plot_kwargs``.\n fill_kwargs : dict\n Keywords passed to the fill under the line (use fill_kwargs={'alpha': 0} to disable fill).\n Ignored for 2D KDE. Passed to :func:`arviz.plot_kde` as ``fill_kwargs``.\n rug_kwargs : dict\n Keywords passed to the rug plot. Ignored if ``rug=False`` or for 2D KDE\n Use ``space`` keyword (float) to control the position of the rugplot.\n The larger this number the lower the rugplot. Passed to\n :func:`arviz.plot_kde` as ``rug_kwargs``.\n contour_kwargs : dict\n Keywords passed to the contourplot. Ignored for 1D KDE.\n contourf_kwargs : dict\n Keywords passed to :meth:`matplotlib.axes.Axes.contourf`. Ignored for 1D KDE.\n pcolormesh_kwargs : dict\n Keywords passed to :meth:`matplotlib.axes.Axes.pcolormesh`. Ignored for 1D KDE.\n hist_kwargs : dict\n Keyword arguments used to customize the histogram. Ignored when plotting a KDE.\n They are passed to :meth:`matplotlib.axes.Axes.hist` if using matplotlib,\n or to :meth:`bokeh.plotting.figure.quad` if using bokeh. In bokeh case,\n the following extra keywords are also supported:\n\n * ``color``: replaces the ``fill_color`` and ``line_color`` of the ``quad`` method\n * ``bins``: taken from ``hist_kwargs`` and passed to :func:`numpy.histogram` instead\n * ``density``: normalize histogram to represent a probability density function,\n Defaults to ``True``\n\n * ``cumulative``: plot the cumulative counts. Defaults to ``False``.\n\n is_circular : {False, True, \"radians\", \"degrees\"}, default False\n Select input type {\"radians\", \"degrees\"} for circular histogram or KDE plot. If True,\n default input type is \"radians\". When this argument is present, it interprets the\n values passed are from a circular variable measured in radians and a circular KDE is\n used. Inputs in \"degrees\" will undergo an internal conversion to radians. Only valid\n for 1D KDE.\n ax : matplotlib_axes or bokeh_figure, optional\n Matplotlib or bokeh targets on which to plot. If not supplied, Arviz will create\n its own plot area (and return it).\n backend : {\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_kwargs :dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : matplotlib axes or bokeh figure\n\n See Also\n --------\n plot_posterior : Plot Posterior densities in the style of John K. Kruschke's book.\n plot_density : Generate KDE plots for continuous variables and histograms for discrete ones.\n plot_kde : 1D or 2D KDE plot taking into account boundary conditions.\n\n Examples\n --------\n Plot an integer distribution\n\n .. plot::\n :context: close-figs\n\n >>> import numpy as np\n >>> import arviz as az\n >>> a = np.random.poisson(4, 1000)\n >>> az.plot_dist(a)\n\n Plot a continuous distribution\n\n .. plot::\n :context: close-figs\n\n >>> b = np.random.normal(0, 1, 1000)\n >>> az.plot_dist(b)\n\n Add a rug under the Gaussian distribution\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_dist(b, rug=True)\n\n Segment into quantiles\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_dist(b, rug=True, quantiles=[.25, .5, .75])\n\n Plot as the cumulative distribution\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_dist(b, rug=True, quantiles=[.25, .5, .75], cumulative=True)\n \n source"},{"id":143,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_dist_comparison","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_dist_comparison-Tuple","content":" ArviZPythonPlots.plot_dist_comparison — Method Plot to compare fitted and unfitted distributions.\n\n The resulting plots will show the compared distributions both on\n separate axes (particularly useful when one of them is substantially tighter\n than another), and plotted together, displaying a grid of three plots per\n distribution.\n\n Parameters\n ----------\n data : InferenceData\n Any object that can be converted to an :class:`arviz.InferenceData` object\n containing the posterior/prior data. Refer to documentation of\n :func:`arviz.convert_to_dataset` for details.\n kind : {\"latent\", \"observed\"}, default \"latent\"\n kind of plot to display The \"latent\" option includes {\"prior\", \"posterior\"},\n and the \"observed\" option includes\n {\"observed_data\", \"prior_predictive\", \"posterior_predictive\"}.\n figsize : (float, float), optional\n Figure size. If ``None`` it will be defined automatically.\n textsize : float\n Text size scaling factor for labels, titles and lines. If ``None`` it will be\n autoscaled based on `figsize`.\n var_names : str, list, list of lists, optional\n if str, plot the variable. if list, plot all the variables in list\n of all groups. if list of lists, plot the vars of groups in respective lists.\n See :ref:`this section ` for usage examples.\n coords : dict\n Dictionary mapping dimensions to selected coordinates to be plotted.\n Dimensions without a mapping specified will include all coordinates for\n that dimension. See :ref:`this section ` for usage examples.\n combine_dims : set_like of str, optional\n List of dimensions to reduce. Defaults to reducing only the \"chain\" and \"draw\" dimensions.\n See :ref:`this section ` for usage examples.\n transform : callable\n Function to transform data (defaults to `None` i.e. the identity function).\n legend : bool\n Add legend to figure. By default True.\n labeller : Labeller, optional\n Class providing the method ``make_pp_label`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n ax : (nvars, 3) array-like of matplotlib_axes, optional\n Matplotlib axes: The ax argument should have shape (nvars, 3), where the\n last column is for the combined before/after plots and columns 0 and 1 are\n for the before and after plots, respectively.\n prior_kwargs : dicts, optional\n Additional keywords passed to :func:`arviz.plot_dist` for prior/predictive groups.\n posterior_kwargs : dicts, optional\n Additional keywords passed to :func:`arviz.plot_dist` for posterior/predictive groups.\n observed_kwargs : dicts, optional\n Additional keywords passed to :func:`arviz.plot_dist` for observed_data group.\n backend : {\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : 2D ndarray of matplotlib_axes\n Returned object will have shape (nvars, 3),\n where the last column is the combined plot and the first columns are the single plots.\n\n See Also\n --------\n plot_bpv : Plot Bayesian p-value for observed data and Posterior/Prior predictive.\n\n Examples\n --------\n Plot the prior/posterior plot for specified vars and coords.\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data('rugby')\n >>> az.plot_dist_comparison(data, var_names=[\"defs\"], coords={\"team\" : [\"Italy\"]})\n\n \n source"},{"id":144,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_dot","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_dot-Tuple","content":" ArviZPythonPlots.plot_dot — Method Plot distribution as dot plot or quantile dot plot.\n\n This function uses the Wilkinson's Algorithm [1]_ to allot dots to bins.\n The quantile dot plots was inspired from [2]_.\n\n Parameters\n ----------\n values : array-like\n Values to plot from an unknown continuous or discrete distribution.\n binwidth : float, optional\n Width of the bin for drawing the dot plot.\n dotsize : float, default 1\n The size of the dots relative to the bin width. The default makes dots be\n just about as wide as the bin width.\n stackratio : float, default 1\n The distance between the center of the dots in the same stack relative to the bin height.\n The default makes dots in the same stack just touch each other.\n point_interval : bool, default False\n Plots the point interval. Uses ``hdi_prob`` to plot the HDI interval\n point_estimate : str, optional\n Plot point estimate per variable. Values should be ``mean``, ``median``, ``mode`` or None.\n Defaults to ``auto`` i.e. it falls back to default set in rcParams.\n dotcolor : string, optional\n The color of the dots. Should be a valid matplotlib color.\n intervalcolor : string, optional\n The color of the interval. Should be a valid matplotlib color.\n linewidth : int, default None\n Line width throughout. If None it will be autoscaled based on `figsize`.\n markersize : int, default None\n Markersize throughout. If None it will be autoscaled based on `figsize`.\n markercolor : string, optional\n The color of the marker when plot_interval is True. Should be a valid matplotlib color.\n marker : string, default \"o\"\n The shape of the marker. Valid for matplotlib backend.\n hdi_prob : float, optional\n Valid only when point_interval is True. Plots HDI for chosen percentage of density.\n Defaults to ``stats.hdi_prob`` rcParam. See :ref:`this section `\n for usage examples.\n rotated : bool, default False\n Whether to rotate the dot plot by 90 degrees.\n nquantiles : int, default 50\n Number of quantiles to plot, used for quantile dot plots.\n quartiles : bool, default True\n If True then the quartile interval will be plotted with the HDI.\n figsize : (float,float), optional\n Figure size. If ``None`` it will be defined automatically.\n plot_kwargs : dict, optional\n Keywords passed for customizing the dots. Passed to :class:`mpl:matplotlib.patches.Circle`\n in matplotlib and :meth:`bokeh.plotting.figure.circle` in bokeh.\n backend :{\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n ax : axes, optional\n Matplotlib_axes or bokeh_figure.\n show : bool, optional\n Call backend show function.\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n\n Returns\n -------\n axes : matplotlib_axes or bokeh_figure\n\n See Also\n --------\n plot_dist : Plot distribution as histogram or kernel density estimates.\n\n References\n ----------\n .. [1] Leland Wilkinson (1999) Dot Plots, The American Statistician, 53:3, 276-281,\n DOI: 10.1080/00031305.1999.10474474\n .. [2] Matthew Kay, Tara Kola, Jessica R. Hullman,\n and Sean A. Munson. 2016. When (ish) is My Bus? User-centered Visualizations of Uncertainty\n in Everyday, Mobile Predictive Systems. DOI:https://doi.org/10.1145/2858036.2858558\n\n Examples\n --------\n Plot dot plot for a set of data points\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> import numpy as np\n >>> values = np.random.normal(0, 1, 500)\n >>> az.plot_dot(values)\n\n Manually adjust number of quantiles to plot\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_dot(values, nquantiles=100)\n\n Add a point interval under the dot plot\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_dot(values, point_interval=True)\n\n Rotate the dot plots by 90 degrees i.e swap x and y axis\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_dot(values, point_interval=True, rotated=True)\n\n \n source"},{"id":145,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_ecdf","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_ecdf-Tuple","content":" ArviZPythonPlots.plot_ecdf — Method Plot ECDF or ECDF-Difference Plot with Confidence bands.\n\n Plots of the empirical CDF estimates of an array. When `values2` argument is provided,\n the two empirical CDFs are overlaid with the distribution of `values` on top\n (in a darker shade) and confidence bands in a more transparent shade. Optionally, the difference\n between the two empirical CDFs can be computed, and the PIT for a single dataset or a comparison\n between two samples.\n\n Notes\n -----\n This plot computes the confidence bands with the simulated based algorithm presented in [1]_.\n\n Parameters\n ----------\n values : array-like\n Values to plot from an unknown continuous or discrete distribution.\n values2 : array-like, optional\n Values to compare to the original sample.\n cdf : callable, optional\n Cumulative distribution function of the distribution to compare the original sample.\n difference : bool, default False\n If True then plot ECDF-difference plot otherwise ECDF plot.\n pit : bool, default False\n If True plots the ECDF or ECDF-diff of PIT of sample.\n confidence_bands : bool, default None\n If True plots the simultaneous or pointwise confidence bands with `1 - fpr`\n confidence level.\n pointwise : bool, default False\n If True plots pointwise confidence bands otherwise simultaneous bands.\n npoints : int, default 100\n This denotes the granularity size of our plot i.e the number of evaluation points\n for the ecdf or ecdf-difference plots.\n num_trials : int, default 500\n The number of random ECDFs to generate for constructing simultaneous confidence bands.\n fpr : float, default 0.05\n The type I error rate s.t `1 - fpr` denotes the confidence level of bands.\n figsize : (float,float), optional\n Figure size. If `None` it will be defined automatically.\n fill_band : bool, default True\n If True it fills in between to mark the area inside the confidence interval. Otherwise,\n plot the border lines.\n plot_kwargs : dict, optional\n Additional kwargs passed to :func:`mpl:matplotlib.pyplot.step` or\n :meth:`bokeh.plotting.figure.step`\n fill_kwargs : dict, optional\n Additional kwargs passed to :func:`mpl:matplotlib.pyplot.fill_between` or\n :meth:`bokeh:bokeh.plotting.Figure.varea`\n plot_outline_kwargs : dict, optional\n Additional kwargs passed to :meth:`mpl:matplotlib.axes.Axes.plot` or\n :meth:`bokeh:bokeh.plotting.Figure.line`\n ax :axes, optional\n Matplotlib axes or bokeh figures.\n show : bool, optional\n Call backend show function.\n backend : {\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n\n Returns\n -------\n axes : matplotlib_axes or bokeh_figure\n\n References\n ----------\n .. [1] Säilynoja, T., Bürkner, P.C. and Vehtari, A., 2021. Graphical Test for\n Discrete Uniformity and its Applications in Goodness of Fit Evaluation and\n Multiple Sample Comparison. arXiv preprint arXiv:2103.10522.\n\n Examples\n --------\n Plot ecdf plot for a given sample\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> from scipy.stats import uniform, binom, norm\n\n >>> sample = norm(0,1).rvs(1000)\n >>> az.plot_ecdf(sample)\n\n Plot ecdf plot with confidence bands for comparing a given sample w.r.t a given distribution\n\n .. plot::\n :context: close-figs\n\n >>> distribution = norm(0,1)\n >>> az.plot_ecdf(sample, cdf = distribution.cdf, confidence_bands = True)\n\n Plot ecdf-difference plot with confidence bands for comparing a given sample\n w.r.t a given distribution\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_ecdf(sample, cdf = distribution.cdf,\n >>> confidence_bands = True, difference = True)\n\n Plot ecdf plot with confidence bands for PIT of sample for comparing a given sample\n w.r.t a given distribution\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_ecdf(sample, cdf = distribution.cdf,\n >>> confidence_bands = True, pit = True)\n\n Plot ecdf-difference plot with confidence bands for PIT of sample for comparing a given\n sample w.r.t a given distribution\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_ecdf(sample, cdf = distribution.cdf,\n >>> confidence_bands = True, difference = True, pit = True)\n\n You could also plot the above w.r.t another sample rather than a given distribution.\n For eg: Plot ecdf-difference plot with confidence bands for PIT of sample for\n comparing a given sample w.r.t a given sample\n\n .. plot::\n :context: close-figs\n\n >>> sample2 = norm(0,1).rvs(5000)\n >>> az.plot_ecdf(sample, sample2, confidence_bands = True, difference = True, pit = True)\n\n \n source"},{"id":146,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_elpd","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_elpd-Tuple","content":" ArviZPythonPlots.plot_elpd — Method Plot pointwise elpd differences between two or more models.\n\n Pointwise model comparison based on their expected log pointwise predictive density (ELPD).\n\n Notes\n -----\n The ELPD is estimated either by Pareto smoothed importance sampling leave-one-out\n cross-validation (LOO) or using the widely applicable information criterion (WAIC).\n We recommend LOO in line with the work presented by [1]_.\n\n Parameters\n ----------\n compare_dict : mapping of {str : ELPDData or InferenceData}\n A dictionary mapping the model name to the object containing inference data or the result\n of :func:`arviz.loo` or :func:`arviz.waic` functions.\n Refer to :func:`arviz.convert_to_inference_data` for details on possible dict items.\n color : str or array_like, default \"C0\"\n Colors of the scatter plot. If color is a str all dots will have the same color.\n If it is the size of the observations, each dot will have the specified color.\n Otherwise, it will be interpreted as a list of the dims to be used for the color code.\n xlabels : bool, default False\n Use coords as xticklabels.\n figsize : (float, float), optional\n If `None`, size is (8 + numvars, 8 + numvars).\n textsize : float, optional\n Text size for labels. If `None` it will be autoscaled based on `figsize`.\n coords : mapping, optional\n Coordinates of points to plot. **All** values are used for computation, but only a\n subset can be plotted for convenience. See :ref:`this section `\n for usage examples.\n legend : bool, default False\n Include a legend to the plot. Only taken into account when color argument is a dim name.\n threshold : float, optional\n If some elpd difference is larger than ``threshold * elpd.std()``, show its label. If\n `None`, no observations will be highlighted.\n ic : str, optional\n Information Criterion (\"loo\" for PSIS-LOO, \"waic\" for WAIC) used to compare models.\n Defaults to ``rcParams[\"stats.information_criterion\"]``.\n Only taken into account when input is :class:`arviz.InferenceData`.\n scale : str, optional\n Scale argument passed to :func:`arviz.loo` or :func:`arviz.waic`, see their docs for\n details. Only taken into account when values in ``compare_dict`` are\n :class:`arviz.InferenceData`.\n var_name : str, optional\n Argument passed to to :func:`arviz.loo` or :func:`arviz.waic`, see their docs for\n details. Only taken into account when values in ``compare_dict`` are\n :class:`arviz.InferenceData`.\n plot_kwargs : dicts, optional\n Additional keywords passed to :meth:`matplotlib.axes.Axes.scatter`.\n ax : axes, optional\n :class:`matplotlib.axes.Axes` or :class:`bokeh.plotting.Figure`.\n backend : {\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : matplotlib_axes or bokeh_figure\n\n See Also\n --------\n plot_compare : Summary plot for model comparison.\n loo : Compute Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO-CV).\n waic : Compute the widely applicable information criterion.\n\n References\n ----------\n .. [1] Vehtari et al. (2016). Practical Bayesian model evaluation using leave-one-out\n cross-validation and WAIC https://arxiv.org/abs/1507.04544\n\n Examples\n --------\n Compare pointwise PSIS-LOO for centered and non centered models of the 8-schools problem\n using matplotlib.\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> idata1 = az.load_arviz_data(\"centered_eight\")\n >>> idata2 = az.load_arviz_data(\"non_centered_eight\")\n >>> az.plot_elpd(\n >>> {\"centered model\": idata1, \"non centered model\": idata2},\n >>> xlabels=True\n >>> )\n\n .. bokeh-plot::\n :source-position: above\n\n import arviz as az\n idata1 = az.load_arviz_data(\"centered_eight\")\n idata2 = az.load_arviz_data(\"non_centered_eight\")\n az.plot_elpd(\n {\"centered model\": idata1, \"non centered model\": idata2},\n backend=\"bokeh\"\n )\n\n \n source"},{"id":147,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_energy","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_energy-Tuple","content":" ArviZPythonPlots.plot_energy — Method Plot energy transition distribution and marginal energy distribution in HMC algorithms.\n\n This may help to diagnose poor exploration by gradient-based algorithms like HMC or NUTS.\n The energy function in HMC can identify posteriors with heavy tailed distributions, that\n in practice are challenging for sampling.\n\n This plot is in the style of the one used in [1]_.\n\n Parameters\n ----------\n data : obj\n :class:`xarray.Dataset`, or any object that can be converted (must represent\n ``sample_stats`` and have an ``energy`` variable).\n kind : str, optional\n Type of plot to display (\"kde\", \"hist\").\n bfmi : bool, default True\n If True add to the plot the value of the estimated Bayesian fraction of missing\n information.\n figsize : (float, float), optional\n Figure size. If `None` it will be defined automatically.\n legend : bool, default True\n Flag for plotting legend.\n fill_alpha : tuple, default (1, 0.75)\n Alpha blending value for the shaded area under the curve, between 0\n (no shade) and 1 (opaque).\n fill_color : tuple of valid matplotlib color, default ('C0', 'C5')\n Color for Marginal energy distribution and Energy transition distribution.\n bw : float or str, optional\n If numeric, indicates the bandwidth and must be positive.\n If str, indicates the method to estimate the bandwidth and must be\n one of \"scott\", \"silverman\", \"isj\" or \"experimental\". Defaults to \"experimental\".\n Only works if ``kind='kde'``.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If `None` it will be autoscaled\n based on `figsize`.\n fill_kwargs : dicts, optional\n Additional keywords passed to :func:`arviz.plot_kde` (to control the shade).\n plot_kwargs : dicts, optional\n Additional keywords passed to :func:`arviz.plot_kde` or :func:`matplotlib.pyplot.hist`\n (if ``type='hist'``).\n ax : axes, optional\n :class:`matplotlib.axes.Axes` or :class:`bokeh.plotting.Figure`.\n backend : {\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : matplotlib axes or bokeh figures\n\n See Also\n --------\n bfmi : Calculate the estimated Bayesian fraction of missing information (BFMI).\n\n References\n ----------\n .. [1] Betancourt (2016). Diagnosing Suboptimal Cotangent Disintegrations in\n Hamiltonian Monte Carlo https://arxiv.org/abs/1604.00695\n\n Examples\n --------\n Plot a default energy plot\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data('centered_eight')\n >>> az.plot_energy(data)\n\n Represent energy plot via histograms\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_energy(data, kind='hist')\n\n \n source"},{"id":148,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_ess","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_ess-Tuple","content":" ArviZPythonPlots.plot_ess — Method Generate quantile, local, or evolution ESS plots.\n\n The local and the quantile ESS plots are recommended for checking\n that there are enough samples for all the explored regions of the\n parameter space. Checking local and quantile ESS is particularly\n relevant when working with HDI intervals as opposed to ESS bulk,\n which is suitable for point estimates.\n\n Parameters\n ----------\n idata : InferenceData\n Any object that can be converted to an :class:`arviz.InferenceData` object\n Refer to documentation of :func:`arviz.convert_to_dataset` for details.\n var_names : list of str, optional\n Variables to be plotted. Prefix the variables by ``~`` when you want to exclude\n them from the plot. See :ref:`this section ` for usage examples.\n filter_vars : {None, \"like\", \"regex\"}, default None\n If `None` (default), interpret `var_names` as the real variables names. If \"like\",\n interpret `var_names` as substrings of the real variables names. If \"regex\",\n interpret `var_names` as regular expressions on the real variables names. See\n :ref:`this section ` for usage examples.\n kind : {\"local\", \"quantile\", \"evolution\"}, default \"local\"\n Specify the kind of plot:\n\n * The ``kind=\"local\"`` argument generates the ESS' local efficiency for\n estimating quantiles of a desired posterior.\n * The ``kind=\"quantile\"`` argument generates the ESS' local efficiency\n for estimating small-interval probability of a desired posterior.\n * The ``kind=\"evolution\"`` argument generates the estimated ESS'\n with incrised number of iterations of a desired posterior.\n\n relative : bool, default False\n Show relative ess in plot ``ress = ess / N``.\n coords : dict, optional\n Coordinates of `var_names` to be plotted. Passed to :meth:`xarray.Dataset.sel`.\n See :ref:`this section ` for usage examples.\n grid : tuple, optional\n Number of rows and columns. By default, the rows and columns are\n automatically inferred. See :ref:`this section ` for usage examples.\n figsize : (float, float), optional\n Figure size. If ``None`` it will be defined automatically.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If ``None`` it will be autoscaled\n based on `figsize`.\n rug : bool, default False\n Add a `rug plot `_ for a specific subset of values.\n rug_kind : str, default \"diverging\"\n Variable in sample stats to use as rug mask. Must be a boolean variable.\n n_points : int, default 20\n Number of points for which to plot their quantile/local ess or number of subsets\n in the evolution plot.\n extra_methods : bool, default False\n Plot mean and sd ESS as horizontal lines. Not taken into account if ``kind = 'evolution'``.\n min_ess : int, default 400\n Minimum number of ESS desired. If ``relative=True`` the line is plotted at\n ``min_ess / n_samples`` for local and quantile kinds and as a curve following\n the ``min_ess / n`` dependency in evolution kind.\n labeller : Labeller, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n ax : 2D array-like of matplotlib_axes or bokeh_figure, optional\n A 2D array of locations into which to plot the densities. If not supplied, ArviZ will create\n its own array of plot areas (and return it).\n extra_kwargs : dict, optional\n If evolution plot, `extra_kwargs` is used to plot ess tail and differentiate it\n from ess bulk. Otherwise, passed to extra methods lines.\n text_kwargs : dict, optional\n Only taken into account when ``extra_methods=True``. kwargs passed to ax.annotate\n for extra methods lines labels. It accepts the additional\n key ``x`` to set ``xy=(text_kwargs[\"x\"], mcse)``\n hline_kwargs : dict, optional\n kwargs passed to :func:`~matplotlib.axes.Axes.axhline` or to :class:`~bokeh.models.Span`\n depending on the backend for the horizontal minimum ESS line.\n For relative ess evolution plots the kwargs are passed to\n :func:`~matplotlib.axes.Axes.plot` or to :class:`~bokeh.plotting.figure.line`\n rug_kwargs : dict\n kwargs passed to rug plot.\n backend : {\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n **kwargs\n Passed as-is to :meth:`mpl:matplotlib.axes.Axes.hist` or\n :meth:`mpl:matplotlib.axes.Axes.plot` function depending on the\n value of `kind`.\n\n Returns\n -------\n axes : matplotlib_axes or bokeh_figure\n\n See Also\n --------\n ess : Calculate estimate of the effective sample size.\n\n References\n ----------\n .. [1] Vehtari et al. (2019). Rank-normalization, folding, and\n localization: An improved Rhat for assessing convergence of\n MCMC https://arxiv.org/abs/1903.08008\n\n Examples\n --------\n Plot local ESS.\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> idata = az.load_arviz_data(\"centered_eight\")\n >>> coords = {\"school\": [\"Choate\", \"Lawrenceville\"]}\n >>> az.plot_ess(\n ... idata, kind=\"local\", var_names=[\"mu\", \"theta\"], coords=coords\n ... )\n\n Plot ESS evolution as the number of samples increase. When the model is converging properly,\n both lines in this plot should be roughly linear.\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_ess(\n ... idata, kind=\"evolution\", var_names=[\"mu\", \"theta\"], coords=coords\n ... )\n\n Customize local ESS plot to look like reference paper.\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_ess(\n ... idata, kind=\"local\", var_names=[\"mu\"], drawstyle=\"steps-mid\", color=\"k\",\n ... linestyle=\"-\", marker=None, rug=True, rug_kwargs={\"color\": \"r\"}\n ... )\n\n Customize ESS evolution plot to look like reference paper.\n\n .. plot::\n :context: close-figs\n\n >>> extra_kwargs = {\"color\": \"lightsteelblue\"}\n >>> az.plot_ess(\n ... idata, kind=\"evolution\", var_names=[\"mu\"],\n ... color=\"royalblue\", extra_kwargs=extra_kwargs\n ... )\n\n \n source"},{"id":149,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_forest","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_forest-Tuple","content":" ArviZPythonPlots.plot_forest — Method Forest plot to compare HDI intervals from a number of distributions.\n\n Generate forest or ridge plots to compare distributions from a model or list of models.\n Additionally, the function can display effective sample sizes (ess) and Rhats to visualize\n convergence diagnostics alongside the distributions.\n\n Parameters\n ----------\n data : InferenceData\n Any object that can be converted to an :class:`arviz.InferenceData` object\n Refer to documentation of :func:`arviz.convert_to_dataset` for details.\n kind : {\"foresplot\", \"ridgeplot\"}, default \"forestplot\"\n Specify the kind of plot:\n\n * The ``kind=\"forestplot\"`` generates credible intervals, where the central points are the\n estimated posterior means, the thick lines are the central quartiles, and the thin lines\n represent the :math:`100\\times`(`hdi_prob`)% highest density intervals.\n * The ``kind=\"ridgeplot\"`` option generates density plots (kernel density estimate or\n histograms) in the same graph. Ridge plots can be configured to have different overlap,\n truncation bounds and quantile markers.\n\n model_names : list of str, optional\n List with names for the models in the list of data. Useful when plotting more that one\n dataset.\n var_names : list of str, optional\n Variables to be plotted. Prefix the variables by ``~`` when you want to exclude\n them from the plot. See :ref:`this section ` for usage examples.\n combine_dims : set_like of str, optional\n List of dimensions to reduce. Defaults to reducing only the \"chain\" and \"draw\" dimensions.\n See :ref:`this section ` for usage examples.\n filter_vars : {None, \"like\", \"regex\"}, default None\n If `None` (default), interpret `var_names` as the real variables names. If \"like\",\n interpret `var_names` as substrings of the real variables names. If \"regex\",\n interpret `var_names` as regular expressions on the real variables names. See\n :ref:`this section ` for usage examples.\n transform : callable, optional\n Function to transform data (defaults to None i.e.the identity function).\n coords : dict, optional\n Coordinates of ``var_names`` to be plotted. Passed to :meth:`xarray.Dataset.sel`.\n See :ref:`this section ` for usage examples.\n combined : bool, default False\n Flag for combining multiple chains into a single chain. If False, chains will\n be plotted separately. See :ref:`this section ` for usage examples.\n hdi_prob : float, default 0.94\n Plots highest posterior density interval for chosen percentage of density.\n See :ref:`this section ` for usage examples.\n rope : tuple or dictionary of tuples\n Lower and upper values of the Region of Practical Equivalence. If a list with one interval\n only is provided, the ROPE will be displayed across the y-axis. If more than one\n interval is provided the length of the list should match the number of variables.\n quartiles : bool, default True\n Flag for plotting the interquartile range, in addition to the ``hdi_prob`` intervals.\n r_hat : bool, default False\n Flag for plotting Split R-hat statistics. Requires 2 or more chains.\n ess : bool, default False\n Flag for plotting the effective sample size.\n colors : list or string, optional\n list with valid matplotlib colors, one color per model. Alternative a string can be passed.\n If the string is `cycle`, it will automatically chose a color per model from the matplotlibs\n cycle. If a single color is passed, eg 'k', 'C2', 'red' this color will be used for all\n models. Defaults to 'cycle'.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If `None` it will be autoscaled based\n on ``figsize``.\n linewidth : int, optional\n Line width throughout. If `None` it will be autoscaled based on ``figsize``.\n markersize : int, optional\n Markersize throughout. If `None` it will be autoscaled based on ``figsize``.\n legend : bool, optional\n Show a legend with the color encoded model information.\n Defaults to True, if there are multiple models.\n labeller : Labeller, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n ridgeplot_alpha: float, optional\n Transparency for ridgeplot fill. If ``ridgeplot_alpha=0``, border is colored by model,\n otherwise a `black` outline is used.\n ridgeplot_overlap : float, default 2\n Overlap height for ridgeplots.\n ridgeplot_kind : string, optional\n By default (\"auto\") continuous variables are plotted using KDEs and discrete ones using\n histograms. To override this use \"hist\" to plot histograms and \"density\" for KDEs.\n ridgeplot_truncate : bool, default True\n Whether to truncate densities according to the value of ``hdi_prob``.\n ridgeplot_quantiles : list, optional\n Quantiles in ascending order used to segment the KDE. Use [.25, .5, .75] for quartiles.\n figsize : (float, float), optional\n Figure size. If `None`, it will be defined automatically.\n ax : axes, optional\n :class:`matplotlib.axes.Axes` or :class:`bokeh.plotting.Figure`.\n backend : {\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_config : dict, optional\n Currently specifies the bounds to use for bokeh axes. Defaults to value set in ``rcParams``.\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n 1D ndarray of matplotlib_axes or bokeh_figures\n\n See Also\n --------\n plot_posterior : Plot Posterior densities in the style of John K. Kruschke's book.\n plot_density : Generate KDE plots for continuous variables and histograms for discrete ones.\n summary : Create a data frame with summary statistics.\n\n Examples\n --------\n Forestplot\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> non_centered_data = az.load_arviz_data('non_centered_eight')\n >>> axes = az.plot_forest(non_centered_data,\n >>> kind='forestplot',\n >>> var_names=[\"^the\"],\n >>> filter_vars=\"regex\",\n >>> combined=True,\n >>> figsize=(9, 7))\n >>> axes[0].set_title('Estimated theta for 8 schools model')\n\n Forestplot with multiple datasets\n\n .. plot::\n :context: close-figs\n\n >>> centered_data = az.load_arviz_data('centered_eight')\n >>> axes = az.plot_forest([non_centered_data, centered_data],\n >>> model_names = [\"non centered eight\", \"centered eight\"],\n >>> kind='forestplot',\n >>> var_names=[\"^the\"],\n >>> filter_vars=\"regex\",\n >>> combined=True,\n >>> figsize=(9, 7))\n >>> axes[0].set_title('Estimated theta for 8 schools models')\n\n Forestplot with ropes\n\n .. plot::\n :context: close-figs\n\n >>> rope = {'theta': [{'school': 'Choate', 'rope': (2, 4)}], 'mu': [{'rope': (-2, 2)}]}\n >>> axes = az.plot_forest(non_centered_data,\n >>> rope=rope,\n >>> var_names='~tau',\n >>> combined=True,\n >>> figsize=(9, 7))\n >>> axes[0].set_title('Estimated theta for 8 schools model')\n\n\n Ridgeplot\n\n .. plot::\n :context: close-figs\n\n >>> axes = az.plot_forest(non_centered_data,\n >>> kind='ridgeplot',\n >>> var_names=['theta'],\n >>> combined=True,\n >>> ridgeplot_overlap=3,\n >>> colors='white',\n >>> figsize=(9, 7))\n >>> axes[0].set_title('Estimated theta for 8 schools model')\n\n Ridgeplot non-truncated and with quantiles\n\n .. plot::\n :context: close-figs\n\n >>> axes = az.plot_forest(non_centered_data,\n >>> kind='ridgeplot',\n >>> var_names=['theta'],\n >>> combined=True,\n >>> ridgeplot_truncate=False,\n >>> ridgeplot_quantiles=[.25, .5, .75],\n >>> ridgeplot_overlap=0.7,\n >>> colors='white',\n >>> figsize=(9, 7))\n >>> axes[0].set_title('Estimated theta for 8 schools model')\n \n source"},{"id":150,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_hdi","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_hdi-Tuple","content":" ArviZPythonPlots.plot_hdi — Method \n Plot HDI intervals for regression data.\n\n Parameters\n ----------\n x : array-like\n Values to plot.\n y : array-like, optional\n Values from which to compute the HDI. Assumed shape ``(chain, draw, \\*shape)``.\n Only optional if ``hdi_data`` is present.\n hdi_data : array_like, optional\n Precomputed HDI values to use. Assumed shape is ``(*x.shape, 2)``.\n hdi_prob : float, optional\n Probability for the highest density interval. Defaults to ``stats.hdi_prob`` rcParam.\n color : str, optional\n Color used for the limits of the HDI and fill. Should be a valid matplotlib color.\n circular : bool, optional\n Whether to compute the HDI taking into account ``x`` is a circular variable\n (in the range [-np.pi, np.pi]) or not. Defaults to False (i.e non-circular variables).\n smooth : boolean, optional\n If True the result will be smoothed by first computing a linear interpolation of the data\n over a regular grid and then applying the Savitzky-Golay filter to the interpolated data.\n Defaults to True.\n smooth_kwargs : dict, optional\n Additional keywords modifying the Savitzky-Golay filter. See\n :func:`scipy:scipy.signal.savgol_filter` for details.\n figsize : tuple\n Figure size. If None it will be defined automatically.\n fill_kwargs : dict, optional\n Keywords passed to :meth:`mpl:matplotlib.axes.Axes.fill_between`\n (use ``fill_kwargs={'alpha': 0}`` to disable fill) or to\n :meth:`bokeh.plotting.Figure.patch`.\n plot_kwargs : dict, optional\n HDI limits keyword arguments, passed to :meth:`mpl:matplotlib.axes.Axes.plot` or\n :meth:`bokeh.plotting.Figure.patch`.\n hdi_kwargs : dict, optional\n Keyword arguments passed to :func:`~arviz.hdi`. Ignored if ``hdi_data`` is present.\n ax : axes, optional\n Matplotlib axes or bokeh figures.\n backend : {\"matplotlib\",\"bokeh\"}, optional\n Select plotting backend.\n backend_kwargs : bool, optional\n These are kwargs specific to the backend being used, passed to\n :meth:`mpl:matplotlib.axes.Axes.plot` or\n :meth:`bokeh.plotting.Figure.patch`.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : matplotlib axes or bokeh figures\n\n See Also\n --------\n hdi : Calculate highest density interval (HDI) of array for given probability.\n\n Examples\n --------\n Plot HDI interval of simulated regression data using `y` argument:\n\n .. plot::\n :context: close-figs\n\n >>> import numpy as np\n >>> import arviz as az\n >>> x_data = np.random.normal(0, 1, 100)\n >>> y_data = np.random.normal(2 + x_data * 0.5, 0.5, size=(2, 50, 100))\n >>> az.plot_hdi(x_data, y_data)\n\n ``plot_hdi`` can also be given precalculated values with the argument ``hdi_data``. This example\n shows how to use :func:`~arviz.hdi` to precalculate the values and pass these values to\n ``plot_hdi``. Similarly to an example in ``hdi`` we are using the ``input_core_dims``\n argument of :func:`~arviz.wrap_xarray_ufunc` to manually define the dimensions over which\n to calculate the HDI.\n\n .. plot::\n :context: close-figs\n\n >>> hdi_data = az.hdi(y_data, input_core_dims=[[\"draw\"]])\n >>> ax = az.plot_hdi(x_data, hdi_data=hdi_data[0], color=\"r\", fill_kwargs={\"alpha\": .2})\n >>> az.plot_hdi(x_data, hdi_data=hdi_data[1], color=\"k\", ax=ax, fill_kwargs={\"alpha\": .2})\n\n ``plot_hdi`` can also be used with Inference Data objects. Here we use the posterior predictive\n to plot the HDI interval.\n\n .. plot::\n :context: close-figs\n\n >>> X = np.random.normal(0,1,100)\n >>> Y = np.random.normal(2 + X * 0.5, 0.5, size=(2,10,100))\n >>> idata = az.from_dict(posterior={\"y\": Y}, constant_data={\"x\":X})\n >>> x_data = idata.constant_data.x\n >>> y_data = idata.posterior.y\n >>> az.plot_hdi(x_data, y_data)\n\n \n source"},{"id":151,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_kde","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_kde-Tuple","content":" ArviZPythonPlots.plot_kde — Method 1D or 2D KDE plot taking into account boundary conditions.\n\n Parameters\n ----------\n values : array-like\n Values to plot\n values2 : array-like, optional\n Values to plot. If present, a 2D KDE will be estimated\n cumulative : bool\n If true plot the estimated cumulative distribution function. Defaults to False.\n Ignored for 2D KDE\n rug : bool\n If True adds a rugplot. Defaults to False. Ignored for 2D KDE\n label : string\n Text to include as part of the legend\n bw : float or str, optional\n If numeric, indicates the bandwidth and must be positive.\n If str, indicates the method to estimate the bandwidth and must be\n one of \"scott\", \"silverman\", \"isj\" or \"experimental\" when ``is_circular`` is False\n and \"taylor\" (for now) when ``is_circular`` is True.\n Defaults to \"default\" which means \"experimental\" when variable is not circular\n and \"taylor\" when it is.\n adaptive : bool, optional.\n If True, an adaptative bandwidth is used. Only valid for 1D KDE.\n Defaults to False.\n quantiles : list\n Quantiles in ascending order used to segment the KDE.\n Use [.25, .5, .75] for quartiles. Defaults to None.\n rotated : bool\n Whether to rotate the 1D KDE plot 90 degrees.\n contour : bool\n If True plot the 2D KDE using contours, otherwise plot a smooth 2D KDE.\n Defaults to True.\n hdi_probs : list\n Plots highest density credibility regions for the provided probabilities for a 2D KDE.\n Defaults to matplotlib chosen levels with no fixed probability associated.\n fill_last : bool\n If True fill the last contour of the 2D KDE plot. Defaults to False.\n figsize : (float, float), optional\n Figure size. If None it will be defined automatically.\n textsize : float\n Text size scaling factor for labels, titles and lines. If None it will be autoscaled based\n on ``figsize``. Not implemented for bokeh backend.\n plot_kwargs : dict\n Keywords passed to the pdf line of a 1D KDE. See :meth:`mpl:matplotlib.axes.Axes.plot`\n or :meth:`bokeh:bokeh.plotting.Figure.line` for a description of accepted values.\n fill_kwargs : dict\n Keywords passed to the fill under the line (use ``fill_kwargs={'alpha': 0}``\n to disable fill). Ignored for 2D KDE. Passed to\n :meth:`bokeh.plotting.Figure.patch`.\n rug_kwargs : dict\n Keywords passed to the rug plot. Ignored if ``rug=False`` or for 2D KDE\n Use ``space`` keyword (float) to control the position of the rugplot. The larger this number\n the lower the rugplot. Passed to :class:`bokeh:bokeh.models.glyphs.Scatter`.\n contour_kwargs : dict\n Keywords passed to :meth:`mpl:matplotlib.axes.Axes.contour`\n to draw contour lines or :meth:`bokeh.plotting.Figure.patch`.\n Ignored for 1D KDE.\n contourf_kwargs : dict\n Keywords passed to :meth:`mpl:matplotlib.axes.Axes.contourf`\n to draw filled contours. Ignored for 1D KDE.\n pcolormesh_kwargs : dict\n Keywords passed to :meth:`mpl:matplotlib.axes.Axes.pcolormesh` or\n :meth:`bokeh.plotting.Figure.image`.\n Ignored for 1D KDE.\n is_circular : {False, True, \"radians\", \"degrees\"}. Default False.\n Select input type {\"radians\", \"degrees\"} for circular histogram or KDE plot. If True,\n default input type is \"radians\". When this argument is present, it interprets ``values``\n is a circular variable measured in radians and a circular KDE is used. Inputs in\n \"degrees\" will undergo an internal conversion to radians.\n ax : axes, optional\n Matplotlib axes or bokeh figures.\n legend : bool\n Add legend to the figure. By default True.\n backend: str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default \"matplotlib\".\n backend_kwargs: bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or\n :func:`bokeh.plotting.figure`. For additional documentation\n check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n return_glyph : bool, optional\n Internal argument to return glyphs for bokeh\n\n Returns\n -------\n axes : matplotlib.Axes or bokeh.plotting.Figure\n Object containing the kde plot\n glyphs : list, optional\n Bokeh glyphs present in plot. Only provided if ``return_glyph`` is True.\n\n See Also\n --------\n kde : One dimensional density estimation.\n plot_dist : Plot distribution as histogram or kernel density estimates.\n\n Examples\n --------\n Plot default KDE\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> non_centered = az.load_arviz_data('non_centered_eight')\n >>> mu_posterior = np.concatenate(non_centered.posterior[\"mu\"].values)\n >>> tau_posterior = np.concatenate(non_centered.posterior[\"tau\"].values)\n >>> az.plot_kde(mu_posterior)\n\n\n Plot KDE with rugplot\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(mu_posterior, rug=True)\n\n Plot KDE with adaptive bandwidth\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(mu_posterior, adaptive=True)\n\n Plot KDE with a different bandwidth estimator\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(mu_posterior, bw=\"scott\")\n\n Plot KDE with a bandwidth specified manually\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(mu_posterior, bw=0.4)\n\n Plot KDE for a circular variable\n\n .. plot::\n :context: close-figs\n\n >>> rvs = np.random.vonmises(mu=np.pi, kappa=2, size=500)\n >>> az.plot_kde(rvs, is_circular=True)\n\n\n Plot a cumulative distribution\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(mu_posterior, cumulative=True)\n\n\n\n Rotate plot 90 degrees\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(mu_posterior, rotated=True)\n\n\n Plot 2d contour KDE\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(mu_posterior, values2=tau_posterior)\n\n\n Plot 2d contour KDE, without filling and contour lines using viridis cmap\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(mu_posterior, values2=tau_posterior,\n ... contour_kwargs={\"colors\":None, \"cmap\":plt.cm.viridis},\n ... contourf_kwargs={\"alpha\":0});\n\n Plot 2d contour KDE, set the number of levels to 3.\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(\n ... mu_posterior, values2=tau_posterior,\n ... contour_kwargs={\"levels\":3}, contourf_kwargs={\"levels\":3}\n ... );\n\n Plot 2d contour KDE with 30%, 60% and 90% HDI contours.\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(mu_posterior, values2=tau_posterior, hdi_probs=[0.3, 0.6, 0.9])\n\n Plot 2d smooth KDE\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(mu_posterior, values2=tau_posterior, contour=False)\n\n \n source"},{"id":152,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_khat","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_khat-Tuple","content":" ArviZPythonPlots.plot_khat — Method \n Plot Pareto tail indices for diagnosing convergence.\n\n Parameters\n ----------\n khats : ELPDData containing Pareto shapes information or array of\n Pareto tail indices.\n color : str or array_like, optional\n Colors of the scatter plot, if color is a str all dots will\n have the same color, if it is the size of the observations,\n each dot will have the specified color, otherwise, it will be\n interpreted as a list of the dims to be used for the color\n code. If Matplotlib c argument is passed, it will override\n the color argument\n xlabels : bool, optional\n Use coords as xticklabels\n show_hlines : bool, optional\n Show the horizontal lines, by default at the values [0, 0.5, 0.7, 1].\n show_bins : bool, optional\n Show the percentage of khats falling in each bin, as delimited by hlines.\n bin_format : str, optional\n The string is used as formatting guide calling ``bin_format.format(count, pct)``.\n threshold : float, optional\n Show the labels of k values larger than threshold. Defaults to `None`,\n no observations will be highlighted.\n hover_label : bool, optional\n Show the datapoint label when hovering over it with the mouse. Requires an interactive\n backend.\n hover_format : str, optional\n String used to format the hover label via ``hover_format.format(idx, coord_label)``\n figsize : (float, float), optional\n Figure size. If None it will be defined automatically.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If None it will be autoscaled based\n on figsize.\n coords : mapping, optional\n Coordinates of points to plot. **All** values are used for computation, but only a\n a subset can be plotted for convenience.\n legend : bool, optional\n Include a legend to the plot. Only taken into account when color argument is a dim name.\n markersize : int, optional\n markersize for scatter plot. Defaults to `None` in which case it will\n be chosen based on autoscaling for figsize.\n ax : axes, optional\n Matplotlib axes or bokeh figures.\n hlines_kwargs : dictionary, optional\n Additional keywords passed to\n :meth:`matplotlib.axes.Axes.hlines`.\n backend : str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default \"matplotlib\".\n backend_kwargs : bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or\n :func:`bokeh.plotting.figure`.\n show : bool, optional\n Call backend show function.\n kwargs :\n Additional keywords passed to\n :meth:`matplotlib.axes.Axes.scatter`.\n\n Returns\n -------\n axes : matplotlib_axes or bokeh_figures\n\n See Also\n --------\n psislw : Pareto smoothed importance sampling (PSIS).\n\n Examples\n --------\n Plot estimated pareto shape parameters showing how many fall in each category.\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> radon = az.load_arviz_data(\"radon\")\n >>> loo_radon = az.loo(radon, pointwise=True)\n >>> az.plot_khat(loo_radon, show_bins=True)\n\n Show xlabels\n\n .. plot::\n :context: close-figs\n\n >>> centered_eight = az.load_arviz_data(\"centered_eight\")\n >>> khats = az.loo(centered_eight, pointwise=True).pareto_k\n >>> az.plot_khat(khats, xlabels=True, threshold=1)\n\n Use custom color scheme\n\n .. plot::\n :context: close-figs\n\n >>> counties = radon.posterior.County[radon.constant_data.county_idx].values\n >>> colors = [\n ... \"blue\" if county[-1] in (\"A\", \"N\") else \"green\" for county in counties\n ... ]\n >>> az.plot_khat(loo_radon, color=colors)\n\n Notes\n -----\n The Generalized Pareto distribution (GPD) may be used to diagnose\n convergence rates for importance sampling. GPD has parameters\n offset, scale, and shape. The shape parameter is usually denoted\n with ``k``. ``k`` also tells how many finite moments the\n distribution has. The pre-asymptotic convergence rate of\n importance sampling can be estimated based on the fractional\n number of finite moments of the importance ratio distribution. GPD\n is fitted to the largest importance ratios and the estimated shape\n parameter ``k``, i.e., ``\\hat{k}`` can then be used as a diagnostic\n (most importantly if ``\\hat{k} > 0.7``, then the convergence rate\n is impractically low). See [1]_.\n\n References\n ----------\n .. [1] Vehtari, A., Simpson, D., Gelman, A., Yao, Y., Gabry, J.,\n 2019. Pareto Smoothed Importance Sampling. arXiv:1507.02646 [stat].\n\n \n source"},{"id":153,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_lm","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_lm-Tuple","content":" ArviZPythonPlots.plot_lm — Method Posterior predictive and mean plots for regression-like data.\n\n Parameters\n ----------\n y : str or DataArray or ndarray\n If str, variable name from ``observed_data``.\n idata : InferenceData, Optional\n Optional only if ``y`` is not str.\n x : str, tuple of strings, DataArray or array-like, optional\n If str or tuple, variable name from ``constant_data``.\n If ndarray, could be 1D, or 2D for multiple plots.\n If None, coords name of ``y`` (``y`` should be DataArray).\n y_model : str or Sequence, Optional\n If str, variable name from ``posterior``.\n Its dimensions should be same as ``y`` plus added chains and draws.\n y_hat : str, Optional\n If str, variable name from ``posterior_predictive``.\n Its dimensions should be same as ``y`` plus added chains and draws.\n num_samples : int, Optional, Default 50\n Significant if ``kind_pp`` is \"samples\" or ``kind_model`` is \"lines\".\n Number of samples to be drawn from posterior predictive or\n kind_pp : {\"samples\", \"hdi\"}, Default \"samples\"\n Options to visualize uncertainty in data.\n kind_model : {\"lines\", \"hdi\"}, Default \"lines\"\n Options to visualize uncertainty in mean of the data.\n plot_dim : str, Optional\n Necessary if ``y`` is multidimensional.\n backend : str, Optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default \"matplotlib\".\n y_kwargs : dict, optional\n Passed to :meth:`mpl:matplotlib.axes.Axes.plot` in matplotlib\n and :meth:`bokeh:bokeh.plotting.Figure.circle` in bokeh\n y_hat_plot_kwargs : dict, optional\n Passed to :meth:`mpl:matplotlib.axes.Axes.plot` in matplotlib\n and :meth:`bokeh:bokeh.plotting.Figure.circle` in bokeh\n y_hat_fill_kwargs : dict, optional\n Passed to :func:`arviz.plot_hdi`\n y_model_plot_kwargs : dict, optional\n Passed to :meth:`mpl:matplotlib.axes.Axes.plot` in matplotlib\n and :meth:`bokeh:bokeh.plotting.Figure.line` in bokeh\n y_model_fill_kwargs : dict, optional\n Significant if ``kind_model`` is \"hdi\". Passed to :func:`arviz.plot_hdi`\n y_model_mean_kwargs : dict, optional\n Passed to :meth:`mpl:matplotlib.axes.Axes.plot` in matplotlib\n and :meth:`bokeh:bokeh.plotting.Figure.line` in bokeh\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used. Passed to\n :func:`matplotlib.pyplot.subplots` or\n :func:`bokeh.plotting.figure`.\n figsize : (float, float), optional\n Figure size. If None it will be defined automatically.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If None it will be\n autoscaled based on ``figsize``.\n axes : 2D numpy array-like of matplotlib_axes or bokeh_figures, optional\n A 2D array of locations into which to plot the densities. If not supplied, Arviz will create\n its own array of plot areas (and return it).\n show : bool, optional\n Call backend show function.\n legend : bool, optional\n Add legend to figure. By default True.\n grid : bool, optional\n Add grid to figure. By default True.\n\n\n Returns\n -------\n axes: matplotlib axes or bokeh figures\n\n See Also\n --------\n plot_ts : Plot timeseries data\n plot_ppc : Plot for posterior/prior predictive checks\n\n Examples\n --------\n Plot regression default plot\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> import numpy as np\n >>> import xarray as xr\n >>> idata = az.load_arviz_data('regression1d')\n >>> x = xr.DataArray(np.linspace(0, 1, 100))\n >>> idata.posterior[\"y_model\"] = idata.posterior[\"intercept\"] + idata.posterior[\"slope\"]*x\n >>> az.plot_lm(idata=idata, y=\"y\", x=x)\n\n Plot regression data and mean uncertainty\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_lm(idata=idata, y=\"y\", x=x, y_model=\"y_model\")\n\n Plot regression data and mean uncertainty in hdi form\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_lm(\n ... idata=idata, y=\"y\", x=x, y_model=\"y_model\", kind_pp=\"hdi\", kind_model=\"hdi\"\n ... )\n\n Plot regression data for multi-dimensional y using plot_dim\n\n .. plot::\n :context: close-figs\n\n >>> data = az.from_dict(\n ... observed_data = { \"y\": np.random.normal(size=(5, 7)) },\n ... posterior_predictive = {\"y\": np.random.randn(4, 1000, 5, 7) / 2},\n ... dims={\"y\": [\"dim1\", \"dim2\"]},\n ... coords={\"dim1\": range(5), \"dim2\": range(7)}\n ... )\n >>> az.plot_lm(idata=data, y=\"y\", plot_dim=\"dim1\")\n \n source"},{"id":154,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_loo_pit","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_loo_pit-Tuple","content":" ArviZPythonPlots.plot_loo_pit — Method Plot Leave-One-Out (LOO) probability integral transformation (PIT) predictive checks.\n\n Parameters\n ----------\n idata : InferenceData\n :class:`arviz.InferenceData` object.\n y : array, DataArray or str\n Observed data. If str, ``idata`` must be present and contain the observed data group\n y_hat : array, DataArray or str\n Posterior predictive samples for ``y``. It must have the same shape as y plus an\n extra dimension at the end of size n_samples (chains and draws stacked). If str or\n None, ``idata`` must contain the posterior predictive group. If None, ``y_hat`` is taken\n equal to y, thus, y must be str too.\n log_weights : array or DataArray\n Smoothed log_weights. It must have the same shape as ``y_hat``\n ecdf : bool, optional\n Plot the difference between the LOO-PIT Empirical Cumulative Distribution Function\n (ECDF) and the uniform CDF instead of LOO-PIT kde.\n In this case, instead of overlaying uniform distributions, the beta ``hdi_prob``\n around the theoretical uniform CDF is shown. This approximation only holds\n for large S and ECDF values not very close to 0 nor 1. For more information, see\n `Vehtari et al. (2019)`, `Appendix G `_.\n ecdf_fill : bool, optional\n Use :meth:`matplotlib.axes.Axes.fill_between` to mark the area\n inside the credible interval. Otherwise, plot the\n border lines.\n n_unif : int, optional\n Number of datasets to simulate and overlay from the uniform distribution.\n use_hdi : bool, optional\n Compute expected hdi values instead of overlaying the sampled uniform distributions.\n hdi_prob : float, optional\n Probability for the highest density interval. Works with ``use_hdi=True`` or ``ecdf=True``.\n figsize : (float, float), optional\n If None, size is (8 + numvars, 8 + numvars)\n textsize : int, optional\n Text size for labels. If None it will be autoscaled based on ``figsize``.\n labeller : Labeller, optional\n Class providing the method ``make_pp_label`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n color : str or array_like, optional\n Color of the LOO-PIT estimated pdf plot. If ``plot_unif_kwargs`` has no \"color\" key,\n a slightly lighter color than this argument will be used for the uniform kde lines.\n This will ensure that LOO-PIT kde and uniform kde have different default colors.\n legend : bool, optional\n Show the legend of the figure.\n ax : axes, optional\n Matplotlib axes or bokeh figures.\n plot_kwargs : dict, optional\n Additional keywords passed to :meth:`matplotlib.axes.Axes.plot`\n for LOO-PIT line (kde or ECDF)\n plot_unif_kwargs : dict, optional\n Additional keywords passed to :meth:`matplotlib.axes.Axes.plot` for\n overlaid uniform distributions or for beta credible interval\n lines if ``ecdf=True``\n hdi_kwargs : dict, optional\n Additional keywords passed to :meth:`matplotlib.axes.Axes.axhspan`\n fill_kwargs : dict, optional\n Additional kwargs passed to :meth:`matplotlib.axes.Axes.fill_between`\n backend : str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default \"matplotlib\".\n backend_kwargs : bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or\n :func:`bokeh.plotting.figure`. For additional documentation\n check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : matplotlib_axes or bokeh_figures\n\n See Also\n --------\n plot_bpv : Plot Bayesian p-value for observed data and Posterior/Prior predictive.\n loo_pit : Compute leave one out (PSIS-LOO) probability integral transform (PIT) values.\n\n References\n ----------\n * Gabry et al. (2017) see https://arxiv.org/abs/1709.01449\n * https://mc-stan.org/bayesplot/reference/PPC-loo.html\n * Gelman et al. BDA (2014) Section 6.3\n\n Examples\n --------\n Plot LOO-PIT predictive checks overlaying the KDE of the LOO-PIT values to several\n realizations of uniform variable sampling with the same number of observations.\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> idata = az.load_arviz_data(\"radon\")\n >>> az.plot_loo_pit(idata=idata, y=\"y\")\n\n Fill the area containing the 94% highest density interval of the difference between uniform\n variables empirical CDF and the real uniform CDF. A LOO-PIT ECDF clearly outside of these\n theoretical boundaries indicates that the observations and the posterior predictive\n samples do not follow the same distribution.\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_loo_pit(idata=idata, y=\"y\", ecdf=True)\n\n \n source"},{"id":155,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_mcse","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_mcse-Tuple","content":" ArviZPythonPlots.plot_mcse — Method Plot quantile or local Monte Carlo Standard Error.\n\n Parameters\n ----------\n idata : obj\n Any object that can be converted to an :class:`arviz.InferenceData` object\n Refer to documentation of :func:`arviz.convert_to_dataset` for details\n var_names : list of variable names, optional\n Variables to be plotted. Prefix the variables by ``~`` when you want to exclude\n them from the plot.\n filter_vars : {None, \"like\", \"regex\"}, optional, default=None\n If `None` (default), interpret var_names as the real variables names. If \"like\",\n interpret var_names as substrings of the real variables names. If \"regex\",\n interpret var_names as regular expressions on the real variables names. A la\n `pandas.filter`.\n coords : dict, optional\n Coordinates of var_names to be plotted. Passed to :meth:`xarray.Dataset.sel`\n errorbar : bool, optional\n Plot quantile value +/- mcse instead of plotting mcse.\n grid : tuple\n Number of rows and columns. Defaults to None, the rows and columns are\n automatically inferred.\n figsize : (float, float), optional\n Figure size. If None it will be defined automatically.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If None it will be autoscaled based\n on figsize.\n extra_methods : bool, optional\n Plot mean and sd MCSE as horizontal lines. Only taken into account when\n ``errorbar=False``.\n rug : bool\n Plot rug plot of values diverging or that reached the max tree depth.\n rug_kind : bool\n Variable in sample stats to use as rug mask. Must be a boolean variable.\n n_points : int\n Number of points for which to plot their quantile/local ess or number of subsets\n in the evolution plot.\n labeller : Labeller, optional\n Class providing the method `make_label_vert` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n ax : 2D array-like of matplotlib_axes or bokeh_figures, optional\n A 2D array of locations into which to plot the densities. If not supplied, Arviz will create\n its own array of plot areas (and return it).\n rug_kwargs : dict\n kwargs passed to rug plot in\n :meth:`mpl:matplotlib.axes.Axes.plot` or :class:`bokeh:bokeh.models.glyphs.Scatter`.\n extra_kwargs : dict, optional\n kwargs passed as extra method lines in\n :meth:`mpl:matplotlib.axes.Axes.axhline` or :class:`bokeh:bokeh.models.Span`\n text_kwargs : dict, optional\n kwargs passed to :meth:`mpl:matplotlib.axes.Axes.annotate` for extra methods lines labels.\n It accepts the additional key ``x`` to set ``xy=(text_kwargs[\"x\"], mcse)``.\n text_kwargs are ignored for the bokeh plotting backend.\n backend : str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default \"matplotlib\".\n backend_kwargs : bool, optional\n These are kwargs specific to the backend being passed to\n :func:`matplotlib.pyplot.subplots` or :func:`bokeh.plotting.figure`.\n show: bool, optional\n Call backend show function.\n **kwargs\n Passed as-is to :meth:`mpl:matplotlib.axes.Axes.hist` or\n :meth:`mpl:matplotlib.axes.Axes.plot` in matplotlib depending on the value of `kind`.\n\n Returns\n -------\n axes : matplotlib axes or bokeh figures\n\n See Also\n --------\n :func:`arviz.mcse`: Calculate Markov Chain Standard Error statistic.\n\n References\n ----------\n * Vehtari et al. (2019) see https://arxiv.org/abs/1903.08008\n\n Examples\n --------\n Plot quantile Monte Carlo Standard Error.\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> idata = az.load_arviz_data(\"centered_eight\")\n >>> coords = {\"school\": [\"Deerfield\", \"Lawrenceville\"]}\n >>> az.plot_mcse(\n ... idata, var_names=[\"mu\", \"theta\"], coords=coords\n ... )\n\n \n source"},{"id":156,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_pair","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_pair-Tuple","content":" ArviZPythonPlots.plot_pair — Method \n Plot a scatter, kde and/or hexbin matrix with (optional) marginals on the diagonal.\n\n Parameters\n ----------\n data: obj\n Any object that can be converted to an :class:`arviz.InferenceData` object.\n Refer to documentation of :func:`arviz.convert_to_dataset` for details\n group: str, optional\n Specifies which InferenceData group should be plotted. Defaults to 'posterior'.\n var_names: list of variable names, optional\n Variables to be plotted, if None all variable are plotted. Prefix the\n variables by ``~`` when you want to exclude them from the plot.\n filter_vars: {None, \"like\", \"regex\"}, optional, default=None\n If `None` (default), interpret var_names as the real variables names. If \"like\",\n interpret var_names as substrings of the real variables names. If \"regex\",\n interpret var_names as regular expressions on the real variables names. A la\n ``pandas.filter``.\n combine_dims : set_like of str, optional\n List of dimensions to reduce. Defaults to reducing only the \"chain\" and \"draw\" dimensions.\n See the :ref:`this section ` for usage examples.\n coords: mapping, optional\n Coordinates of var_names to be plotted. Passed to :meth:`xarray.Dataset.sel`.\n marginals: bool, optional\n If True pairplot will include marginal distributions for every variable\n figsize: figure size tuple\n If None, size is (8 + numvars, 8 + numvars)\n textsize: int\n Text size for labels. If None it will be autoscaled based on ``figsize``.\n kind : str or List[str]\n Type of plot to display (scatter, kde and/or hexbin)\n gridsize: int or (int, int), optional\n Only works for ``kind=hexbin``. The number of hexagons in the x-direction.\n The corresponding number of hexagons in the y-direction is chosen\n such that the hexagons are approximately regular. Alternatively, gridsize\n can be a tuple with two elements specifying the number of hexagons\n in the x-direction and the y-direction.\n divergences: Boolean\n If True divergences will be plotted in a different color, only if group is either 'prior'\n or 'posterior'.\n colorbar: bool\n If True a colorbar will be included as part of the plot (Defaults to False).\n Only works when ``kind=hexbin``\n labeller : labeller instance, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot.\n Read the :ref:`label_guide` for more details and usage examples.\n ax: axes, optional\n Matplotlib axes or bokeh figures.\n divergences_kwargs: dicts, optional\n Additional keywords passed to :meth:`matplotlib.axes.Axes.scatter` for divergences\n scatter_kwargs:\n Additional keywords passed to :meth:`matplotlib.axes.Axes.scatter` when using scatter kind\n kde_kwargs: dict, optional\n Additional keywords passed to :func:`arviz.plot_kde` when using kde kind\n hexbin_kwargs: dict, optional\n Additional keywords passed to :meth:`matplotlib.axes.Axes.hexbin` when\n using hexbin kind\n backend: str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default \"matplotlib\".\n backend_kwargs: bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or\n :func:`bokeh.plotting.figure`.\n marginal_kwargs: dict, optional\n Additional keywords passed to :func:`arviz.plot_dist`, modifying the\n marginal distributions plotted in the diagonal.\n point_estimate: str, optional\n Select point estimate from 'mean', 'mode' or 'median'. The point estimate will be\n plotted using a scatter marker and vertical/horizontal lines.\n point_estimate_kwargs: dict, optional\n Additional keywords passed to :meth:`matplotlib.axes.Axes.axvline`,\n :meth:`matplotlib.axes.Axes.axhline` (matplotlib) or\n :class:`bokeh:bokeh.models.Span` (bokeh)\n point_estimate_marker_kwargs: dict, optional\n Additional keywords passed to :meth:`matplotlib.axes.Axes.scatter`\n or :meth:`bokeh:bokeh.plotting.Figure.square` in point\n estimate plot. Not available in bokeh\n reference_values: dict, optional\n Reference values for the plotted variables. The Reference values will be plotted\n using a scatter marker\n reference_values_kwargs: dict, optional\n Additional keywords passed to :meth:`matplotlib.axes.Axes.plot` or\n :meth:`bokeh:bokeh.plotting.Figure.circle` in reference values plot\n show: bool, optional\n Call backend show function.\n\n Returns\n -------\n axes: matplotlib axes or bokeh figures\n\n Examples\n --------\n KDE Pair Plot\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> centered = az.load_arviz_data('centered_eight')\n >>> coords = {'school': ['Choate', 'Deerfield']}\n >>> az.plot_pair(centered,\n >>> var_names=['theta', 'mu', 'tau'],\n >>> kind='kde',\n >>> coords=coords,\n >>> divergences=True,\n >>> textsize=18)\n\n Hexbin pair plot\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_pair(centered,\n >>> var_names=['theta', 'mu'],\n >>> coords=coords,\n >>> textsize=18,\n >>> kind='hexbin')\n\n Pair plot showing divergences and select variables with regular expressions\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_pair(centered,\n ... var_names=['^t', 'mu'],\n ... filter_vars=\"regex\",\n ... coords=coords,\n ... divergences=True,\n ... textsize=18)\n \n source"},{"id":157,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_parallel","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_parallel-Tuple","content":" ArviZPythonPlots.plot_parallel — Method \n Plot parallel coordinates plot showing posterior points with and without divergences.\n\n Described by https://arxiv.org/abs/1709.01449\n\n Parameters\n ----------\n data: obj\n Any object that can be converted to an :class:`arviz.InferenceData` object\n refer to documentation of :func:`arviz.convert_to_dataset` for details\n var_names: list of variable names\n Variables to be plotted, if `None` all variables are plotted. Can be used to change the\n order of the plotted variables. Prefix the variables by ``~`` when you want to exclude\n them from the plot.\n filter_vars: {None, \"like\", \"regex\"}, optional, default=None\n If `None` (default), interpret var_names as the real variables names. If \"like\",\n interpret var_names as substrings of the real variables names. If \"regex\",\n interpret var_names as regular expressions on the real variables names. A la\n ``pandas.filter``.\n coords: mapping, optional\n Coordinates of ``var_names`` to be plotted.\n Passed to :meth:`xarray.Dataset.sel`.\n figsize: tuple\n Figure size. If None it will be defined automatically.\n textsize: float\n Text size scaling factor for labels, titles and lines. If None it will be autoscaled based\n on ``figsize``.\n legend: bool\n Flag for plotting legend (defaults to True)\n colornd: valid matplotlib color\n color for non-divergent points. Defaults to 'k'\n colord: valid matplotlib color\n color for divergent points. Defaults to 'C1'\n shadend: float\n Alpha blending value for non-divergent points, between 0 (invisible) and 1 (opaque).\n Defaults to .025\n labeller : labeller instance, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot.\n Read the :ref:`label_guide` for more details and usage examples.\n ax: axes, optional\n Matplotlib axes or bokeh figures.\n norm_method: str\n Method for normalizing the data. Methods include normal, minmax and rank.\n Defaults to none.\n backend: str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default \"matplotlib\".\n backend_config: dict, optional\n Currently specifies the bounds to use for bokeh axes.\n Defaults to value set in ``rcParams``.\n backend_kwargs: bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or\n :func:`bokeh.plotting.figure`.\n show: bool, optional\n Call backend show function.\n\n Returns\n -------\n axes: matplotlib axes or bokeh figures\n\n See Also\n --------\n plot_pair : Plot a scatter, kde and/or hexbin matrix with (optional) marginals on the diagonal.\n plot_trace : Plot distribution (histogram or kernel density estimates) and sampled values\n or rank plot\n\n Examples\n --------\n Plot default parallel plot\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data('centered_eight')\n >>> az.plot_parallel(data, var_names=[\"mu\", \"tau\"])\n\n\n Plot parallel plot with normalization\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_parallel(data, var_names=[\"theta\", \"tau\", \"mu\"], norm_method=\"normal\")\n\n Plot parallel plot with minmax\n\n .. plot::\n :context: close-figs\n\n >>> ax = az.plot_parallel(data, var_names=[\"theta\", \"tau\", \"mu\"], norm_method=\"minmax\")\n >>> ax.set_xticklabels(ax.get_xticklabels(), rotation=45)\n\n Plot parallel plot with rank\n\n .. plot::\n :context: close-figs\n\n >>> ax = az.plot_parallel(data, var_names=[\"theta\", \"tau\", \"mu\"], norm_method=\"rank\")\n >>> ax.set_xticklabels(ax.get_xticklabels(), rotation=45)\n \n source"},{"id":158,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_posterior","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_posterior-Tuple","content":" ArviZPythonPlots.plot_posterior — Method Plot Posterior densities in the style of John K. Kruschke's book.\n\n Parameters\n ----------\n data: obj\n Any object that can be converted to an :class:`arviz.InferenceData` object.\n Refer to the documentation of :func:`arviz.convert_to_dataset` for details\n var_names: list of variable names\n Variables to be plotted, two variables are required. Prefix the variables with ``~``\n when you want to exclude them from the plot.\n filter_vars: {None, \"like\", \"regex\"}, optional, default=None\n If `None` (default), interpret var_names as the real variables names. If \"like\",\n interpret var_names as substrings of the real variables names. If \"regex\",\n interpret var_names as regular expressions on the real variables names. A la\n ``pandas.filter``.\n combine_dims : set_like of str, optional\n List of dimensions to reduce. Defaults to reducing only the \"chain\" and \"draw\" dimensions.\n See the :ref:`this section ` for usage examples.\n transform: callable\n Function to transform data (defaults to None i.e.the identity function)\n coords: mapping, optional\n Coordinates of var_names to be plotted. Passed to :meth:`xarray.Dataset.sel`\n grid : tuple\n Number of rows and columns. Defaults to None, the rows and columns are\n automatically inferred.\n figsize: tuple\n Figure size. If None it will be defined automatically.\n textsize: float\n Text size scaling factor for labels, titles and lines. If None it will be autoscaled based\n on ``figsize``.\n hdi_prob: float, optional\n Plots highest density interval for chosen percentage of density.\n Use 'hide' to hide the highest density interval. Defaults to 0.94.\n multimodal: bool\n If true (default) it may compute more than one credible interval if the distribution is\n multimodal and the modes are well separated.\n skipna : bool\n If true ignores nan values when computing the hdi and point estimates. Defaults to false.\n round_to: int, optional\n Controls formatting of floats. Defaults to 2 or the integer part, whichever is bigger.\n point_estimate: Optional[str]\n Plot point estimate per variable. Values should be 'mean', 'median', 'mode' or None.\n Defaults to 'auto' i.e. it falls back to default set in rcParams.\n group: str, optional\n Specifies which InferenceData group should be plotted. Defaults to 'posterior'.\n rope: tuple or dictionary of tuples\n Lower and upper values of the Region Of Practical Equivalence. If a list is provided, its\n length should match the number of variables.\n ref_val: float or dictionary of floats\n display the percentage below and above the values in ref_val. Must be None (default),\n a constant, a list or a dictionary like see an example below. If a list is provided, its\n length should match the number of variables.\n rope_color: str, optional\n Specifies the color of ROPE and displayed percentage within ROPE\n ref_val_color: str, optional\n Specifies the color of the displayed percentage\n kind: str\n Type of plot to display (kde or hist) For discrete variables this argument is ignored and\n a histogram is always used. Defaults to rcParam ``plot.density_kind``\n bw: float or str, optional\n If numeric, indicates the bandwidth and must be positive.\n If str, indicates the method to estimate the bandwidth and must be\n one of \"scott\", \"silverman\", \"isj\" or \"experimental\" when `circular` is False\n and \"taylor\" (for now) when `circular` is True.\n Defaults to \"default\" which means \"experimental\" when variable is not circular\n and \"taylor\" when it is. Only works if `kind == kde`.\n circular: bool, optional\n If True, it interprets the values passed are from a circular variable measured in radians\n and a circular KDE is used. Only valid for 1D KDE. Defaults to False.\n Only works if `kind == kde`.\n bins: integer or sequence or 'auto', optional\n Controls the number of bins,accepts the same keywords :func:`matplotlib.pyplot.hist` does.\n Only works if `kind == hist`. If None (default) it will use `auto` for continuous variables\n and `range(xmin, xmax + 1)` for discrete variables.\n labeller : labeller instance, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n ax: numpy array-like of matplotlib axes or bokeh figures, optional\n A 2D array of locations into which to plot the densities. If not supplied, Arviz will create\n its own array of plot areas (and return it).\n backend: str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default \"matplotlib\".\n backend_kwargs: bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :func:`bokeh.plotting.figure`\n show: bool, optional\n Call backend show function.\n **kwargs\n Passed as-is to :func:`matplotlib.pyplot.hist` or :func:`matplotlib.pyplot.plot` function\n depending on the value of `kind`.\n\n Returns\n -------\n axes: matplotlib axes or bokeh figures\n\n See Also\n --------\n plot_dist : Plot distribution as histogram or kernel density estimates.\n plot_density : Generate KDE plots for continuous variables and histograms for discrete ones.\n plot_forest : Forest plot to compare HDI intervals from a number of distributions.\n\n Examples\n --------\n Show a default kernel density plot following style of John Kruschke\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data('centered_eight')\n >>> az.plot_posterior(data)\n\n Plot subset variables by specifying variable name exactly\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_posterior(data, var_names=['mu'])\n\n Plot Region of Practical Equivalence (rope) and select variables with regular expressions\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_posterior(data, var_names=['mu', '^the'], filter_vars=\"regex\", rope=(-1, 1))\n\n Plot Region of Practical Equivalence for selected distributions\n\n .. plot::\n :context: close-figs\n\n >>> rope = {'mu': [{'rope': (-2, 2)}], 'theta': [{'school': 'Choate', 'rope': (2, 4)}]}\n >>> az.plot_posterior(data, var_names=['mu', 'theta'], rope=rope)\n\n Using `coords` argument to plot only a subset of data\n\n .. plot::\n :context: close-figs\n\n >>> coords = {\"school\": [\"Choate\",\"Phillips Exeter\"]}\n >>> az.plot_posterior(data, var_names=[\"mu\", \"theta\"], coords=coords)\n\n Add reference lines\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_posterior(data, var_names=['mu', 'theta'], ref_val=0)\n\n Show point estimate of distribution\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_posterior(data, var_names=['mu', 'theta'], point_estimate='mode')\n\n Show reference values using variable names and coordinates\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_posterior(data, ref_val= {\"theta\": [{\"school\": \"Deerfield\", \"ref_val\": 4},\n ... {\"school\": \"Choate\", \"ref_val\": 3}]})\n\n Show reference values using a list\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_posterior(data, ref_val=[1] + [5] * 8 + [1])\n\n\n Plot posterior as a histogram\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_posterior(data, var_names=['mu'], kind='hist')\n\n Change size of highest density interval\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_posterior(data, var_names=['mu'], hdi_prob=.75)\n \n source"},{"id":159,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_ppc","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_ppc-Tuple","content":" ArviZPythonPlots.plot_ppc — Method \n Plot for posterior/prior predictive checks.\n\n Parameters\n ----------\n data: az.InferenceData object\n :class:`arviz.InferenceData` object containing the observed and posterior/prior\n predictive data.\n kind: str\n Type of plot to display (\"kde\", \"cumulative\", or \"scatter\"). Defaults to `kde`.\n alpha: float\n Opacity of posterior/prior predictive density curves.\n Defaults to 0.2 for ``kind = kde`` and cumulative, for scatter defaults to 0.7.\n mean: bool\n Whether or not to plot the mean posterior/prior predictive distribution.\n Defaults to ``True``.\n observed: bool, default True\n Whether or not to plot the observed data.\n observed: bool, default False\n Whether or not to plot a rug plot for the observed data. Only valid if `observed` is\n `True` and for kind `kde` or `cumulative`.\n color: str\n Valid matplotlib ``color``. Defaults to ``C0``.\n color: list\n List with valid matplotlib colors corresponding to the posterior/prior predictive\n distribution, observed data and mean of the posterior/prior predictive distribution.\n Defaults to [\"C0\", \"k\", \"C1\"].\n grid : tuple\n Number of rows and columns. Defaults to None, the rows and columns are\n automatically inferred.\n figsize: tuple\n Figure size. If None, it will be defined automatically.\n textsize: float\n Text size scaling factor for labels, titles and lines. If None, it will be\n autoscaled based on ``figsize``.\n data_pairs: dict\n Dictionary containing relations between observed data and posterior/prior predictive data.\n Dictionary structure:\n\n - key = data var_name\n - value = posterior/prior predictive var_name\n\n For example, ``data_pairs = {'y' : 'y_hat'}``\n If None, it will assume that the observed data and the posterior/prior\n predictive data have the same variable name.\n var_names: list of variable names\n Variables to be plotted, if `None` all variable are plotted. Prefix the\n variables by ``~`` when you want to exclude them from the plot.\n filter_vars: {None, \"like\", \"regex\"}, optional, default=None\n If `None` (default), interpret var_names as the real variables names. If \"like\",\n interpret var_names as substrings of the real variables names. If \"regex\",\n interpret var_names as regular expressions on the real variables names. A la\n ``pandas.filter``.\n coords: dict\n Dictionary mapping dimensions to selected coordinates to be plotted.\n Dimensions without a mapping specified will include all coordinates for\n that dimension. Defaults to including all coordinates for all\n dimensions if None.\n flatten: list\n List of dimensions to flatten in ``observed_data``. Only flattens across the coordinates\n specified in the ``coords`` argument. Defaults to flattening all of the dimensions.\n flatten_pp: list\n List of dimensions to flatten in posterior_predictive/prior_predictive. Only flattens\n across the coordinates specified in the ``coords`` argument. Defaults to flattening all\n of the dimensions. Dimensions should match flatten excluding dimensions for ``data_pairs``\n parameters. If ``flatten`` is defined and ``flatten_pp`` is None, then\n ``flatten_pp = flatten``.\n num_pp_samples: int\n The number of posterior/prior predictive samples to plot. For ``kind`` = 'scatter' and\n ``animation = False`` if defaults to a maximum of 5 samples and will set jitter to 0.7.\n unless defined. Otherwise it defaults to all provided samples.\n random_seed: int\n Random number generator seed passed to ``numpy.random.seed`` to allow\n reproducibility of the plot. By default, no seed will be provided\n and the plot will change each call if a random sample is specified\n by ``num_pp_samples``.\n jitter: float\n If ``kind`` is \"scatter\", jitter will add random uniform noise to the height\n of the ppc samples and observed data. By default 0.\n animated: bool\n Create an animation of one posterior/prior predictive sample per frame.\n Defaults to ``False``. Only works with matploblib backend.\n To run animations inside a notebook you have to use the `nbAgg` matplotlib's backend.\n Try with `%matplotlib notebook` or `%matplotlib nbAgg`. You can switch back to the\n default matplotlib's backend with `%matplotlib inline` or `%matplotlib auto`.\n If switching back and forth between matplotlib's backend, you may need to run twice the cell\n with the animation.\n If you experience problems rendering the animation try setting\n `animation_kwargs({'blit':False}`) or changing the matplotlib's backend (e.g. to TkAgg)\n If you run the animation from a script write `ax, ani = az.plot_ppc(.)`\n animation_kwargs : dict\n Keywords passed to :class:`matplotlib.animation.FuncAnimation`. Ignored with\n matplotlib backend.\n legend : bool\n Add legend to figure. By default ``True``.\n labeller : labeller instance, optional\n Class providing the method ``make_pp_label`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n ax: numpy array-like of matplotlib axes or bokeh figures, optional\n A 2D array of locations into which to plot the densities. If not supplied, Arviz will create\n its own array of plot areas (and return it).\n backend: str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default to \"matplotlib\".\n backend_kwargs: bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :func:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n group: {\"prior\", \"posterior\"}, optional\n Specifies which InferenceData group should be plotted. Defaults to 'posterior'.\n Other value can be 'prior'.\n show: bool, optional\n Call backend show function.\n\n Returns\n -------\n axes: matplotlib axes or bokeh figures\n\n See Also\n --------\n plot_bpv: Plot Bayesian p-value for observed data and Posterior/Prior predictive.\n plot_lm: Posterior predictive and mean plots for regression-like data.\n plot_ppc: plot for posterior/prior predictive checks.\n plot_ts: Plot timeseries data.\n\n Examples\n --------\n Plot the observed data KDE overlaid on posterior predictive KDEs.\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data('radon')\n >>> az.plot_ppc(data, data_pairs={\"y\":\"y\"})\n\n Plot the overlay with empirical CDFs.\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_ppc(data, kind='cumulative')\n\n Use the ``coords`` and ``flatten`` parameters to plot selected variable dimensions\n across multiple plots. We will now modify the dimension ``obs_id`` to contain\n indicate the name of the county where the measure was taken. The change has to\n be done on both ``posterior_predictive`` and ``observed_data`` groups, which is\n why we will use :meth:`~arviz.InferenceData.map` to apply the same function to\n both groups. Afterwards, we will select the counties to be plotted with the\n ``coords`` arg.\n\n .. plot::\n :context: close-figs\n\n >>> obs_county = data.posterior[\"County\"][data.constant_data[\"county_idx\"]]\n >>> data = data.assign_coords(obs_id=obs_county, groups=\"observed_vars\")\n >>> az.plot_ppc(data, coords={'obs_id': ['ANOKA', 'BELTRAMI']}, flatten=[])\n\n Plot the overlay using a stacked scatter plot that is particularly useful\n when the sample sizes are small.\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_ppc(data, kind='scatter', flatten=[],\n >>> coords={'obs_id': ['AITKIN', 'BELTRAMI']})\n\n Plot random posterior predictive sub-samples.\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_ppc(data, num_pp_samples=30, random_seed=7)\n \n source"},{"id":160,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_rank","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_rank-Tuple","content":" ArviZPythonPlots.plot_rank — Method Plot rank order statistics of chains.\n\n From the paper: Rank plots are histograms of the ranked posterior draws (ranked over all\n chains) plotted separately for each chain.\n If all of the chains are targeting the same posterior, we expect the ranks in each chain to be\n uniform, whereas if one chain has a different location or scale parameter, this will be\n reflected in the deviation from uniformity. If rank plots of all chains look similar, this\n indicates good mixing of the chains.\n\n This plot was introduced by Aki Vehtari, Andrew Gelman, Daniel Simpson, Bob Carpenter,\n Paul-Christian Burkner (2019): Rank-normalization, folding, and localization: An improved R-hat\n for assessing convergence of MCMC. arXiv preprint https://arxiv.org/abs/1903.08008\n\n\n Parameters\n ----------\n data: obj\n Any object that can be converted to an :class:`arviz.InferenceData` object.\n Refer to documentation of :func:`arviz.convert_to_dataset` for details\n var_names: string or list of variable names\n Variables to be plotted. Prefix the variables by ``~`` when you want to exclude\n them from the plot.\n filter_vars: {None, \"like\", \"regex\"}, optional, default=None\n If `None` (default), interpret var_names as the real variables names. If \"like\",\n interpret var_names as substrings of the real variables names. If \"regex\",\n interpret var_names as regular expressions on the real variables names. A la\n ``pandas.filter``.\n transform: callable\n Function to transform data (defaults to None i.e.the identity function)\n coords: mapping, optional\n Coordinates of var_names to be plotted. Passed to :meth:`xarray.Dataset.sel`\n bins: None or passed to np.histogram\n Binning strategy used for histogram. By default uses twice the result of Sturges' formula.\n See :func:`numpy.histogram` documentation for, other available arguments.\n kind: string\n If bars (defaults), ranks are represented as stacked histograms (one per chain). If vlines\n ranks are represented as vertical lines above or below ``ref_line``.\n colors: string or list of strings\n List with valid matplotlib colors, one color per model. Alternative a string can be passed.\n If the string is `cycle`, it will automatically choose a color per model from matplotlib's\n cycle. If a single color is passed, e.g. 'k', 'C2' or 'red' this color will be used for all\n models. Defaults to `cycle`.\n ref_line: boolean\n Whether to include a dashed line showing where a uniform distribution would lie\n labels: bool\n whether to plot or not the x and y labels, defaults to True\n labeller : labeller instance, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n grid : tuple\n Number of rows and columns. Defaults to None, the rows and columns are\n automatically inferred.\n figsize: tuple\n Figure size. If None it will be defined automatically.\n ax: numpy array-like of matplotlib axes or bokeh figures, optional\n A 2D array of locations into which to plot the densities. If not supplied, ArviZ will create\n its own array of plot areas (and return it).\n backend: str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default \"matplotlib\".\n ref_line_kwargs : dict, optional\n Reference line keyword arguments, passed to :meth:`mpl:matplotlib.axes.Axes.axhline` or\n :class:`bokeh:bokeh.models.Span`.\n bar_kwargs : dict, optional\n Bars keyword arguments, passed to :meth:`mpl:matplotlib.axes.Axes.bar` or\n :meth:`bokeh:bokeh.plotting.Figure.vbar`.\n vlines_kwargs : dict, optional\n Vlines keyword arguments, passed to :meth:`mpl:matplotlib.axes.Axes.vlines` or\n :meth:`bokeh:bokeh.plotting.Figure.multi_line`.\n marker_vlines_kwargs : dict, optional\n Marker for the vlines keyword arguments, passed to :meth:`mpl:matplotlib.axes.Axes.plot` or\n :meth:`bokeh:bokeh.plotting.Figure.circle`.\n backend_kwargs: bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or\n :func:`bokeh.plotting.figure`. For additional documentation\n check the plotting method of the backend.\n show: bool, optional\n Call backend show function.\n\n Returns\n -------\n axes: matplotlib axes or bokeh figures\n\n See Also\n --------\n plot_trace : Plot distribution (histogram or kernel density estimates) and\n sampled values or rank plot.\n\n Examples\n --------\n Show a default rank plot\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data('centered_eight')\n >>> az.plot_rank(data)\n\n Recreate Figure 13 from the arxiv preprint\n\n .. plot::\n :context: close-figs\n\n >>> data = az.load_arviz_data('centered_eight')\n >>> az.plot_rank(data, var_names='tau')\n\n Use vlines to compare results for centered vs noncentered models\n\n .. plot::\n :context: close-figs\n\n >>> import matplotlib.pyplot as plt\n >>> centered_data = az.load_arviz_data('centered_eight')\n >>> noncentered_data = az.load_arviz_data('non_centered_eight')\n >>> _, ax = plt.subplots(1, 2, figsize=(12, 3))\n >>> az.plot_rank(centered_data, var_names=\"mu\", kind='vlines', ax=ax[0])\n >>> az.plot_rank(noncentered_data, var_names=\"mu\", kind='vlines', ax=ax[1])\n\n Change the aesthetics using kwargs\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_rank(noncentered_data, var_names=\"mu\", kind=\"vlines\",\n >>> vlines_kwargs={'lw':0}, marker_vlines_kwargs={'lw':3});\n \n source"},{"id":161,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_separation","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_separation-Tuple","content":" ArviZPythonPlots.plot_separation — Method Separation plot for binary outcome models.\n\n Model predictions are sorted and plotted using a color code according to\n the observed data.\n\n Parameters\n ----------\n idata : InferenceData\n :class:`arviz.InferenceData` object.\n y : array, DataArray or str\n Observed data. If str, ``idata`` must be present and contain the observed data group\n y_hat : array, DataArray or str\n Posterior predictive samples for ``y``. It must have the same shape as ``y``. If str or\n None, ``idata`` must contain the posterior predictive group.\n y_hat_line : bool, optional\n Plot the sorted ``y_hat`` predictions.\n expected_events : bool, optional\n Plot the total number of expected events.\n figsize : figure size tuple, optional\n If None, size is (8 + numvars, 8 + numvars)\n textsize: int, optional\n Text size for labels. If None it will be autoscaled based on ``figsize``.\n color : str, optional\n Color to assign to the positive class. The negative class will be plotted using the\n same color and an `alpha=0.3` transparency.\n legend : bool, optional\n Show the legend of the figure.\n ax: axes, optional\n Matplotlib axes or bokeh figures.\n plot_kwargs : dict, optional\n Additional keywords passed to :meth:`mpl:matplotlib.axes.Axes.bar` or\n :meth:`bokeh:bokeh.plotting.Figure.vbar` for separation plot.\n y_hat_line_kwargs : dict, optional\n Additional keywords passed to ax.plot for ``y_hat`` line.\n exp_events_kwargs : dict, optional\n Additional keywords passed to ax.scatter for ``expected_events`` marker.\n backend: str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default \"matplotlib\".\n backend_kwargs: bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or\n :func:`bokeh.plotting.figure`.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : matplotlib axes or bokeh figures\n\n See Also\n --------\n plot_ppc : Plot for posterior/prior predictive checks.\n\n References\n ----------\n .. [1] Greenhill, B. *et al.*, The Separation Plot: A New Visual Method\n for Evaluating the Fit of Binary Models, *American Journal of\n Political Science*, (2011) see https://doi.org/10.1111/j.1540-5907.2011.00525.x\n\n Examples\n --------\n Separation plot for a logistic regression model.\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> idata = az.load_arviz_data('classification10d')\n >>> az.plot_separation(idata=idata, y='outcome', y_hat='outcome', figsize=(8, 1))\n\n \n source"},{"id":162,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_trace","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_trace-Tuple","content":" ArviZPythonPlots.plot_trace — Method Plot distribution (histogram or kernel density estimates) and sampled values or rank plot.\n\n If `divergences` data is available in `sample_stats`, will plot the location of divergences as\n dashed vertical lines.\n\n Parameters\n ----------\n data: obj\n Any object that can be converted to an :class:`arviz.InferenceData` object\n Refer to documentation of :func:`arviz.convert_to_dataset` for details\n var_names: str or list of str, optional\n One or more variables to be plotted. Prefix the variables by ``~`` when you want\n to exclude them from the plot.\n filter_vars: {None, \"like\", \"regex\"}, optional, default=None\n If `None` (default), interpret var_names as the real variables names. If \"like\",\n interpret var_names as substrings of the real variables names. If \"regex\",\n interpret var_names as regular expressions on the real variables names. A la\n ``pandas.filter``.\n coords: dict of {str: slice or array_like}, optional\n Coordinates of var_names to be plotted. Passed to :meth:`xarray.Dataset.sel`\n divergences: {\"bottom\", \"top\", None}, optional\n Plot location of divergences on the traceplots.\n kind: {\"trace\", \"rank_bars\", \"rank_vlines\"}, optional\n Choose between plotting sampled values per iteration and rank plots.\n transform: callable, optional\n Function to transform data (defaults to None i.e.the identity function)\n figsize: tuple of (float, float), optional\n If None, size is (12, variables * 2)\n rug: bool, optional\n If True adds a rugplot of samples. Defaults to False. Ignored for 2D KDE.\n Only affects continuous variables.\n lines: list of tuple of (str, dict, array_like), optional\n List of (var_name, {'coord': selection}, [line, positions]) to be overplotted as\n vertical lines on the density and horizontal lines on the trace.\n circ_var_names : str or list of str, optional\n List of circular variables to account for when plotting KDE.\n circ_var_units : str\n Whether the variables in ``circ_var_names`` are in \"degrees\" or \"radians\".\n compact: bool, optional\n Plot multidimensional variables in a single plot.\n compact_prop: str or dict {str: array_like}, optional\n Defines the property name and the property values to distinguish different\n dimensions with compact=True.\n When compact=True it defaults to color, it is\n ignored otherwise.\n combined: bool, optional\n Flag for combining multiple chains into a single line. If False (default), chains will be\n plotted separately.\n chain_prop: str or dict {str: array_like}, optional\n Defines the property name and the property values to distinguish different chains.\n If compact=True it defaults to linestyle,\n otherwise it uses the color to distinguish\n different chains.\n legend: bool, optional\n Add a legend to the figure with the chain color code.\n plot_kwargs, fill_kwargs, rug_kwargs, hist_kwargs: dict, optional\n Extra keyword arguments passed to :func:`arviz.plot_dist`. Only affects continuous\n variables.\n trace_kwargs: dict, optional\n Extra keyword arguments passed to :meth:`matplotlib.axes.Axes.plot`\n labeller : labeller instance, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n rank_kwargs : dict, optional\n Extra keyword arguments passed to :func:`arviz.plot_rank`\n axes: axes, optional\n Matplotlib axes or bokeh figures.\n backend: {\"matplotlib\", \"bokeh\"}, optional\n Select plotting backend.\n backend_config: dict, optional\n Currently specifies the bounds to use for bokeh axes. Defaults to value set in rcParams.\n backend_kwargs: dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or\n :func:`bokeh.plotting.figure`.\n show: bool, optional\n Call backend show function.\n\n Returns\n -------\n axes: matplotlib axes or bokeh figures\n\n See Also\n --------\n plot_rank : Plot rank order statistics of chains.\n\n Examples\n --------\n Plot a subset variables and select them with partial naming\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data('non_centered_eight')\n >>> coords = {'school': ['Choate', 'Lawrenceville']}\n >>> az.plot_trace(data, var_names=('theta'), filter_vars=\"like\", coords=coords)\n\n Show all dimensions of multidimensional variables in the same plot\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_trace(data, compact=True)\n\n Display a rank plot instead of trace\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_trace(data, var_names=[\"mu\", \"tau\"], kind=\"rank_bars\")\n\n Combine all chains into one distribution and select variables with regular expressions\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_trace(\n >>> data, var_names=('^theta'), filter_vars=\"regex\", coords=coords, combined=True\n >>> )\n\n\n Plot reference lines against distribution and trace\n\n .. plot::\n :context: close-figs\n\n >>> lines = (('theta_t',{'school': \"Choate\"}, [-1]),)\n >>> az.plot_trace(data, var_names=('theta_t', 'theta'), coords=coords, lines=lines)\n\n \n source"},{"id":163,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_violin","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_violin-Tuple","content":" ArviZPythonPlots.plot_violin — Method Plot posterior of traces as violin plot.\n\n Notes\n -----\n If multiple chains are provided for a variable they will be combined\n\n Parameters\n ----------\n data: obj\n Any object that can be converted to an :class:`arviz.InferenceData` object\n Refer to documentation of :func:`arviz.convert_to_dataset` for details\n var_names: list of variable names, optional\n Variables to be plotted, if None all variable are plotted. Prefix the\n variables by ``~`` when you want to exclude them from the plot.\n combine_dims : set_like of str, optional\n List of dimensions to reduce. Defaults to reducing only the \"chain\" and \"draw\" dimensions.\n See the :ref:`this section ` for usage examples.\n filter_vars: {None, \"like\", \"regex\"}, optional, default=None\n If `None` (default), interpret var_names as the real variables names. If \"like\",\n interpret var_names as substrings of the real variables names. If \"regex\",\n interpret var_names as regular expressions on the real variables names. A la\n ``pandas.filter``.\n transform: callable\n Function to transform data (defaults to None i.e. the identity function).\n quartiles: bool, optional\n Flag for plotting the interquartile range, in addition to the ``hdi_prob`` * 100%\n intervals. Defaults to ``True``.\n rug: bool\n If ``True`` adds a jittered rugplot. Defaults to ``False``.\n side : {\"both\", \"left\", \"right\"}, default \"both\"\n If ``both``, both sides of the violin plot are rendered. If ``left`` or ``right``, only\n the respective side is rendered. By separately plotting left and right halfs with\n different data, split violin plots can be achieved.\n hdi_prob: float, optional\n Plots highest posterior density interval for chosen percentage of density.\n Defaults to 0.94.\n shade: float\n Alpha blending value for the shaded area under the curve, between 0\n (no shade) and 1 (opaque). Defaults to 0.\n bw: float or str, optional\n If numeric, indicates the bandwidth and must be positive.\n If str, indicates the method to estimate the bandwidth and must be\n one of \"scott\", \"silverman\", \"isj\" or \"experimental\" when ``circular`` is ``False``\n and \"taylor\" (for now) when ``circular`` is ``True``.\n Defaults to \"default\" which means \"experimental\" when variable is not circular\n and \"taylor\" when it is.\n circular: bool, optional.\n If ``True``, it interprets `values` is a circular variable measured in radians\n and a circular KDE is used. Defaults to ``False``.\n grid : tuple\n Number of rows and columns. Defaults to None, the rows and columns are\n automatically inferred.\n figsize: tuple\n Figure size. If None it will be defined automatically.\n textsize: int\n Text size of the point_estimates, axis ticks, and highest density interval. If None it will\n be autoscaled based on ``figsize``.\n labeller : labeller instance, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n sharex: bool\n Defaults to ``True``, violinplots share a common x-axis scale.\n sharey: bool\n Defaults to ``True``, violinplots share a common y-axis scale.\n ax: numpy array-like of matplotlib axes or bokeh figures, optional\n A 2D array of locations into which to plot the densities. If not supplied, Arviz will create\n its own array of plot areas (and return it).\n shade_kwargs: dicts, optional\n Additional keywords passed to :meth:`matplotlib.axes.Axes.fill_between`, or\n :meth:`matplotlib.axes.Axes.barh` to control the shade.\n rug_kwargs: dict\n Keywords passed to the rug plot. If true only the right half side of the violin will be\n plotted.\n backend: str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default to \"matplotlib\".\n backend_kwargs: bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :func:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show: bool, optional\n Call backend show function.\n\n Returns\n -------\n axes: matplotlib axes or bokeh figures\n\n See Also\n --------\n plot_forest: Forest plot to compare HDI intervals from a number of distributions.\n\n Examples\n --------\n Show a default violin plot\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data('centered_eight')\n >>> az.plot_violin(data)\n\n \n source"},{"id":166,"pagetitle":"rcParams","title":"rcParams","ref":"/ArviZPythonPlots/stable/api/rcparams/#rcparams-api","content":" rcParams ArviZPythonPlots.rcParams ArviZPythonPlots.rc_context"},{"id":167,"pagetitle":"rcParams","title":"Reference","ref":"/ArviZPythonPlots/stable/api/rcparams/#Reference","content":" Reference"},{"id":168,"pagetitle":"rcParams","title":"ArviZPythonPlots.rcParams","ref":"/ArviZPythonPlots/stable/api/rcparams/#ArviZPythonPlots.rcParams","content":" ArviZPythonPlots.rcParams — Constant Class to contain ArviZ default parameters.\n\n It is implemented as a dict with validation when setting items.\n \n source"},{"id":169,"pagetitle":"rcParams","title":"ArviZPythonPlots.rc_context","ref":"/ArviZPythonPlots/stable/api/rcparams/#ArviZPythonPlots.rc_context-Tuple","content":" ArviZPythonPlots.rc_context — Method \n Return a context manager for managing rc settings.\n\n Parameters\n ----------\n rc : dict, optional\n Mapping containing the rcParams to modify temporally.\n fname : str, optional\n Filename of the file containing the rcParams to use inside the rc_context.\n\n Examples\n --------\n This allows one to do::\n\n with az.rc_context(fname='pystan.rc'):\n idata = az.load_arviz_data(\"radon\")\n az.plot_posterior(idata, var_names=[\"gamma\"])\n\n The plot would have settings from 'screen.rc'\n\n A dictionary can also be passed to the context manager::\n\n with az.rc_context(rc={'plot.max_subplots': None}, fname='pystan.rc'):\n idata = az.load_arviz_data(\"radon\")\n az.plot_posterior(idata, var_names=[\"gamma\"])\n\n The 'rc' dictionary takes precedence over the settings loaded from\n 'fname'. Passing a dictionary only is also valid.\n \n source"},{"id":172,"pagetitle":"Plotting styles","title":"Plotting styles","ref":"/ArviZPythonPlots/stable/api/style/#style-api","content":" Plotting styles ArviZPythonPlots.styles ArviZPythonPlots.use_style"},{"id":173,"pagetitle":"Plotting styles","title":"Reference","ref":"/ArviZPythonPlots/stable/api/style/#Reference","content":" Reference"},{"id":174,"pagetitle":"Plotting styles","title":"ArviZPythonPlots.styles","ref":"/ArviZPythonPlots/stable/api/style/#ArviZPythonPlots.styles-Tuple{}","content":" ArviZPythonPlots.styles — Method styles() -> Vector{String} Get all available matplotlib styles for use with use_style source"},{"id":175,"pagetitle":"Plotting styles","title":"ArviZPythonPlots.use_style","ref":"/ArviZPythonPlots/stable/api/style/#ArviZPythonPlots.use_style-Tuple{Any}","content":" ArviZPythonPlots.use_style — Method use_style(style::String)\nuse_style(style::Vector{String}) Use matplotlib style settings from a style specification style . The style name of \"default\" is reserved for reverting back to the default style settings. ArviZ-specific styles include [\"arviz-whitegrid\", \"arviz-darkgrid\", \"arviz-colors\", \"arviz-white\", \"arviz-doc\"] . To see all available style specifications, use styles() . If a Vector of styles is provided, they are applied from first to last. source"},{"id":178,"pagetitle":"Examples gallery","title":"Example Gallery","ref":"/ArviZPythonPlots/stable/examples/#Example-Gallery","content":" Example Gallery"},{"id":179,"pagetitle":"Examples gallery","title":"Autocorrelation Plot","ref":"/ArviZPythonPlots/stable/examples/#Autocorrelation-Plot","content":" Autocorrelation Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"centered_eight\")\nplot_autocorr(data; var_names=[\"tau\", \"mu\"])\ngcf() See plot_autocorr"},{"id":180,"pagetitle":"Examples gallery","title":"Bayes Factor Plot","ref":"/ArviZPythonPlots/stable/examples/#Bayes-Factor-Plot","content":" Bayes Factor Plot using ArviZ, ArviZPythonPlots\n\nuse_style(\"arviz-darkgrid\")\n\nidata = from_namedtuple((a = 1 .+ randn(5_000) ./ 2,), prior=(a = randn(5_000),))\nplot_bf(idata; var_name=\"a\", ref_val=0)\ngcf() See plot_bf"},{"id":181,"pagetitle":"Examples gallery","title":"Bayesian P-Value Posterior Plot","ref":"/ArviZPythonPlots/stable/examples/#Bayesian-P-Value-Posterior-Plot","content":" Bayesian P-Value Posterior Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"regression1d\")\nplot_bpv(data)\ngcf() See plot_bpv"},{"id":182,"pagetitle":"Examples gallery","title":"Bayesian P-Value with Median T Statistic Posterior Plot","ref":"/ArviZPythonPlots/stable/examples/#Bayesian-P-Value-with-Median-T-Statistic-Posterior-Plot","content":" Bayesian P-Value with Median T Statistic Posterior Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"regression1d\")\nplot_bpv(data; kind=\"t_stat\", t_stat=\"0.5\")\ngcf() See plot_bpv"},{"id":183,"pagetitle":"Examples gallery","title":"Compare Plot","ref":"/ArviZPythonPlots/stable/examples/#Compare-Plot","content":" Compare Plot using ArviZ, ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\nmodel_compare = compare(\n (\n var\"Centered 8 schools\" = load_example_data(\"centered_eight\"),\n var\"Non-centered 8 schools\" = load_example_data(\"non_centered_eight\"),\n ),\n)\nplot_compare(model_compare; figsize=(12, 4))\ngcf() See compare , plot_compare"},{"id":184,"pagetitle":"Examples gallery","title":"Density Plot","ref":"/ArviZPythonPlots/stable/examples/#Density-Plot","content":" Density Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ncentered_data = load_example_data(\"centered_eight\")\nnon_centered_data = load_example_data(\"non_centered_eight\")\nplot_density(\n [centered_data, non_centered_data];\n data_labels=[\"Centered\", \"Non Centered\"],\n var_names=[\"theta\"],\n shade=0.1,\n)\ngcf() See plot_density"},{"id":185,"pagetitle":"Examples gallery","title":"Dist Plot","ref":"/ArviZPythonPlots/stable/examples/#Dist-Plot","content":" Dist Plot using ArviZPythonPlots, Distributions, Random\n\nRandom.seed!(308)\n\nuse_style(\"arviz-darkgrid\")\n\na = rand(Poisson(4), 1000)\nb = rand(Normal(0, 1), 1000)\n_, ax = subplots(1, 2; figsize=(10, 4))\nplot_dist(a; color=\"C1\", label=\"Poisson\", ax=ax[0])\nplot_dist(b; color=\"C2\", label=\"Gaussian\", ax=ax[1])\ngcf() See plot_dist"},{"id":186,"pagetitle":"Examples gallery","title":"Dot Plot","ref":"/ArviZPythonPlots/stable/examples/#Dot-Plot","content":" Dot Plot using ArviZPythonPlots\n\nuse_style(\"arviz-darkgrid\")\n\ndata = randn(1000)\nplot_dot(data; dotcolor=\"C1\", point_interval=true)\ntitle(\"Gaussian Distribution\")\ngcf() See plot_dot"},{"id":187,"pagetitle":"Examples gallery","title":"ECDF Plot","ref":"/ArviZPythonPlots/stable/examples/#ECDF-Plot","content":" ECDF Plot using ArviZPythonPlots, Distributions\n\nuse_style(\"arviz-darkgrid\")\n\nsample = randn(1_000)\ndist = Normal()\nplot_ecdf(sample; cdf=x -> cdf(dist, x), confidence_bands=true)\ngcf() See plot_ecdf"},{"id":188,"pagetitle":"Examples gallery","title":"ELPD Plot","ref":"/ArviZPythonPlots/stable/examples/#ELPD-Plot","content":" ELPD Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\nd1 = load_example_data(\"centered_eight\")\nd2 = load_example_data(\"non_centered_eight\")\nplot_elpd(Dict(\"Centered eight\" => d1, \"Non centered eight\" => d2); xlabels=true)\ngcf() See plot_elpd"},{"id":189,"pagetitle":"Examples gallery","title":"Energy Plot","ref":"/ArviZPythonPlots/stable/examples/#Energy-Plot","content":" Energy Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"centered_eight\")\nplot_energy(data; figsize=(12, 8))\ngcf() See plot_energy"},{"id":190,"pagetitle":"Examples gallery","title":"ESS Evolution Plot","ref":"/ArviZPythonPlots/stable/examples/#ESS-Evolution-Plot","content":" ESS Evolution Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\nidata = load_example_data(\"radon\")\nplot_ess(idata; var_names=[\"b\"], kind=\"evolution\")\ngcf() See plot_ess"},{"id":191,"pagetitle":"Examples gallery","title":"ESS Local Plot","ref":"/ArviZPythonPlots/stable/examples/#ESS-Local-Plot","content":" ESS Local Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\nidata = load_example_data(\"non_centered_eight\")\nplot_ess(idata; var_names=[\"mu\"], kind=\"local\", marker=\"_\", ms=20, mew=2, rug=true)\ngcf() See plot_ess"},{"id":192,"pagetitle":"Examples gallery","title":"ESS Quantile Plot","ref":"/ArviZPythonPlots/stable/examples/#ESS-Quantile-Plot","content":" ESS Quantile Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\nidata = load_example_data(\"radon\")\nplot_ess(idata; var_names=[\"sigma\"], kind=\"quantile\", color=\"C4\")\ngcf() See plot_ess"},{"id":193,"pagetitle":"Examples gallery","title":"Forest Plot","ref":"/ArviZPythonPlots/stable/examples/#Forest-Plot","content":" Forest Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ncentered_data = load_example_data(\"centered_eight\")\nnon_centered_data = load_example_data(\"non_centered_eight\")\nplot_forest(\n [centered_data, non_centered_data];\n model_names=[\"Centered\", \"Non Centered\"],\n var_names=[\"mu\"],\n)\ntitle(\"Estimated theta for eight schools model\")\ngcf() See plot_forest"},{"id":194,"pagetitle":"Examples gallery","title":"Ridge Plot","ref":"/ArviZPythonPlots/stable/examples/#Ridge-Plot","content":" Ridge Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\nrugby_data = load_example_data(\"rugby\")\nplot_forest(\n rugby_data;\n kind=\"ridgeplot\",\n var_names=[\"defs\"],\n linewidth=4,\n combined=true,\n ridgeplot_overlap=1.5,\n colors=\"blue\",\n figsize=(9, 4),\n)\ntitle(\"Relative defensive strength\\nof Six Nation rugby teams\")\ngcf() See plot_forest"},{"id":195,"pagetitle":"Examples gallery","title":"Plot HDI","ref":"/ArviZPythonPlots/stable/examples/#Plot-HDI","content":" Plot HDI using Random\nusing ArviZPythonPlots\n\nRandom.seed!(308)\n\nuse_style(\"arviz-darkgrid\")\n\nx_data = randn(100)\ny_data = 2 .+ x_data .* 0.5\ny_data_rep = 0.5 .* randn(200, 100) .+ transpose(y_data)\n\nplot(x_data, y_data; color=\"C6\")\nplot_hdi(x_data, y_data_rep; color=\"k\", plot_kwargs=Dict(\"ls\" => \"--\"))\ngcf() See plot_hdi"},{"id":196,"pagetitle":"Examples gallery","title":"Joint Plot","ref":"/ArviZPythonPlots/stable/examples/#Joint-Plot","content":" Joint Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"non_centered_eight\")\nplot_pair(\n data;\n var_names=[\"theta\"],\n coords=Dict(\"school\" => [\"Choate\", \"Phillips Andover\"]),\n kind=\"hexbin\",\n marginals=true,\n figsize=(10, 10),\n)\ngcf() See plot_pair"},{"id":197,"pagetitle":"Examples gallery","title":"KDE Plot","ref":"/ArviZPythonPlots/stable/examples/#KDE-Plot","content":" KDE Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"centered_eight\")\n\n## Combine different posterior draws from different chains\nobs = data.posterior_predictive.obs\nsize_obs = size(obs)\ny_hat = reshape(obs, prod(size_obs[1:2]), size_obs[3:end]...)\n\nplot_kde(\n y_hat;\n label=\"Estimated Effect\\n of SAT Prep\",\n rug=true,\n plot_kwargs=Dict(\"linewidth\" => 2, \"color\" => \"black\"),\n rug_kwargs=Dict(\"color\" => \"black\"),\n)\ngcf() See plot_kde"},{"id":198,"pagetitle":"Examples gallery","title":"2d KDE","ref":"/ArviZPythonPlots/stable/examples/#d-KDE","content":" 2d KDE using Random\nusing ArviZPythonPlots\n\nRandom.seed!(308)\n\nuse_style(\"arviz-darkgrid\")\n\nplot_kde(rand(100), rand(100))\ngcf() See plot_kde"},{"id":199,"pagetitle":"Examples gallery","title":"KDE Quantiles Plot","ref":"/ArviZPythonPlots/stable/examples/#KDE-Quantiles-Plot","content":" KDE Quantiles Plot using Random\nusing Distributions\nusing ArviZPythonPlots\n\nRandom.seed!(308)\n\nuse_style(\"arviz-darkgrid\")\n\ndist = rand(Beta(rand(Uniform(0.5, 10)), 5), 1000)\nplot_kde(dist; quantiles=[0.25, 0.5, 0.75])\ngcf() See plot_kde"},{"id":200,"pagetitle":"Examples gallery","title":"Pareto Shape Plot","ref":"/ArviZPythonPlots/stable/examples/#Pareto-Shape-Plot","content":" Pareto Shape Plot using ArviZ, ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\nidata = load_example_data(\"radon\")\nloo_data = loo(idata)\nplot_khat(loo_data; show_bins=true)\ngcf() See loo , plot_khat"},{"id":201,"pagetitle":"Examples gallery","title":"LOO-PIT ECDF Plot","ref":"/ArviZPythonPlots/stable/examples/#LOO-PIT-ECDF-Plot","content":" LOO-PIT ECDF Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\nidata = load_example_data(\"radon\")\n\nplot_loo_pit(idata; y=\"y\", ecdf=true, color=\"maroon\")\ngcf() See loo_pit , plot_loo_pit"},{"id":202,"pagetitle":"Examples gallery","title":"LOO-PIT Overlay Plot","ref":"/ArviZPythonPlots/stable/examples/#LOO-PIT-Overlay-Plot","content":" LOO-PIT Overlay Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\nidata = load_example_data(\"non_centered_eight\")\nplot_loo_pit(; idata, y=\"obs\", color=\"indigo\")\ngcf() See loo_pit , plot_loo_pit"},{"id":203,"pagetitle":"Examples gallery","title":"Quantile Monte Carlo Standard Error Plot","ref":"/ArviZPythonPlots/stable/examples/#Quantile-Monte-Carlo-Standard-Error-Plot","content":" Quantile Monte Carlo Standard Error Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"centered_eight\")\nplot_mcse(data; var_names=[\"tau\", \"mu\"], rug=true, extra_methods=true)\ngcf() See plot_mcse"},{"id":204,"pagetitle":"Examples gallery","title":"Quantile MCSE Errobar Plot","ref":"/ArviZPythonPlots/stable/examples/#Quantile-MCSE-Errobar-Plot","content":" Quantile MCSE Errobar Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"radon\")\nplot_mcse(data; var_names=[\"sigma_a\"], color=\"C4\", errorbar=true)\ngcf() See plot_mcse"},{"id":205,"pagetitle":"Examples gallery","title":"Pair Plot","ref":"/ArviZPythonPlots/stable/examples/#Pair-Plot","content":" Pair Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ncentered = load_example_data(\"centered_eight\")\ncoords = Dict(\"school\" => [\"Choate\", \"Deerfield\"])\nplot_pair(\n centered; var_names=[\"theta\", \"mu\", \"tau\"], coords, divergences=true, textsize=22\n)\ngcf() See plot_pair"},{"id":206,"pagetitle":"Examples gallery","title":"Hexbin Pair Plot","ref":"/ArviZPythonPlots/stable/examples/#Hexbin-Pair-Plot","content":" Hexbin Pair Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ncentered = load_example_data(\"centered_eight\")\ncoords = Dict(\"school\" => [\"Choate\", \"Deerfield\"])\nplot_pair(\n centered;\n var_names=[\"theta\", \"mu\", \"tau\"],\n kind=\"hexbin\",\n coords,\n colorbar=true,\n divergences=true,\n)\ngcf() See plot_pair"},{"id":207,"pagetitle":"Examples gallery","title":"KDE Pair Plot","ref":"/ArviZPythonPlots/stable/examples/#KDE-Pair-Plot","content":" KDE Pair Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ncentered = load_example_data(\"centered_eight\")\ncoords = Dict(\"school\" => [\"Choate\", \"Deerfield\"])\nplot_pair(\n centered;\n var_names=[\"theta\", \"mu\", \"tau\"],\n kind=\"kde\",\n coords,\n divergences=true,\n textsize=22,\n)\ngcf() See plot_pair"},{"id":208,"pagetitle":"Examples gallery","title":"Point Estimate Pair Plot","ref":"/ArviZPythonPlots/stable/examples/#Point-Estimate-Pair-Plot","content":" Point Estimate Pair Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ncentered = load_example_data(\"centered_eight\")\ncoords = Dict(\"school\" => [\"Choate\", \"Deerfield\"])\nplot_pair(\n centered;\n var_names=[\"mu\", \"theta\"],\n kind=[\"scatter\", \"kde\"],\n kde_kwargs=Dict(\"fill_last\" => false),\n marginals=true,\n coords,\n point_estimate=\"median\",\n figsize=(10, 8),\n)\ngcf() See plot_pair"},{"id":209,"pagetitle":"Examples gallery","title":"Parallel Plot","ref":"/ArviZPythonPlots/stable/examples/#Parallel-Plot","content":" Parallel Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"centered_eight\")\nax = plot_parallel(data; var_names=[\"theta\", \"tau\", \"mu\"])\nax.set_xticklabels(ax.get_xticklabels(); rotation=70)\ndraw()\ngcf() See plot_parallel"},{"id":210,"pagetitle":"Examples gallery","title":"Posterior Plot","ref":"/ArviZPythonPlots/stable/examples/#Posterior-Plot","content":" Posterior Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"centered_eight\")\ncoords = Dict(\"school\" => [\"Choate\"])\nplot_posterior(data; var_names=[\"mu\", \"theta\"], coords, rope=(-1, 1))\ngcf() See plot_posterior"},{"id":211,"pagetitle":"Examples gallery","title":"Posterior Predictive Check Plot","ref":"/ArviZPythonPlots/stable/examples/#Posterior-Predictive-Check-Plot","content":" Posterior Predictive Check Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"non_centered_eight\")\nplot_ppc(data; data_pairs=Dict(\"obs\" => \"obs\"), alpha=0.03, figsize=(12, 6), textsize=14)\ngcf() See plot_ppc"},{"id":212,"pagetitle":"Examples gallery","title":"Posterior Predictive Check Cumulative Plot","ref":"/ArviZPythonPlots/stable/examples/#Posterior-Predictive-Check-Cumulative-Plot","content":" Posterior Predictive Check Cumulative Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"non_centered_eight\")\nplot_ppc(data; alpha=0.3, kind=\"cumulative\", figsize=(12, 6), textsize=14)\ngcf() See plot_ppc"},{"id":213,"pagetitle":"Examples gallery","title":"Rank Plot","ref":"/ArviZPythonPlots/stable/examples/#Rank-Plot","content":" Rank Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"centered_eight\")\nplot_rank(data; var_names=[\"tau\", \"mu\"])\ngcf() See plot_rank"},{"id":214,"pagetitle":"Examples gallery","title":"Regression Plot","ref":"/ArviZPythonPlots/stable/examples/#Regression-Plot","content":" Regression Plot using ArviZ, ArviZPythonPlots, ArviZExampleData, DimensionalData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"regression1d\")\nx = range(0, 1; length=100)\nposterior = data.posterior\nconstant_data = convert_to_dataset((; x); default_dims=())\ny_model = broadcast_dims(muladd, posterior.intercept, posterior.slope, constant_data.x)\nposterior = merge(posterior, (; y_model))\ndata = merge(data, InferenceData(; posterior, constant_data))\nplot_lm(\"y\"; idata=data, x=\"x\", y_model=\"y_model\")\ngcf() See plot_lm"},{"id":215,"pagetitle":"Examples gallery","title":"Separation Plot","ref":"/ArviZPythonPlots/stable/examples/#Separation-Plot","content":" Separation Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"classification10d\")\nplot_separation(data; y=\"outcome\", y_hat=\"outcome\", figsize=(8, 1))\ngcf() See plot_separation"},{"id":216,"pagetitle":"Examples gallery","title":"Trace Plot","ref":"/ArviZPythonPlots/stable/examples/#Trace-Plot","content":" Trace Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"non_centered_eight\")\nplot_trace(data; var_names=[\"tau\", \"mu\"])\ngcf() See plot_trace"},{"id":217,"pagetitle":"Examples gallery","title":"Violin Plot","ref":"/ArviZPythonPlots/stable/examples/#Violin-Plot","content":" Violin Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"non_centered_eight\")\nplot_violin(data; var_names=[\"mu\", \"tau\"])\ngcf() See plot_violin"},{"id":218,"pagetitle":"Examples gallery","title":"Styles","ref":"/ArviZPythonPlots/stable/examples/#Styles","content":" Styles using ArviZPythonPlots, Distributions, PythonCall\n\nx = range(0, 1; length=100)\ndist = pdf.(Beta(2, 5), x)\n\nstyle_list = [\n \"default\",\n [\"default\", \"arviz-colors\"],\n \"arviz-darkgrid\",\n \"arviz-whitegrid\",\n \"arviz-white\",\n \"arviz-grayscale\",\n [\"arviz-white\", \"arviz-redish\"],\n [\"arviz-white\", \"arviz-bluish\"],\n [\"arviz-white\", \"arviz-orangish\"],\n [\"arviz-white\", \"arviz-brownish\"],\n [\"arviz-white\", \"arviz-purplish\"],\n [\"arviz-white\", \"arviz-cyanish\"],\n [\"arviz-white\", \"arviz-greenish\"],\n [\"arviz-white\", \"arviz-royish\"],\n [\"arviz-white\", \"arviz-viridish\"],\n [\"arviz-white\", \"arviz-plasmish\"],\n \"arviz-doc\",\n \"arviz-docgrid\",\n]\n\nfig = figure(; figsize=(20, 10))\nfor (idx, style) in enumerate(style_list)\n pywith(pyplot.style.context(style; after_reset=true)) do _\n ax = fig.add_subplot(5, 4, idx; label=idx)\n colors = pyplot.rcParams[\"axes.prop_cycle\"].by_key()[\"color\"]\n for i in 0:(length(colors) - 1)\n ax.plot(x, dist .- i, \"C$i\"; label=\"C$i\")\n end\n ax.set_title(style)\n ax.set_xlabel(\"x\")\n ax.set_ylabel(\"f(x)\"; rotation=0, labelpad=15)\n ax.set_xticklabels([])\n end\nend\ntight_layout()\ngcf()"},{"id":221,"pagetitle":"Home","title":"PosteriorStats","ref":"/PosteriorStats/stable/#PosteriorStats","content":" PosteriorStats PosteriorStats implements widely-used and well-characterized statistical analyses for the Bayesian workflow. These functions generally estimate properties of posterior and/or posterior predictive distributions. The default implementations defined here operate on Monte Carlo samples. See the API for details."},{"id":222,"pagetitle":"Home","title":"Extending this package","ref":"/PosteriorStats/stable/#Extending-this-package","content":" Extending this package The methods defined here are intended to be extended by two types of packages. packages that implement data types for storing Monte Carlo samples packages that implement other representations for posterior distributions than Monte Carlo draws"},{"id":225,"pagetitle":"API","title":"API","ref":"/PosteriorStats/stable/api/#API","content":" API"},{"id":226,"pagetitle":"API","title":"Summary statistics","ref":"/PosteriorStats/stable/api/#Summary-statistics","content":" Summary statistics"},{"id":227,"pagetitle":"API","title":"PosteriorStats.SummaryStats","ref":"/PosteriorStats/stable/api/#PosteriorStats.SummaryStats","content":" PosteriorStats.SummaryStats — Type A container for a column table of values computed by summarize . This object implements the Tables and TableTraits interfaces and has a custom show method. name : The name of the collection of summary statistics, used as the table title in display. data : The summary statistics for each parameter, with an optional first column parameter containing the parameter names. source"},{"id":228,"pagetitle":"API","title":"PosteriorStats.default_diagnostics","ref":"/PosteriorStats/stable/api/#PosteriorStats.default_diagnostics","content":" PosteriorStats.default_diagnostics — Function default_diagnostics(focus=Statistics.mean; kwargs...) Default diagnostics to be computed with summarize . The value of focus determines the diagnostics to be returned: Statistics.mean : mcse_mean , mcse_std , ess_tail , ess_bulk , rhat Statistics.median : mcse_median , ess_tail , ess_bulk , rhat source"},{"id":229,"pagetitle":"API","title":"PosteriorStats.default_stats","ref":"/PosteriorStats/stable/api/#PosteriorStats.default_stats","content":" PosteriorStats.default_stats — Function default_stats(focus=Statistics.mean; prob_interval=0.94, kwargs...) Default statistics to be computed with summarize . The value of focus determines the statistics to be returned: Statistics.mean : mean , std , hdi_3% , hdi_97% Statistics.median : median , mad , eti_3% , eti_97% If prob_interval is set to a different value than the default, then different HDI and ETI statistics are computed accordingly. hdi refers to the highest-density interval, while eti refers to the equal-tailed interval (i.e. the credible interval computed from symmetric quantiles). See also: hdi source"},{"id":230,"pagetitle":"API","title":"PosteriorStats.default_summary_stats","ref":"/PosteriorStats/stable/api/#PosteriorStats.default_summary_stats","content":" PosteriorStats.default_summary_stats — Function default_summary_stats(focus=Statistics.mean; kwargs...) Combinatiton of default_stats and default_diagnostics to be used with summarize . source"},{"id":231,"pagetitle":"API","title":"PosteriorStats.summarize","ref":"/PosteriorStats/stable/api/#PosteriorStats.summarize","content":" PosteriorStats.summarize — Function summarize(data, stats_funs...; name=\"SummaryStats\", [var_names]) -> SummaryStats Compute the summary statistics in stats_funs on each param in data . stats_funs is a collection of functions that reduces a matrix with shape (draws, chains) to a scalar or a collection of scalars. Alternatively, an item in stats_funs may be a Pair of the form name => fun specifying the name to be used for the statistic or of the form (name1, ...) => fun when the function returns a collection. When the function returns a collection, the names in this latter format must be provided. If no stats functions are provided, then those specified in default_summary_stats are computed. var_names specifies the names of the parameters in data . If not provided, the names are inferred from data . To support computing summary statistics from a custom object, overload this method specifying the type of data . See also SummaryStats , default_summary_stats , default_stats , default_diagnostics . Examples Compute mean , std and the Monte Carlo standard error (MCSE) of the mean estimate: julia> using Statistics, StatsBase\n\njulia> x = randn(1000, 4, 3) .+ reshape(0:10:20, 1, 1, :);\n\njulia> summarize(x, mean, std, :mcse_mean => sem; name=\"Mean/Std\")\nMean/Std\n mean std mcse_mean\n 1 0.0003 0.990 0.016\n 2 10.02 0.988 0.016\n 3 19.98 0.988 0.016 Avoid recomputing the mean by using mean_and_std , and provide parameter names: julia> summarize(x, (:mean, :std) => mean_and_std, mad; var_names=[:a, :b, :c])\nSummaryStats\n mean std mad\n a 0.000305 0.990 0.978\n b 10.0 0.988 0.995\n c 20.0 0.988 0.979 Note that when an estimator and its MCSE are both computed, the MCSE is used to determine the number of significant digits that will be displayed. julia> summarize(x; var_names=[:a, :b, :c])\nSummaryStats\n mean std hdi_3% hdi_97% mcse_mean mcse_std ess_tail ess_bulk r ⋯\n a 0.0003 0.99 -1.92 1.78 0.016 0.012 3567 3663 1 ⋯\n b 10.02 0.99 8.17 11.9 0.016 0.011 3841 3906 1 ⋯\n c 19.98 0.99 18.1 21.9 0.016 0.012 3892 3749 1 ⋯\n 1 column omitted Compute just the statistics with an 89% HDI on all parameters, and provide the parameter names: julia> summarize(x, default_stats(; prob_interval=0.89)...; var_names=[:a, :b, :c])\nSummaryStats\n mean std hdi_5.5% hdi_94.5%\n a 0.000305 0.990 -1.63 1.52\n b 10.0 0.988 8.53 11.6\n c 20.0 0.988 18.5 21.6 Compute the summary stats focusing on Statistics.median : julia> summarize(x, default_summary_stats(median)...; var_names=[:a, :b, :c])\nSummaryStats\n median mad eti_3% eti_97% mcse_median ess_tail ess_median rhat\n a 0.004 0.978 -1.83 1.89 0.020 3567 3336 1.00\n b 10.02 0.995 8.17 11.9 0.023 3841 3787 1.00\n c 19.99 0.979 18.1 21.9 0.020 3892 3829 1.00 source"},{"id":232,"pagetitle":"API","title":"General statistics","ref":"/PosteriorStats/stable/api/#General-statistics","content":" General statistics"},{"id":233,"pagetitle":"API","title":"PosteriorStats.hdi","ref":"/PosteriorStats/stable/api/#PosteriorStats.hdi","content":" PosteriorStats.hdi — Function hdi(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper) Estimate the unimodal highest density interval (HDI) of samples for the probability prob . The HDI is the minimum width Bayesian credible interval (BCI). That is, it is the smallest possible interval containing (100*prob) % of the probability mass. [Hyndman1996] samples is an array of shape (draws[, chains[, params...]]) . If multiple parameters are present, then lower and upper are arrays with the shape (params...,) , computed separately for each marginal. This implementation uses the algorithm of [ChenShao1999] . Note Any default value of prob is arbitrary. The default value of prob=0.94 instead of a more common default like prob=0.95 is chosen to reminder the user of this arbitrariness. Examples Here we calculate the 83% HDI for a normal random variable: julia> x = randn(2_000);\n\njulia> hdi(x; prob=0.83) |> pairs\npairs(::NamedTuple) with 2 entries:\n :lower => -1.38266\n :upper => 1.25982 We can also calculate the HDI for a 3-dimensional array of samples: julia> x = randn(1_000, 1, 1) .+ reshape(0:5:10, 1, 1, :);\n\njulia> hdi(x) |> pairs\npairs(::NamedTuple) with 2 entries:\n :lower => [-1.9674, 3.0326, 8.0326]\n :upper => [1.90028, 6.90028, 11.9003] source"},{"id":234,"pagetitle":"API","title":"PosteriorStats.hdi!","ref":"/PosteriorStats/stable/api/#PosteriorStats.hdi!","content":" PosteriorStats.hdi! — Function hdi!(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper) A version of hdi that sorts samples in-place while computing the HDI. source"},{"id":235,"pagetitle":"API","title":"PosteriorStats.r2_score","ref":"/PosteriorStats/stable/api/#PosteriorStats.r2_score","content":" PosteriorStats.r2_score — Function r2_score(y_true::AbstractVector, y_pred::AbstractVecOrMat) -> (; r2, r2_std) $R²$ for linear Bayesian regression models. [GelmanGoodrich2019] Arguments y_true : Observed data of length noutputs y_pred : Predicted data with size (ndraws[, nchains], noutputs) Examples julia> using ArviZExampleData\n\njulia> idata = load_example_data(\"regression1d\");\n\njulia> y_true = idata.observed_data.y;\n\njulia> y_pred = PermutedDimsArray(idata.posterior_predictive.y, (:draw, :chain, :y_dim_0));\n\njulia> r2_score(y_true, y_pred) |> pairs\npairs(::NamedTuple) with 2 entries:\n :r2 => 0.683197\n :r2_std => 0.0368838 source"},{"id":236,"pagetitle":"API","title":"LOO and WAIC","ref":"/PosteriorStats/stable/api/#LOO-and-WAIC","content":" LOO and WAIC"},{"id":237,"pagetitle":"API","title":"PosteriorStats.AbstractELPDResult","ref":"/PosteriorStats/stable/api/#PosteriorStats.AbstractELPDResult","content":" PosteriorStats.AbstractELPDResult — Type abstract type AbstractELPDResult An abstract type representing the result of an ELPD computation. Every subtype stores estimates of both the expected log predictive density ( elpd ) and the effective number of parameters p , as well as standard errors and pointwise estimates of each, from which other relevant estimates can be computed. Subtypes implement the following functions: elpd_estimates information_criterion source"},{"id":238,"pagetitle":"API","title":"PosteriorStats.PSISLOOResult","ref":"/PosteriorStats/stable/api/#PosteriorStats.PSISLOOResult","content":" PosteriorStats.PSISLOOResult — Type Results of Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO). See also: loo , AbstractELPDResult estimates : Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p) pointwise : Pointwise estimates psis_result : Pareto-smoothed importance sampling (PSIS) results source"},{"id":239,"pagetitle":"API","title":"PosteriorStats.WAICResult","ref":"/PosteriorStats/stable/api/#PosteriorStats.WAICResult","content":" PosteriorStats.WAICResult — Type Results of computing the widely applicable information criterion (WAIC). See also: waic , AbstractELPDResult estimates : Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p) pointwise : Pointwise estimates source"},{"id":240,"pagetitle":"API","title":"PosteriorStats.elpd_estimates","ref":"/PosteriorStats/stable/api/#PosteriorStats.elpd_estimates","content":" PosteriorStats.elpd_estimates — Function elpd_estimates(result::AbstractELPDResult; pointwise=false) -> (; elpd, elpd_mcse, lpd) Return the (E)LPD estimates from the result . source"},{"id":241,"pagetitle":"API","title":"PosteriorStats.information_criterion","ref":"/PosteriorStats/stable/api/#PosteriorStats.information_criterion","content":" PosteriorStats.information_criterion — Function information_criterion(elpd, scale::Symbol) Compute the information criterion for the given scale from the elpd estimate. scale must be one of (:deviance, :log, :negative_log) . See also: loo , waic source information_criterion(result::AbstractELPDResult, scale::Symbol; pointwise=false) Compute information criterion for the given scale from the existing ELPD result . scale must be one of (:deviance, :log, :negative_log) . If pointwise=true , then pointwise estimates are returned. source"},{"id":242,"pagetitle":"API","title":"PosteriorStats.loo","ref":"/PosteriorStats/stable/api/#PosteriorStats.loo","content":" PosteriorStats.loo — Function loo(log_likelihood; reff=nothing, kwargs...) -> PSISLOOResult{<:NamedTuple,<:NamedTuple} Compute the Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO). [Vehtari2017] [LOOFAQ] log_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]) . Keywords reff::Union{Real,AbstractArray{<:Real}} : The relative effective sample size(s) of the likelihood values. If an array, it must have the same data dimensions as the corresponding log-likelihood variable. If not provided, then this is estimated using MCMCDiagnosticTools.ess . kwargs : Remaining keywords are forwarded to [ PSIS.psis ]. See also: PSISLOOResult , waic Examples Manually compute $R_\\mathrm{eff}$ and calculate PSIS-LOO of a model: julia> using ArviZExampleData, MCMCDiagnosticTools\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> reff = ess(log_like; kind=:basic, split_chains=1, relative=true);\n\njulia> loo(log_like; reff)\nPSISLOOResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.34\n\nand PSISResult with 500 draws, 4 chains, and 8 parameters\nPareto shape (k) diagnostic values:\n Count Min. ESS\n (-Inf, 0.5] good 7 (87.5%) 151\n (0.5, 0.7] okay 1 (12.5%) 446 source"},{"id":243,"pagetitle":"API","title":"PosteriorStats.waic","ref":"/PosteriorStats/stable/api/#PosteriorStats.waic","content":" PosteriorStats.waic — Function waic(log_likelihood::AbstractArray) -> WAICResult{<:NamedTuple,<:NamedTuple} Compute the widely applicable information criterion (WAIC). [Watanabe2010] [Vehtari2017] [LOOFAQ] log_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]) . See also: WAICResult , loo Examples Calculate WAIC of a model: julia> using ArviZExampleData\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> waic(log_like)\nWAICResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.33 source"},{"id":244,"pagetitle":"API","title":"Model comparison","ref":"/PosteriorStats/stable/api/#Model-comparison","content":" Model comparison"},{"id":245,"pagetitle":"API","title":"PosteriorStats.ModelComparisonResult","ref":"/PosteriorStats/stable/api/#PosteriorStats.ModelComparisonResult","content":" PosteriorStats.ModelComparisonResult — Type ModelComparisonResult Result of model comparison using ELPD. This struct implements the Tables and TableTraits interfaces. Each field returns a collection of the corresponding entry for each model: name : Names of the models, if provided. rank : Ranks of the models (ordered by decreasing ELPD) elpd_diff : ELPD of a model subtracted from the largest ELPD of any model elpd_diff_mcse : Monte Carlo standard error of the ELPD difference weight : Model weights computed with weights_method elpd_result : AbstactELPDResult s for each model, which can be used to access useful stats like ELPD estimates, pointwise estimates, and Pareto shape values for PSIS-LOO weights_method : Method used to compute model weights with model_weights source"},{"id":246,"pagetitle":"API","title":"PosteriorStats.compare","ref":"/PosteriorStats/stable/api/#PosteriorStats.compare","content":" PosteriorStats.compare — Function compare(models; kwargs...) -> ModelComparisonResult Compare models based on their expected log pointwise predictive density (ELPD). The ELPD is estimated either by Pareto smoothed importance sampling leave-one-out cross-validation (LOO) or using the widely applicable information criterion (WAIC). We recommend loo. Read more theory here - in a paper by some of the leading authorities on model comparison dx.doi.org/10.1111/1467-9868.00353 Arguments models : a Tuple , NamedTuple , or AbstractVector whose values are either AbstractELPDResult entries or any argument to elpd_method . Keywords weights_method::AbstractModelWeightsMethod=Stacking() : the method to be used to weight the models. See model_weights for details elpd_method=loo : a method that computes an AbstractELPDResult from an argument in models . sort::Bool=true : Whether to sort models by decreasing ELPD. Returns ModelComparisonResult : A container for the model comparison results. The fields contain a similar collection to models . Examples Compare the centered and non centered models of the eight school problem using the defaults: loo and Stacking weights. A custom myloo method formates the inputs as expected by loo . julia> using ArviZExampleData\n\njulia> models = (\n centered=load_example_data(\"centered_eight\"),\n non_centered=load_example_data(\"non_centered_eight\"),\n );\n\njulia> function myloo(idata)\n log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1))\n return loo(log_like)\n end;\n\njulia> mc = compare(models; elpd_method=myloo)\n┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.\n└ @ PSIS ~/.julia/packages/PSIS/...\nModelComparisonResult with Stacking weights\n rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯\n non_centered 1 -31 1.4 0 0.0 1.0 0.9 ⋯\n centered 2 -31 1.4 0.06 0.067 0.0 0.9 ⋯\n 1 column omitted\njulia> mc.weight |> pairs\npairs(::NamedTuple) with 2 entries:\n :non_centered => 1.0\n :centered => 5.34175e-19 Compare the same models from pre-computed PSIS-LOO results and computing BootstrappedPseudoBMA weights: julia> elpd_results = mc.elpd_result;\n\njulia> compare(elpd_results; weights_method=BootstrappedPseudoBMA())\nModelComparisonResult with BootstrappedPseudoBMA weights\n rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯\n non_centered 1 -31 1.4 0 0.0 0.52 0.9 ⋯\n centered 2 -31 1.4 0.06 0.067 0.48 0.9 ⋯\n 1 column omitted source"},{"id":247,"pagetitle":"API","title":"PosteriorStats.model_weights","ref":"/PosteriorStats/stable/api/#PosteriorStats.model_weights","content":" PosteriorStats.model_weights — Function model_weights(elpd_results; method=Stacking())\nmodel_weights(method::AbstractModelWeightsMethod, elpd_results) Compute weights for each model in elpd_results using method . elpd_results is a Tuple , NamedTuple , or AbstractVector with AbstractELPDResult entries. The weights are returned in the same type of collection. Stacking is the recommended approach, as it performs well even when the true data generating process is not included among the candidate models. See [YaoVehtari2018] for details. See also: AbstractModelWeightsMethod , compare Examples Compute Stacking weights for two models: julia> using ArviZExampleData\n\njulia> models = (\n centered=load_example_data(\"centered_eight\"),\n non_centered=load_example_data(\"non_centered_eight\"),\n );\n\njulia> elpd_results = map(models) do idata\n log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1))\n return loo(log_like)\n end;\n┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.\n└ @ PSIS ~/.julia/packages/PSIS/...\n\njulia> model_weights(elpd_results; method=Stacking()) |> pairs\npairs(::NamedTuple) with 2 entries:\n :centered => 5.34175e-19\n :non_centered => 1.0 Now we compute BootstrappedPseudoBMA weights for the same models: julia> model_weights(elpd_results; method=BootstrappedPseudoBMA()) |> pairs\npairs(::NamedTuple) with 2 entries:\n :centered => 0.483723\n :non_centered => 0.516277 source The following model weighting methods are available"},{"id":248,"pagetitle":"API","title":"PosteriorStats.AbstractModelWeightsMethod","ref":"/PosteriorStats/stable/api/#PosteriorStats.AbstractModelWeightsMethod","content":" PosteriorStats.AbstractModelWeightsMethod — Type abstract type AbstractModelWeightsMethod An abstract type representing methods for computing model weights. Subtypes implement model_weights (method, elpd_results) . source"},{"id":249,"pagetitle":"API","title":"PosteriorStats.BootstrappedPseudoBMA","ref":"/PosteriorStats/stable/api/#PosteriorStats.BootstrappedPseudoBMA","content":" PosteriorStats.BootstrappedPseudoBMA — Type struct BootstrappedPseudoBMA{R<:Random.AbstractRNG, T<:Real} <: AbstractModelWeightsMethod Model weighting method using pseudo Bayesian Model Averaging using Akaike-type weighting with the Bayesian bootstrap (pseudo-BMA+) [YaoVehtari2018] . The Bayesian bootstrap stabilizes the model weights. BootstrappedPseudoBMA(; rng=Random.default_rng(), samples=1_000, alpha=1)\nBootstrappedPseudoBMA(rng, samples, alpha) Construct the method. rng::Random.AbstractRNG : The random number generator to use for the Bayesian bootstrap samples::Int64 : The number of samples to draw for bootstrapping alpha::Real : The shape parameter in the Dirichlet distribution used for the Bayesian bootstrap. The default (1) corresponds to a uniform distribution on the simplex. See also: Stacking source"},{"id":250,"pagetitle":"API","title":"PosteriorStats.PseudoBMA","ref":"/PosteriorStats/stable/api/#PosteriorStats.PseudoBMA","content":" PosteriorStats.PseudoBMA — Type struct PseudoBMA <: AbstractModelWeightsMethod Model weighting method using pseudo Bayesian Model Averaging (pseudo-BMA) and Akaike-type weighting. PseudoBMA(; regularize=false)\nPseudoBMA(regularize) Construct the method with optional regularization of the weights using the standard error of the ELPD estimate. Note This approach is not recommended, as it produces unstable weight estimates. It is recommended to instead use BootstrappedPseudoBMA to stabilize the weights or Stacking . For details, see [YaoVehtari2018] . See also: Stacking source"},{"id":251,"pagetitle":"API","title":"PosteriorStats.Stacking","ref":"/PosteriorStats/stable/api/#PosteriorStats.Stacking","content":" PosteriorStats.Stacking — Type struct Stacking{O<:Optim.AbstractOptimizer} <: AbstractModelWeightsMethod Model weighting using stacking of predictive distributions [YaoVehtari2018] . Stacking(; optimizer=Optim.LBFGS(), options=Optim.Options()\nStacking(optimizer[, options]) Construct the method, optionally customizing the optimization. optimizer::Optim.AbstractOptimizer : The optimizer to use for the optimization of the weights. The optimizer must support projected gradient optimization via a manifold field. options::Optim.Options : The Optim options to use for the optimization of the weights. See also: BootstrappedPseudoBMA source"},{"id":252,"pagetitle":"API","title":"Predictive checks","ref":"/PosteriorStats/stable/api/#Predictive-checks","content":" Predictive checks"},{"id":253,"pagetitle":"API","title":"PosteriorStats.loo_pit","ref":"/PosteriorStats/stable/api/#PosteriorStats.loo_pit","content":" PosteriorStats.loo_pit — Function loo_pit(y, y_pred, log_weights; kwargs...) -> Union{Real,AbstractArray} Compute leave-one-out probability integral transform (LOO-PIT) checks. Arguments y : array of observations with shape (params...,) y_pred : array of posterior predictive samples with shape (draws, chains, params...) . log_weights : array of normalized log LOO importance weights with shape (draws, chains, params...) . Keywords is_discrete : If not provided, then it is set to true iff elements of y and y_pred are all integer-valued. If true , then data are smoothed using smooth_data to make them non-discrete before estimating LOO-PIT values. kwargs : Remaining keywords are forwarded to smooth_data if data is discrete. Returns pitvals : LOO-PIT values with same size as y . If y is a scalar, then pitvals is a scalar. LOO-PIT is a marginal posterior predictive check. If $y_{-i}$ is the array $y$ of observations with the $i$ th observation left out, and $y_i^*$ is a posterior prediction of the $i$ th observation, then the LOO-PIT value for the $i$ th observation is defined as \\[P(y_i^* \\le y_i \\mid y_{-i}) = \\int_{-\\infty}^{y_i} p(y_i^* \\mid y_{-i}) \\mathrm{d} y_i^*\\] The LOO posterior predictions and the corresponding observations should have similar distributions, so if conditional predictive distributions are well-calibrated, then all LOO-PIT values should be approximately uniformly distributed on $[0, 1]$ . [Gabry2019] Examples Calculate LOO-PIT values using as test quantity the observed values themselves. julia> using ArviZExampleData\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> y = idata.observed_data.obs;\n\njulia> y_pred = PermutedDimsArray(idata.posterior_predictive.obs, (:draw, :chain, :school));\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> log_weights = loo(log_like).psis_result.log_weights;\n\njulia> loo_pit(y, y_pred, log_weights)\n8-element DimArray{Float64,1} with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.943511\n \"Deerfield\" 0.63797\n \"Phillips Andover\" 0.316697\n \"Phillips Exeter\" 0.582252\n \"Hotchkiss\" 0.295321\n \"Lawrenceville\" 0.403318\n \"St. Paul's\" 0.902508\n \"Mt. Hermon\" 0.655275 Calculate LOO-PIT values using as test quantity the square of the difference between each observation and mu . julia> using Statistics\n\njulia> mu = idata.posterior.mu;\n\njulia> T = y .- median(mu);\n\njulia> T_pred = y_pred .- mu;\n\njulia> loo_pit(T .^ 2, T_pred .^ 2, log_weights)\n8-element DimArray{Float64,1} with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.873577\n \"Deerfield\" 0.243686\n \"Phillips Andover\" 0.357563\n \"Phillips Exeter\" 0.149908\n \"Hotchkiss\" 0.435094\n \"Lawrenceville\" 0.220627\n \"St. Paul's\" 0.775086\n \"Mt. Hermon\" 0.296706 source"},{"id":254,"pagetitle":"API","title":"Utilities","ref":"/PosteriorStats/stable/api/#Utilities","content":" Utilities"},{"id":255,"pagetitle":"API","title":"PosteriorStats.smooth_data","ref":"/PosteriorStats/stable/api/#PosteriorStats.smooth_data","content":" PosteriorStats.smooth_data — Function smooth_data(y; dims=:, interp_method=CubicSpline, offset_frac=0.01) Smooth y along dims using interp_method . interp_method is a 2-argument callabale that takes the arguments y and x and returns a DataInterpolations.jl interpolation method, defaulting to a cubic spline interpolator. offset_frac is the fraction of the length of y to use as an offset when interpolating. source Hyndman1996 Rob J. Hyndman (1996) Computing and Graphing Highest Density Regions, Amer. Stat., 50(2): 120-6. DOI: 10.1080/00031305.1996.10474359 jstor . ChenShao1999 Ming-Hui Chen & Qi-Man Shao (1999) Monte Carlo Estimation of Bayesian Credible and HPD Intervals, J Comput. Graph. Stat., 8:1, 69-92. DOI: 10.1080/10618600.1999.10474802 jstor . GelmanGoodrich2019 Andrew Gelman, Ben Goodrich, Jonah Gabry & Aki Vehtari (2019) R-squared for Bayesian Regression Models, The American Statistician, 73:3, 307-9, DOI: 10.1080/00031305.2018.1549100 . Vehtari2017 Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544 LOOFAQ Aki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html Watanabe2010 Watanabe, S. Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory. 11(116):3571−3594, 2010. https://jmlr.csail.mit.edu/papers/v11/watanabe10a.html Vehtari2017 Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544 LOOFAQ Aki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html YaoVehtari2018 Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030 YaoVehtari2018 Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030 YaoVehtari2018 Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030 YaoVehtari2018 Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030 Gabry2019 Gabry, J., Simpson, D., Vehtari, A., Betancourt, M. & Gelman, A. Visualization in Bayesian Workflow. J. R. Stat. Soc. Ser. A Stat. Soc. 182, 389–402 (2019). doi: 10.1111/rssa.12378 arXiv: 1709.01449"},{"id":258,"pagetitle":"Home","title":"PSIS","ref":"/PSIS/stable/#PSIS","content":" PSIS PSIS.jl implements the Pareto smoothed importance sampling (PSIS) algorithm from [VehtariSimpson2021] . Given a set of importance weights used in some estimator, PSIS both improves the reliability of the estimates by smoothing the importance weights and acts as a diagnostic of the reliability of the estimates. See psis for details."},{"id":259,"pagetitle":"Home","title":"Example","ref":"/PSIS/stable/#Example","content":" Example In this example, we use PSIS to smooth log importance ratios for importance sampling 30 isotropic Student $t$ -distributed parameters using standard normal distributions as proposals. using PSIS, Distributions\nproposal = Normal()\ntarget = TDist(7)\nndraws, nchains, nparams = (1_000, 1, 30)\nx = rand(proposal, ndraws, nchains, nparams)\nlog_ratios = logpdf.(target, x) .- logpdf.(proposal, x)\nresult = psis(log_ratios) ┌ Warning: 8 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.\n└ @ PSIS ~/work/PSIS.jl/PSIS.jl/src/core.jl:323\n┌ Warning: 1 parameters had Pareto shape values k > 1. Corresponding importance sampling estimates are likely to be unstable and are unlikely to converge with additional samples.\n└ @ PSIS ~/work/PSIS.jl/PSIS.jl/src/core.jl:326 PSISResult with 1000 draws, 1 chains, and 30 parameters\nPareto shape (k) diagnostic values:\n Count Min. ESS \n (-Inf, 0.5] good 7 (23.3%) 959\n (0.5, 0.7] okay 14 (46.7%) 927\n (0.7, 1] bad 8 (26.7%) ——\n (1, Inf) very bad 1 (3.3%) —— As indicated by the warnings, this is a poor choice of a proposal distribution, and estimates are unlikely to converge (see PSISResult for an explanation of the shape thresholds). When running PSIS with many parameters, it is useful to plot the Pareto shape values to diagnose convergence. See Plotting PSIS results for examples. VehtariSimpson2021 Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO]"},{"id":262,"pagetitle":"API","title":"API","ref":"/PSIS/stable/api/#API","content":" API"},{"id":263,"pagetitle":"API","title":"Core functionality","ref":"/PSIS/stable/api/#Core-functionality","content":" Core functionality"},{"id":264,"pagetitle":"API","title":"PSIS.PSISResult","ref":"/PSIS/stable/api/#PSIS.PSISResult","content":" PSIS.PSISResult — Type PSISResult Result of Pareto-smoothed importance sampling (PSIS) using psis . Properties log_weights : un-normalized Pareto-smoothed log weights weights : normalized Pareto-smoothed weights (allocates a copy) pareto_shape : Pareto $k=ξ$ shape parameter nparams : number of parameters in log_weights ndraws : number of draws in log_weights nchains : number of chains in log_weights reff : the ratio of the effective sample size of the unsmoothed importance ratios and the actual sample size. ess : estimated effective sample size of estimate of mean using smoothed importance samples (see ess_is ) tail_length : length of the upper tail of log_weights that was smoothed tail_dist : the generalized Pareto distribution that was fit to the tail of log_weights . Note that the tail weights are scaled to have a maximum of 1, so tail_dist * exp(maximum(log_ratios)) is the corresponding fit directly to the tail of log_ratios . normalized::Bool :indicates whether log_weights are log-normalized along the sample dimensions. Diagnostic The pareto_shape parameter $k=ξ$ of the generalized Pareto distribution tail_dist can be used to diagnose reliability and convergence of estimates using the importance weights [VehtariSimpson2021] . if $k < \\frac{1}{3}$ , importance sampling is stable, and importance sampling (IS) and PSIS both are reliable. if $k ≤ \\frac{1}{2}$ , then the importance ratio distributon has finite variance, and the central limit theorem holds. As $k$ approaches the upper bound, IS becomes less reliable, while PSIS still works well but with a higher RMSE. if $\\frac{1}{2} < k ≤ 0.7$ , then the variance is infinite, and IS can behave quite poorly. However, PSIS works well in this regime. if $0.7 < k ≤ 1$ , then it quickly becomes impractical to collect enough importance weights to reliably compute estimates, and importance sampling is not recommended. if $k > 1$ , then neither the variance nor the mean of the raw importance ratios exists. The convergence rate is close to zero, and bias can be large with practical sample sizes. See PSISPlots.paretoshapeplot for a diagnostic plot. source"},{"id":265,"pagetitle":"API","title":"PSIS.psis","ref":"/PSIS/stable/api/#PSIS.psis","content":" PSIS.psis — Function psis(log_ratios, reff = 1.0; kwargs...) -> PSISResult\npsis!(log_ratios, reff = 1.0; kwargs...) -> PSISResult Compute Pareto smoothed importance sampling (PSIS) log weights [VehtariSimpson2021] . While psis computes smoothed log weights out-of-place, psis! smooths them in-place. Arguments log_ratios : an array of logarithms of importance ratios, with size (draws, [chains, [parameters...]]) , where chains>1 would be used when chains are generated using Markov chain Monte Carlo. reff::Union{Real,AbstractArray} : the ratio(s) of effective sample size of log_ratios and the actual sample size reff = ess/(draws * chains) , used to account for autocorrelation, e.g. due to Markov chain Monte Carlo. If an array, it must have the size (parameters...,) to match log_ratios . Keywords warn=true : If true , warning messages are delivered normalize=true : If true , the log-weights will be log-normalized so that exp.(log_weights) sums to 1 along the sample dimensions. Returns result : a PSISResult object containing the results of the Pareto-smoothing. A warning is raised if the Pareto shape parameter $k ≥ 0.7$ . See PSISResult for details and PSISPlots.paretoshapeplot for a diagnostic plot. source"},{"id":266,"pagetitle":"API","title":"PSIS.ess_is","ref":"/PSIS/stable/api/#PSIS.ess_is","content":" PSIS.ess_is — Function ess_is(weights; reff=1) Estimate effective sample size (ESS) for importance sampling over the sample dimensions. Given normalized weights $w_{1:n}$ , the ESS is estimated using the L2-norm of the weights: \\[\\mathrm{ESS}(w_{1:n}) = \\frac{r_{\\mathrm{eff}}}{\\sum_{i=1}^n w_i^2}\\] where $r_{\\mathrm{eff}}$ is the relative efficiency of the log_weights . ess_is(result::PSISResult; bad_shape_nan=true) Estimate ESS for Pareto-smoothed importance sampling. Note ESS estimates for Pareto shape values $k > 0.7$ , which are unreliable and misleadingly high, are set to NaN . To avoid this, set bad_shape_nan=false . source"},{"id":267,"pagetitle":"API","title":"Plotting","ref":"/PSIS/stable/api/#Plotting","content":" Plotting"},{"id":268,"pagetitle":"API","title":"PSIS.PSISPlots","ref":"/PSIS/stable/api/#PSIS.PSISPlots","content":" PSIS.PSISPlots — Module A module defining paretoshapeplot for plotting Pareto shape values with Plots.jl source"},{"id":269,"pagetitle":"API","title":"PSIS.PSISPlots.paretoshapeplot","ref":"/PSIS/stable/api/#PSIS.PSISPlots.paretoshapeplot","content":" PSIS.PSISPlots.paretoshapeplot — Function paretoshapeplot(values; showlines=false, ...)\nparetoshapeplot!(values; showlines=false, kwargs...) Plot shape parameters of fitted Pareto tail distributions for diagnosing convergence. values may be either a vector of Pareto shape parameters or a PSIS.PSISResult . If showlines==true , horizontal lines indicating relevant Pareto shape thresholds are drawn. See PSIS.PSISResult for an explanation of the thresholds. All remaining kwargs are forwarded to the plotting function. See psis , PSISResult . Examples using PSIS, Distributions, Plots\nproposal = Normal()\ntarget = TDist(7)\nx = rand(proposal, 1_000, 100)\nlog_ratios = logpdf.(target, x) .- logpdf.(proposal, x)\nresult = psis(log_ratios)\nparetoshapeplot(result) We can also plot the Pareto shape parameters directly: paretoshapeplot(result.pareto_shape) We can also use plot directly: plot(result.pareto_shape; showlines=true) source VehtariSimpson2021 Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO] VehtariSimpson2021 Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO]"},{"id":272,"pagetitle":"Internal","title":"Internal","ref":"/PSIS/stable/internal/#Internal","content":" Internal"},{"id":273,"pagetitle":"Internal","title":"PSIS.GeneralizedPareto","ref":"/PSIS/stable/internal/#PSIS.GeneralizedPareto","content":" PSIS.GeneralizedPareto — Type GeneralizedPareto{T<:Real} The generalized Pareto distribution. This is equivalent to Distributions.GeneralizedPareto and can be converted to one with convert(Distributions.GeneralizedPareto, d) . Constructor GeneralizedPareto(μ, σ, k) Construct the generalized Pareto distribution (GPD) with location parameter $μ$ , scale parameter $σ$ and shape parameter $k$ . Note The shape parameter $k$ is equivalent to the commonly used shape parameter $ξ$ . This is the same parameterization used by [VehtariSimpson2021] and is related to that used by [ZhangStephens2009] as $k \\mapsto -k$ . source"},{"id":274,"pagetitle":"Internal","title":"PSIS.fit_gpd","ref":"/PSIS/stable/internal/#PSIS.fit_gpd-Tuple{AbstractArray}","content":" PSIS.fit_gpd — Method fit_gpd(x; μ=0, kwargs...) Fit a GeneralizedPareto with location μ to the data x . The fit is performed using the Empirical Bayes method of [ZhangStephens2009] . Keywords prior_adjusted::Bool=true , If true , a weakly informative Normal prior centered on $\\frac{1}{2}$ is used for the shape $k$ . sorted::Bool=issorted(x) : If true , x is assumed to be sorted. If false , a sorted copy of x is made. min_points::Int=30 : The minimum number of quadrature points to use when estimating the posterior mean of $\\theta = \\frac{\\xi}{\\sigma}$ . source ZhangStephens2009 Jin Zhang & Michael A. Stephens (2009) A New and Efficient Estimation Method for the Generalized Pareto Distribution, Technometrics, 51:3, 316-325, DOI: 10.1198/tech.2009.08017"},{"id":277,"pagetitle":"Plotting","title":"Plotting PSIS results","ref":"/PSIS/stable/plotting/#Plotting-PSIS-results","content":" Plotting PSIS results PSIS.jl includes plotting recipes for PSISResult using any Plots.jl backend, as well as the utility plotting function PSISPlots.paretoshapeplot . We demonstrate this with a simple example. using PSIS, Distributions\nproposal = Normal()\ntarget = TDist(7)\nndraws, nchains, nparams = (1_000, 1, 20)\nx = rand(proposal, ndraws, nchains, nparams)\nlog_ratios = logpdf.(target, x) .- logpdf.(proposal, x)\nresult = psis(log_ratios) PSISResult with 1000 draws, 1 chains, and 20 parameters\nPareto shape (k) diagnostic values:\n Count Min. ESS \n (-Inf, 0.5] good 4 (20.0%) 959\n (0.5, 0.7] okay 10 (50.0%) 927\n (0.7, 1] bad 6 (30.0%) ——"},{"id":278,"pagetitle":"Plotting","title":"Plots.jl","ref":"/PSIS/stable/plotting/#Plots.jl","content":" Plots.jl PSISResult objects can be plotted directly: using Plots\nplot(result; showlines=true, marker=:+, legend=false, linewidth=2) This is equivalent to calling PSISPlots.paretoshapeplot(result; kwargs...) ."},{"id":281,"pagetitle":"Home","title":"MCMCDiagnosticTools","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools","content":" MCMCDiagnosticTools MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo."},{"id":282,"pagetitle":"Home","title":"Background","ref":"/MCMCDiagnosticTools/stable/#Background","content":" Background Some methods were originally part of Mamba.jl and then MCMCChains.jl . This package is a joint collaboration between the Turing and ArviZ projects."},{"id":283,"pagetitle":"Home","title":"Effective sample size and $\\widehat{R}$","ref":"/MCMCDiagnosticTools/stable/#Effective-sample-size-and-\\\\widehat{R}","content":" Effective sample size and $\\widehat{R}$"},{"id":284,"pagetitle":"Home","title":"MCMCDiagnosticTools.ess","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.ess","content":" MCMCDiagnosticTools.ess — Function ess(\n samples::AbstractArray{<:Union{Missing,Real}};\n kind=:bulk,\n relative::Bool=false,\n autocov_method=AutocovMethod(),\n split_chains::Int=2,\n maxlag::Int=250,\n kwargs...\n) Estimate the effective sample size (ESS) of the samples of shape (draws, [chains[, parameters...]]) with the autocov_method . Optionally, the kind of ESS estimate to be computed can be specified (see below). Some kind s accept additional kwargs . If relative is true , the relative ESS is returned, i.e. ess / (draws * chains) . split_chains indicates the number of chains each chain is split into. When split_chains > 1 , then the diagnostics check for within-chain convergence. When d = mod(draws, split_chains) > 0 , i.e. the chains cannot be evenly split, then 1 draw is discarded after each of the first d splits within each chain. There must be at least 3 draws in each chain after splitting. maxlag indicates the maximum lag for which autocovariance is computed and must be greater than 0. For a given estimand, it is recommended that the ESS is at least 100 * chains and that $\\widehat{R} < 1.01$ . [VehtariGelman2021] See also: AutocovMethod , FFTAutocovMethod , BDAAutocovMethod , rhat , ess_rhat , mcse Kinds of ESS estimates If kind isa a Symbol , it may take one of the following values: :bulk : basic ESS computed on rank-normalized draws. This kind diagnoses poor convergence in the bulk of the distribution due to trends or different locations of the chains. :tail : minimum of the quantile-ESS for the symmetric quantiles where tail_prob=0.1 is the probability in the tails. This kind diagnoses poor convergence in the tails of the distribution. If this kind is chosen, kwargs may contain a tail_prob keyword. :basic : basic ESS, equivalent to specifying kind=Statistics.mean . Note While Bulk-ESS is conceptually related to basic ESS, it is well-defined even if the chains do not have finite variance. [VehtariGelman2021] For each parameter, rank-normalization proceeds by first ranking the inputs using \"tied ranking\" and then transforming the ranks to normal quantiles so that the result is standard normally distributed. This transform is monotonic. Otherwise, kind specifies one of the following estimators, whose ESS is to be estimated: Statistics.mean Statistics.median Statistics.std StatsBase.mad Base.Fix2(Statistics.quantile, p::Real) source"},{"id":285,"pagetitle":"Home","title":"MCMCDiagnosticTools.rhat","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.rhat","content":" MCMCDiagnosticTools.rhat — Function rhat(samples::AbstractArray{Union{Real,Missing}}; kind::Symbol=:rank, split_chains=2) Compute the $\\widehat{R}$ diagnostics for each parameter in samples of shape (draws, [chains[, parameters...]]) . [VehtariGelman2021] kind indicates the kind of $\\widehat{R}$ to compute (see below). split_chains indicates the number of chains each chain is split into. When split_chains > 1 , then the diagnostics check for within-chain convergence. When d = mod(draws, split_chains) > 0 , i.e. the chains cannot be evenly split, then 1 draw is discarded after each of the first d splits within each chain. See also ess , ess_rhat , rstar Kinds of $\\widehat{R}$ The following kind s are supported: :rank : maximum of $\\widehat{R}$ with kind=:bulk and kind=:tail . :bulk : basic $\\widehat{R}$ computed on rank-normalized draws. This kind diagnoses poor convergence in the bulk of the distribution due to trends or different locations of the chains. :tail : $\\widehat{R}$ computed on draws folded around the median and then rank-normalized. This kind diagnoses poor convergence in the tails of the distribution due to different scales of the chains. :basic : Classic $\\widehat{R}$ . source"},{"id":286,"pagetitle":"Home","title":"MCMCDiagnosticTools.ess_rhat","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.ess_rhat","content":" MCMCDiagnosticTools.ess_rhat — Function ess_rhat(\n samples::AbstractArray{<:Union{Missing,Real}};\n kind::Symbol=:rank,\n kwargs...,\n) -> NamedTuple{(:ess, :rhat)} Estimate the effective sample size and $\\widehat{R}$ of the samples of shape (draws, [chains[, parameters...]]) . When both ESS and $\\widehat{R}$ are needed, this method is often more efficient than calling ess and rhat separately. See rhat for a description of supported kind s and ess for a description of kwargs . source The following autocov_method s are supported:"},{"id":287,"pagetitle":"Home","title":"MCMCDiagnosticTools.AutocovMethod","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.AutocovMethod","content":" MCMCDiagnosticTools.AutocovMethod — Type AutocovMethod <: AbstractAutocovMethod The AutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains. It is is based on the discussion by [VehtariGelman2021] and uses the biased estimator of the autocovariance, as discussed by [Geyer1992] . source"},{"id":288,"pagetitle":"Home","title":"MCMCDiagnosticTools.FFTAutocovMethod","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.FFTAutocovMethod","content":" MCMCDiagnosticTools.FFTAutocovMethod — Type FFTAutocovMethod <: AbstractAutocovMethod The FFTAutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains. The algorithm is the same as the one of AutocovMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation. Info To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl . source"},{"id":289,"pagetitle":"Home","title":"MCMCDiagnosticTools.BDAAutocovMethod","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.BDAAutocovMethod","content":" MCMCDiagnosticTools.BDAAutocovMethod — Type BDAAutocovMethod <: AbstractAutocovMethod The BDAAutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains. It is is based on the discussion by [VehtariGelman2021] . and uses the variogram estimator of the autocorrelation function discussed by [BDA3] . source"},{"id":290,"pagetitle":"Home","title":"Monte Carlo standard error","ref":"/MCMCDiagnosticTools/stable/#Monte-Carlo-standard-error","content":" Monte Carlo standard error"},{"id":291,"pagetitle":"Home","title":"MCMCDiagnosticTools.mcse","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.mcse","content":" MCMCDiagnosticTools.mcse — Function mcse(samples::AbstractArray{<:Union{Missing,Real}}; kind=Statistics.mean, kwargs...) Estimate the Monte Carlo standard errors (MCSE) of the estimator kind applied to samples of shape (draws, [chains[, parameters...]]) . See also: ess Kinds of MCSE estimates The estimator whose MCSE should be estimated is specified with kind . kind must accept a vector of the same eltype as samples and return a real estimate. For the following estimators, the effective sample size ess and an estimate of the asymptotic variance are used to compute the MCSE, and kwargs are forwarded to ess : Statistics.mean Statistics.median Statistics.std Base.Fix2(Statistics.quantile, p::Real) For other estimators, the subsampling bootstrap method (SBM) [FlegalJones2011] [Flegal2012] is used as a fallback, and the only accepted kwargs are batch_size , which indicates the size of the overlapping batches used to estimate the MCSE, defaulting to floor(Int, sqrt(draws * chains)) . Note that SBM tends to underestimate the MCSE, especially for highly autocorrelated chains. One should verify that autocorrelation is low by checking the bulk- and tail-ESS values. source"},{"id":292,"pagetitle":"Home","title":"R⋆ diagnostic","ref":"/MCMCDiagnosticTools/stable/#R-diagnostic","content":" R⋆ diagnostic"},{"id":293,"pagetitle":"Home","title":"MCMCDiagnosticTools.rstar","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.rstar","content":" MCMCDiagnosticTools.rstar — Function rstar(\n rng::Random.AbstractRNG=Random.default_rng(),\n classifier,\n samples,\n chain_indices::AbstractVector{Int};\n subset::Real=0.7,\n split_chains::Int=2,\n verbosity::Int=0,\n) Compute the $R^*$ convergence statistic of the table samples with the classifier . samples must be either an AbstractMatrix , an AbstractVector , or a table (i.e. implements the Tables.jl interface) whose rows are draws and whose columns are parameters. chain_indices indicates the chain ids of each row of samples . This method supports ragged chains, i.e. chains of nonequal lengths. source rstar(\n rng::Random.AbstractRNG=Random.default_rng(),\n classifier,\n samples::AbstractArray{<:Real};\n subset::Real=0.7,\n split_chains::Int=2,\n verbosity::Int=0,\n) Compute the $R^*$ convergence statistic of the samples with the classifier . samples is an array of draws with the shape (draws, [chains[, parameters...]]) .` This implementation is an adaption of algorithms 1 and 2 described by Lambert and Vehtari. The classifier has to be a supervised classifier of the MLJ framework (see the MLJ documentation for a list of supported models). It is trained with a subset of the samples from each chain. Each chain is split into split_chains separate chains to additionally check for within-chain convergence. The training of the classifier can be inspected by adjusting the verbosity level. If the classifier is deterministic, i.e., if it predicts a class, the value of the $R^*$ statistic is returned (algorithm 1). If the classifier is probabilistic, i.e., if it outputs probabilities of classes, the scaled Poisson-binomial distribution of the $R^*$ statistic is returned (algorithm 2). Note The correctness of the statistic depends on the convergence of the classifier used internally in the statistic. Examples julia> using MLJBase, MLJIteration, EvoTrees, Statistics, StatisticalMeasures\n\njulia> samples = fill(4.0, 100, 3, 2); One can compute the distribution of the $R^*$ statistic (algorithm 2) with a probabilistic classifier. For instance, we can use a gradient-boosted trees model with nrounds = 100 sequentially stacked trees and learning rate eta = 0.05 : julia> model = EvoTreeClassifier(; nrounds=100, eta=0.05);\n\njulia> distribution = rstar(model, samples);\n\njulia> round(mean(distribution); digits=2)\n1.0f0 Note, however, that it is recommended to determine nrounds based on early-stopping. With the MLJ framework, this can be achieved in the following way (see the MLJ documentation for additional explanations): julia> model = IteratedModel(;\n model=EvoTreeClassifier(; eta=0.05),\n iteration_parameter=:nrounds,\n resampling=Holdout(),\n measures=log_loss,\n controls=[Step(5), Patience(2), NumberLimit(100)],\n retrain=true,\n );\n\njulia> distribution = rstar(model, samples);\n\njulia> round(mean(distribution); digits=2)\n1.0f0 For deterministic classifiers, a single $R^*$ statistic (algorithm 1) is returned. Deterministic classifiers can also be derived from probabilistic classifiers by e.g. predicting the mode. In MLJ this corresponds to a pipeline of models. julia> evotree_deterministic = Pipeline(model; operation=predict_mode);\n\njulia> value = rstar(evotree_deterministic, samples);\n\njulia> round(value; digits=2)\n1.0 References Lambert, B., & Vehtari, A. (2020). $R^*$ : A robust MCMC convergence diagnostic with uncertainty using decision tree classifiers. source"},{"id":294,"pagetitle":"Home","title":"Bayesian fraction of missing information","ref":"/MCMCDiagnosticTools/stable/#Bayesian-fraction-of-missing-information","content":" Bayesian fraction of missing information"},{"id":295,"pagetitle":"Home","title":"MCMCDiagnosticTools.bfmi","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.bfmi","content":" MCMCDiagnosticTools.bfmi — Function bfmi(energy::AbstractVector{<:Real}) -> Real\nbfmi(energy::AbstractMatrix{<:Real}; dims::Int=1) -> AbstractVector{<:Real} Calculate the estimated Bayesian fraction of missing information (BFMI). When sampling with Hamiltonian Monte Carlo (HMC), BFMI quantifies how well momentum resampling matches the marginal energy distribution. The current advice is that values smaller than 0.3 indicate poor sampling. However, this threshold is provisional and may change. A BFMI value below the threshold often indicates poor adaptation of sampling parameters or that the target distribution has heavy tails that were not well explored by the Markov chain. For more information, see Section 6.1 of [Betancourt2018] or [Betancourt2016] for a complete account. energy is either a vector of Hamiltonian energies of draws or a matrix of energies of draws for multiple chains. dims indicates the dimension in energy that contains the draws. The default dims=1 assumes energy has the shape draws or (draws, chains) . If a different shape is provided, dims must be set accordingly. If energy is a vector, a single BFMI value is returned. Otherwise, a vector of BFMI values for each chain is returned. source"},{"id":296,"pagetitle":"Home","title":"Other diagnostics","ref":"/MCMCDiagnosticTools/stable/#Other-diagnostics","content":" Other diagnostics Note These diagnostics are older and less widely used."},{"id":297,"pagetitle":"Home","title":"MCMCDiagnosticTools.discretediag","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.discretediag","content":" MCMCDiagnosticTools.discretediag — Function discretediag(samples::AbstractArray{<:Real,3}; frac=0.3, method=:weiss, nsim=1_000) Compute discrete diagnostic on samples with shape (draws, chains, parameters) . method can be one of :weiss , :hangartner , :DARBOOT , :MCBOOT , :billinsgley , and :billingsleyBOOT . References Benjamin E. Deonovic, & Brian J. Smith. (2017). Convergence diagnostics for MCMC draws of a categorical variable. source"},{"id":298,"pagetitle":"Home","title":"MCMCDiagnosticTools.gelmandiag","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.gelmandiag","content":" MCMCDiagnosticTools.gelmandiag — Function gelmandiag(samples::AbstractArray{<:Real,3}; alpha::Real=0.95) Compute the Gelman, Rubin and Brooks diagnostics [Gelman1992] [Brooks1998] on samples with shape (draws, chains, parameters) . Values of the diagnostic’s potential scale reduction factor (PSRF) that are close to one suggest convergence. As a rule-of-thumb, convergence is rejected if the 97.5 percentile of a PSRF is greater than 1.2. source"},{"id":299,"pagetitle":"Home","title":"MCMCDiagnosticTools.gelmandiag_multivariate","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.gelmandiag_multivariate","content":" MCMCDiagnosticTools.gelmandiag_multivariate — Function gelmandiag_multivariate(samples::AbstractArray{<:Real,3}; alpha::Real=0.05) Compute the multivariate Gelman, Rubin and Brooks diagnostics on samples with shape (draws, chains, parameters) . source"},{"id":300,"pagetitle":"Home","title":"MCMCDiagnosticTools.gewekediag","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.gewekediag","content":" MCMCDiagnosticTools.gewekediag — Function gewekediag(x::AbstractVector{<:Real}; first::Real=0.1, last::Real=0.5, kwargs...) Compute the Geweke diagnostic [Geweke1991] from the first and last proportion of samples x . The diagnostic is designed to asses convergence of posterior means estimated with autocorrelated samples. It computes a normal-based test statistic comparing the sample means in two windows containing proportions of the first and last iterations. Users should ensure that there is sufficient separation between the two windows to assume that their samples are independent. A non-significant test p-value indicates convergence. Significant p-values indicate non-convergence and the possible need to discard initial samples as a burn-in sequence or to simulate additional samples. kwargs are forwarded to mcse . source"},{"id":301,"pagetitle":"Home","title":"MCMCDiagnosticTools.heideldiag","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.heideldiag","content":" MCMCDiagnosticTools.heideldiag — Function heideldiag(\n x::AbstractVector{<:Real}; alpha::Real=0.05, eps::Real=0.1, start::Int=1, kwargs...\n) Compute the Heidelberger and Welch diagnostic [Heidelberger1983] . This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1] . kwargs are forwarded to mcse . source"},{"id":302,"pagetitle":"Home","title":"MCMCDiagnosticTools.rafterydiag","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.rafterydiag","content":" MCMCDiagnosticTools.rafterydiag — Function rafterydiag(\n x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)\n) Compute the Raftery and Lewis diagnostic [Raftery1992] . This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\\theta_q$ , such that $\\Pr(\\theta \\le \\theta_q) = q$ , within a desired degree of accuracy. In particular, if $\\hat{\\theta}_q$ is the estimand and $\\Pr(\\theta \\le \\hat{\\theta}_q) = \\hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s , where $\\Pr(q - r < \\hat{P}_q < q + r) = s$ . Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large). Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value. source VehtariGelman2021 Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008 VehtariGelman2021 Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008 VehtariGelman2021 Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008 Geyer1992 Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483. VehtariGelman2021 Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008 BDA3 Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press. FlegalJones2011 Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf Flegal2012 Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18 Betancourt2018 Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME] Betancourt2016 Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME] Gelman1992 Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472. Brooks1998 Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455. Geweke1991 Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis. Heidelberger1983 Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144. Raftery1992 A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992."},{"id":305,"pagetitle":"Home","title":"InferenceObjects","ref":"/InferenceObjects/stable/#InferenceObjects","content":" InferenceObjects InferenceObjects.jl is a Julia implementation of the InferenceData schema for storing results of Bayesian inference. Its purpose is to serve the following three goals: Usefulness in the analysis of Bayesian inference results. Reproducibility of Bayesian inference analysis. Interoperability between different inference backends and programming languages. The implementation consists primarily of the InferenceData and Dataset structures. InferenceObjects also provides the function convert_to_inference_data , which may be overloaded by inference packages to define how various inference outputs can be converted to an InferenceData . For examples of how InferenceData can be used, see the ArviZ.jl documentation ."},{"id":308,"pagetitle":"Dataset","title":"Dataset","ref":"/InferenceObjects/stable/dataset/#Dataset","content":" Dataset InferenceObjects.Dataset InferenceObjects.convert_to_dataset InferenceObjects.namedtuple_to_dataset"},{"id":309,"pagetitle":"Dataset","title":"Type definition","ref":"/InferenceObjects/stable/dataset/#Type-definition","content":" Type definition"},{"id":310,"pagetitle":"Dataset","title":"InferenceObjects.Dataset","ref":"/InferenceObjects/stable/dataset/#InferenceObjects.Dataset","content":" InferenceObjects.Dataset — Type Dataset{L} <: DimensionalData.AbstractDimStack{L} Container of dimensional arrays sharing some dimensions. This type is an DimensionalData.AbstractDimStack that implements the same interface as DimensionalData.DimStack and has identical usage. When a Dataset is passed to Python, it is converted to an xarray.Dataset without copying the data. That is, the Python object shares the same memory as the Julia object. However, if an xarray.Dataset is passed to Julia, its data must be copied. Constructors Dataset(data::DimensionalData.AbstractDimArray...)\nDataset(data::Tuple{Vararg{<:DimensionalData.AbstractDimArray}})\nDataset(data::NamedTuple{Keys,Vararg{<:DimensionalData.AbstractDimArray}})\nDataset(\n data::NamedTuple,\n dims::Tuple{Vararg{DimensionalData.Dimension}};\n metadata=DimensionalData.NoMetadata(),\n) In most cases, use convert_to_dataset to create a Dataset instead of directly using a constructor. source"},{"id":311,"pagetitle":"Dataset","title":"General conversion","ref":"/InferenceObjects/stable/dataset/#General-conversion","content":" General conversion"},{"id":312,"pagetitle":"Dataset","title":"InferenceObjects.convert_to_dataset","ref":"/InferenceObjects/stable/dataset/#InferenceObjects.convert_to_dataset","content":" InferenceObjects.convert_to_dataset — Function convert_to_dataset(obj; group = :posterior, kwargs...) -> Dataset Convert a supported object to a Dataset . In most cases, this function calls convert_to_inference_data and returns the corresponding group . source"},{"id":313,"pagetitle":"Dataset","title":"InferenceObjects.namedtuple_to_dataset","ref":"/InferenceObjects/stable/dataset/#InferenceObjects.namedtuple_to_dataset","content":" InferenceObjects.namedtuple_to_dataset — Function namedtuple_to_dataset(data; kwargs...) -> Dataset Convert NamedTuple mapping variable names to arrays to a Dataset . Any non-array values will be converted to a 0-dimensional array. Keywords attrs::AbstractDict{<:AbstractString} : a collection of metadata to attach to the dataset, in addition to defaults. Values should be JSON serializable. library::Union{String,Module} : library used for performing inference. Will be attached to the attrs metadata. dims : a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are: Symbol : dimension name Type{<:DimensionsionalData.Dimension} : dimension type DimensionsionalData.Dimension : dimension, potentially with indices Nothing : no dimension name provided, dimension name is automatically generated coords : a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated. source"},{"id":314,"pagetitle":"Dataset","title":"DimensionalData","ref":"/InferenceObjects/stable/dataset/#DimensionalData","content":" DimensionalData As a DimensionalData.AbstractDimStack , Dataset also implements the AbstractDimStack API and can be used like a DimStack . See DimensionalData's documentation for example usage."},{"id":315,"pagetitle":"Dataset","title":"Tables inteface","ref":"/InferenceObjects/stable/dataset/#Tables-inteface","content":" Tables inteface Dataset implements the Tables interface. This allows Dataset s to be used as sources for any function that can accept a table. For example, it's straightforward to: write to CSV with CSV.jl flatten to a DataFrame with DataFrames.jl plot with StatsPlots.jl plot with AlgebraOfGraphics.jl"},{"id":318,"pagetitle":"InferenceData","title":"InferenceData","ref":"/InferenceObjects/stable/inference_data/#InferenceData","content":" InferenceData InferenceObjects.InferenceData Base.cat Base.getindex Base.getproperty Base.merge Base.propertynames Base.setindex InferenceObjects.convert_to_inference_data InferenceObjects.from_dict InferenceObjects.from_namedtuple InferenceObjects.from_netcdf InferenceObjects.to_netcdf"},{"id":319,"pagetitle":"InferenceData","title":"Type definition","ref":"/InferenceObjects/stable/inference_data/#Type-definition","content":" Type definition"},{"id":320,"pagetitle":"InferenceData","title":"InferenceObjects.InferenceData","ref":"/InferenceObjects/stable/inference_data/#InferenceObjects.InferenceData","content":" InferenceObjects.InferenceData — Type InferenceData{group_names,group_types} Container for inference data storage using DimensionalData. This object implements the InferenceData schema . Internally, groups are stored in a NamedTuple , which can be accessed using parent(::InferenceData) . Constructors InferenceData(groups::NamedTuple)\nInferenceData(; groups...) Construct an inference data from either a NamedTuple or keyword arguments of groups. Groups must be Dataset objects. Instead of directly creating an InferenceData , use the exported from_xyz functions or convert_to_inference_data . source"},{"id":321,"pagetitle":"InferenceData","title":"Property interface","ref":"/InferenceObjects/stable/inference_data/#Property-interface","content":" Property interface"},{"id":322,"pagetitle":"InferenceData","title":"Base.getproperty","ref":"/InferenceObjects/stable/inference_data/#Base.getproperty","content":" Base.getproperty — Function getproperty(data::InferenceData, name::Symbol) -> Dataset Get group with the specified name . source"},{"id":323,"pagetitle":"InferenceData","title":"Base.propertynames","ref":"/InferenceObjects/stable/inference_data/#Base.propertynames","content":" Base.propertynames — Function propertynames(data::InferenceData) -> Tuple{Symbol} Get names of groups source"},{"id":324,"pagetitle":"InferenceData","title":"Indexing interface","ref":"/InferenceObjects/stable/inference_data/#Indexing-interface","content":" Indexing interface"},{"id":325,"pagetitle":"InferenceData","title":"Base.getindex","ref":"/InferenceObjects/stable/inference_data/#Base.getindex","content":" Base.getindex — Function Base.getindex(data::InferenceData, groups::Symbol; coords...) -> Dataset\nBase.getindex(data::InferenceData, groups; coords...) -> InferenceData Return a new InferenceData containing the specified groups sliced to the specified coords. coords specifies a dimension name mapping to an index, a DimensionalData.Selector , or an IntervalSets.AbstractInterval . If one or more groups lack the specified dimension, a warning is raised but can be ignored. All groups that contain the dimension must also contain the specified indices, or an exception will be raised. Examples Select data from all groups for just the specified id values. julia> using InferenceObjects, DimensionalData\n\njulia> idata = from_namedtuple(\n (θ=randn(4, 100, 4), τ=randn(4, 100));\n prior=(θ=randn(4, 100, 4), τ=randn(4, 100)),\n observed_data=(y=randn(4),),\n dims=(θ=[:id], y=[:id]),\n coords=(id=[\"a\", \"b\", \"c\", \"d\"],),\n )\nInferenceData with groups:\n > posterior\n > prior\n > observed_data\n\njulia> idata.posterior\nDataset with dimensions:\n Dim{:chain} Sampled 1:4 ForwardOrdered Regular Points,\n Dim{:draw} Sampled 1:100 ForwardOrdered Regular Points,\n Dim{:id} Categorical String[a, b, c, d] ForwardOrdered\nand 2 layers:\n :θ Float64 dims: Dim{:chain}, Dim{:draw}, Dim{:id} (4×100×4)\n :τ Float64 dims: Dim{:chain}, Dim{:draw} (4×100)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2022-08-11T11:15:21.4\"\n\njulia> idata_sel = idata[id=At([\"a\", \"b\"])]\nInferenceData with groups:\n > posterior\n > prior\n > observed_data\n\njulia> idata_sel.posterior\nDataset with dimensions:\n Dim{:chain} Sampled 1:4 ForwardOrdered Regular Points,\n Dim{:draw} Sampled 1:100 ForwardOrdered Regular Points,\n Dim{:id} Categorical String[a, b] ForwardOrdered\nand 2 layers:\n :θ Float64 dims: Dim{:chain}, Dim{:draw}, Dim{:id} (4×100×2)\n :τ Float64 dims: Dim{:chain}, Dim{:draw} (4×100)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2022-08-11T11:15:21.4\" Select data from just the posterior, returning a Dataset if the indices index more than one element from any of the variables: julia> idata[:observed_data, id=At([\"a\"])]\nDataset with dimensions:\n Dim{:id} Categorical String[a] ForwardOrdered\nand 1 layer:\n :y Float64 dims: Dim{:id} (1)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2022-08-11T11:19:25.982\" Note that if a single index is provided, the behavior is still to slice so that the dimension is preserved. source"},{"id":326,"pagetitle":"InferenceData","title":"Base.setindex","ref":"/InferenceObjects/stable/inference_data/#Base.setindex","content":" Base.setindex — Function Base.setindex(data::InferenceData, group::Dataset, name::Symbol) -> InferenceData Create a new InferenceData containing the group with the specified name . If a group with name is already in data , it is replaced. source"},{"id":327,"pagetitle":"InferenceData","title":"Iteration interface","ref":"/InferenceObjects/stable/inference_data/#Iteration-interface","content":" Iteration interface InferenceData also implements the same iteration interface as its underlying NamedTuple . That is, iterating over an InferenceData iterates over its groups."},{"id":328,"pagetitle":"InferenceData","title":"General conversion","ref":"/InferenceObjects/stable/inference_data/#General-conversion","content":" General conversion"},{"id":329,"pagetitle":"InferenceData","title":"InferenceObjects.convert_to_inference_data","ref":"/InferenceObjects/stable/inference_data/#InferenceObjects.convert_to_inference_data","content":" InferenceObjects.convert_to_inference_data — Function convert_to_inference_data(obj; group, kwargs...) -> InferenceData Convert a supported object to an InferenceData object. If obj converts to a single dataset, group specifies which dataset in the resulting InferenceData that is. See convert_to_dataset Arguments obj can be many objects. Basic supported types are: InferenceData : return unchanged Dataset / DimensionalData.AbstractDimStack : add to InferenceData as the only group NamedTuple / AbstractDict : create a Dataset as the only group AbstractArray{<:Real} : create a Dataset as the only group, given an arbitrary name, if the name is not set More specific types may be documented separately. Keywords group::Symbol = :posterior : If obj converts to a single dataset, assign the resulting dataset to this group. dims : a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are: Symbol : dimension name Type{<:DimensionsionalData.Dimension} : dimension type DimensionsionalData.Dimension : dimension, potentially with indices Nothing : no dimension name provided, dimension name is automatically generated coords : a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated. kwargs : remaining keywords forwarded to converter functions source"},{"id":330,"pagetitle":"InferenceData","title":"InferenceObjects.from_dict","ref":"/InferenceObjects/stable/inference_data/#InferenceObjects.from_dict","content":" InferenceObjects.from_dict — Function from_dict(posterior::AbstractDict; kwargs...) -> InferenceData Convert a Dict to an InferenceData . Arguments posterior : The data to be converted. Its strings must be Symbol or AbstractString , and its values must be arrays. Keywords posterior_predictive::Any=nothing : Draws from the posterior predictive distribution sample_stats::Any=nothing : Statistics of the posterior sampling process predictions::Any=nothing : Out-of-sample predictions for the posterior. prior::Dict=nothing : Draws from the prior prior_predictive::Any=nothing : Draws from the prior predictive distribution sample_stats_prior::Any=nothing : Statistics of the prior sampling process observed_data::NamedTuple : Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values. constant_data::NamedTuple : Model constants, data included in the model which is not modeled as a random variable. Keys are parameter names and values. predictions_constant_data::NamedTuple : Constants relevant to the model predictions (i.e. new x values in a linear regression). log_likelihood : Pointwise log-likelihood for the data. It is recommended to use this argument as a NamedTuple whose keys are observed variable names and whose values are log likelihood arrays. library : Name of library that generated the draws coords : Map from named dimension to named indices dims : Map from variable name to names of its dimensions Returns InferenceData : The data with groups corresponding to the provided data Examples using InferenceObjects\nnchains = 2\nndraws = 100\n\ndata = Dict(\n :x => rand(ndraws, nchains),\n :y => randn(2, ndraws, nchains),\n :z => randn(3, 2, ndraws, nchains),\n)\nidata = from_dict(data) source"},{"id":331,"pagetitle":"InferenceData","title":"InferenceObjects.from_namedtuple","ref":"/InferenceObjects/stable/inference_data/#InferenceObjects.from_namedtuple","content":" InferenceObjects.from_namedtuple — Function from_namedtuple(posterior::NamedTuple; kwargs...) -> InferenceData\nfrom_namedtuple(posterior::Vector{Vector{<:NamedTuple}}; kwargs...) -> InferenceData\nfrom_namedtuple(\n posterior::NamedTuple,\n sample_stats::Any,\n posterior_predictive::Any,\n predictions::Any,\n log_likelihood::Any;\n kwargs...\n) -> InferenceData Convert a NamedTuple or container of NamedTuple s to an InferenceData . If containers are passed, they are flattened into a single NamedTuple with array elements whose first dimensions correspond to the dimensions of the containers. Arguments posterior : The data to be converted. It may be of the following types: ::NamedTuple : The keys are the variable names and the values are arrays with dimensions (ndraws, nchains[, sizes...]) . ::Vector{Vector{<:NamedTuple}} : A vector of length nchains whose elements have length ndraws . Keywords posterior_predictive::Any=nothing : Draws from the posterior predictive distribution sample_stats::Any=nothing : Statistics of the posterior sampling process predictions::Any=nothing : Out-of-sample predictions for the posterior. prior=nothing : Draws from the prior. Accepts the same types as posterior . prior_predictive::Any=nothing : Draws from the prior predictive distribution sample_stats_prior::Any=nothing : Statistics of the prior sampling process observed_data::NamedTuple : Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values. constant_data::NamedTuple : Model constants, data included in the model which is not modeled as a random variable. Keys are parameter names and values. predictions_constant_data::NamedTuple : Constants relevant to the model predictions (i.e. new x values in a linear regression). log_likelihood : Pointwise log-likelihood for the data. It is recommended to use this argument as a NamedTuple whose keys are observed variable names and whose values are log likelihood arrays. library : Name of library that generated the draws coords : Map from named dimension to named indices dims : Map from variable name to names of its dimensions Returns InferenceData : The data with groups corresponding to the provided data Note If a NamedTuple is provided for observed_data , constant_data , or predictions constant data`, any non-array values (e.g. integers) are converted to 0-dimensional arrays. Examples using InferenceObjects\nnchains = 2\nndraws = 100\n\ndata1 = (\n x=rand(ndraws, nchains), y=randn(ndraws, nchains, 2), z=randn(ndraws, nchains, 3, 2)\n)\nidata1 = from_namedtuple(data1)\n\ndata2 = [[(x=rand(), y=randn(2), z=randn(3, 2)) for _ in 1:ndraws] for _ in 1:nchains];\nidata2 = from_namedtuple(data2) source"},{"id":332,"pagetitle":"InferenceData","title":"General functions","ref":"/InferenceObjects/stable/inference_data/#General-functions","content":" General functions"},{"id":333,"pagetitle":"InferenceData","title":"Base.cat","ref":"/InferenceObjects/stable/inference_data/#Base.cat","content":" Base.cat — Function cat(data::InferenceData...; [groups=keys(data[1]),] dims) -> InferenceData Concatenate InferenceData objects along the specified dimension dims . Only the groups in groups are concatenated. Remaining groups are merge d into the new InferenceData object. Examples Here is how we can concatenate all groups of two InferenceData objects along the existing chain dimension: julia> coords = (; a_dim=[\"x\", \"y\", \"z\"]);\n\njulia> dims = dims=(; a=[:a_dim]);\n\njulia> data = Dict(:a => randn(100, 4, 3), :b => randn(100, 4));\n\njulia> idata = from_dict(data; coords=coords, dims=dims)\nInferenceData with groups:\n > posterior\n\njulia> idata_cat1 = cat(idata, idata; dims=:chain)\nInferenceData with groups:\n > posterior\n\njulia> idata_cat1.posterior\nDataset with dimensions:\n Dim{:draw},\n Dim{:chain},\n Dim{:a_dim} Categorical{String} String[\"x\", \"y\", \"z\"] ForwardOrdered\nand 2 layers:\n :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim} (100×8×3)\n :b Float64 dims: Dim{:draw}, Dim{:chain} (100×8)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-04-03T18:41:35.779\" Alternatively, we can concatenate along a new run dimension, which will be created. julia> idata_cat2 = cat(idata, idata; dims=:run)\nInferenceData with groups:\n > posterior\n\njulia> idata_cat2.posterior\nDataset with dimensions:\n Dim{:draw},\n Dim{:chain},\n Dim{:a_dim} Categorical{String} String[\"x\", \"y\", \"z\"] ForwardOrdered,\n Dim{:run}\nand 2 layers:\n :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim}, Dim{:run} (100×4×3×2)\n :b Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:run} (100×4×2)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-04-03T18:41:35.779\" We can also concatenate only a subset of groups and merge the rest, which is useful when some groups are present only in some of the InferenceData objects or will be identical in all of them: julia> observed_data = Dict(:y => randn(10));\n\njulia> idata2 = from_dict(data; observed_data=observed_data, coords=coords, dims=dims)\nInferenceData with groups:\n > posterior\n > observed_data\n\njulia> idata_cat3 = cat(idata, idata2; groups=(:posterior,), dims=:run)\nInferenceData with groups:\n > posterior\n > observed_data\n\njulia> idata_cat3.posterior\nDataset with dimensions:\n Dim{:draw},\n Dim{:chain},\n Dim{:a_dim} Categorical{String} String[\"x\", \"y\", \"z\"] ForwardOrdered,\n Dim{:run}\nand 2 layers:\n :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim}, Dim{:run} (100×4×3×2)\n :b Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:run} (100×4×2)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-04-03T18:41:35.779\"\n\njulia> idata_cat3.observed_data\nDataset with dimensions: Dim{:y_dim_1}\nand 1 layer:\n :y Float64 dims: Dim{:y_dim_1} (10)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-02-17T15:11:00.59\" source"},{"id":334,"pagetitle":"InferenceData","title":"Base.merge","ref":"/InferenceObjects/stable/inference_data/#Base.merge","content":" Base.merge — Function merge(data::InferenceData...) -> InferenceData Merge InferenceData objects. The result contains all groups in data and others . If a group appears more than once, the one that occurs last is kept. See also: cat Examples Here we merge an InferenceData containing only a posterior group with one containing only a prior group to create a new one containing both groups. julia> idata1 = from_dict(Dict(:a => randn(100, 4, 3), :b => randn(100, 4)))\nInferenceData with groups:\n > posterior\n\njulia> idata2 = from_dict(; prior=Dict(:a => randn(100, 1, 3), :c => randn(100, 1)))\nInferenceData with groups:\n > prior\n\njulia> idata_merged = merge(idata1, idata2)\nInferenceData with groups:\n > posterior\n > prior source"},{"id":335,"pagetitle":"InferenceData","title":"I/O extensions","ref":"/InferenceObjects/stable/inference_data/#I/O-extensions","content":" I/O extensions The following types of storage are provided via extensions."},{"id":336,"pagetitle":"InferenceData","title":"NetCDF I/O using NCDatasets.jl","ref":"/InferenceObjects/stable/inference_data/#NetCDF-I/O-using-NCDatasets.jl","content":" NetCDF I/O using NCDatasets.jl"},{"id":337,"pagetitle":"InferenceData","title":"InferenceObjects.from_netcdf","ref":"/InferenceObjects/stable/inference_data/#InferenceObjects.from_netcdf","content":" InferenceObjects.from_netcdf — Function from_netcdf(path::AbstractString; kwargs...) -> InferenceData Load an InferenceData from an unopened NetCDF file. Remaining kwargs are passed to NCDatasets.NCDataset . This method loads data eagerly. To instead load data lazily, pass an opened NCDataset to from_netcdf . Note This method requires that NCDatasets is loaded before it can be used. Examples julia> using InferenceObjects, NCDatasets\n\njulia> idata = from_netcdf(\"centered_eight.nc\")\nInferenceData with groups:\n > posterior\n > posterior_predictive\n > sample_stats\n > prior\n > observed_data from_netcdf(ds::NCDatasets.NCDataset; load_mode) -> InferenceData Load an InferenceData from an opened NetCDF file. load_mode defaults to :lazy , which avoids reading variables into memory. Operations on these arrays will be slow. load_mode can also be :eager , which copies all variables into memory. It is then safe to close ds . If load_mode is :lazy and ds is closed after constructing InferenceData , using the variable arrays will have undefined behavior. Examples Here is how we might load an InferenceData from an InferenceData lazily from a web-hosted NetCDF file. julia> using HTTP, InferenceObjects, NCDatasets\n\njulia> resp = HTTP.get(\"https://github.com/arviz-devs/arviz_example_data/blob/main/data/centered_eight.nc?raw=true\");\n\njulia> ds = NCDataset(\"centered_eight\", \"r\"; memory = resp.body);\n\njulia> idata = from_netcdf(ds)\nInferenceData with groups:\n > posterior\n > posterior_predictive\n > sample_stats\n > prior\n > observed_data\n\njulia> idata_copy = copy(idata); # disconnect from the loaded dataset\n\njulia> close(ds); source"},{"id":338,"pagetitle":"InferenceData","title":"InferenceObjects.to_netcdf","ref":"/InferenceObjects/stable/inference_data/#InferenceObjects.to_netcdf","content":" InferenceObjects.to_netcdf — Function to_netcdf(data, dest::AbstractString; group::Symbol=:posterior, kwargs...)\nto_netcdf(data, dest::NCDatasets.NCDataset; group::Symbol=:posterior) Write data to a NetCDF file. data is any type that can be converted to an InferenceData using convert_to_inference_data . If not an InferenceData , then group specifies which group the data represents. dest specifies either the path to the NetCDF file or an opened NetCDF file. If dest is a path, remaining kwargs are passed to NCDatasets.NCDataset . Note This method requires that NCDatasets is loaded before it can be used. Examples julia> using InferenceObjects, NCDatasets\n\njulia> idata = from_namedtuple((; x = randn(4, 100, 3), z = randn(4, 100)))\nInferenceData with groups:\n > posterior\n\njulia> to_netcdf(idata, \"data.nc\")\n\"data.nc\" source"},{"id":341,"pagetitle":"Home","title":"ArviZExampleData","ref":"/ArviZExampleData/stable/#ArviZExampleData","content":" ArviZExampleData This package provides utilities for loading datasets defined in the arviz_example_data repository. The resulting objects are InferenceObjects.jl 's InferenceData . These utilities are used in ArviZ.jl ."},{"id":344,"pagetitle":"API","title":"API","ref":"/ArviZExampleData/stable/api/#API","content":" API"},{"id":345,"pagetitle":"API","title":"ArviZExampleData.describe_example_data","ref":"/ArviZExampleData/stable/api/#ArviZExampleData.describe_example_data","content":" ArviZExampleData.describe_example_data — Function describe_example_data() -> String Return a string containing descriptions of all available datasets. Examples julia> describe_example_data(\"radon\") |> println\nradon\n=====\n\nRadon is a radioactive gas that enters homes through contact points with the ground. It is a carcinogen that is the primary cause of lung cancer in non-smokers. Radon levels vary greatly from household to household.\n\nThis example uses an EPA study of radon levels in houses in Minnesota to construct a model with a hierarchy over households within a county. The model includes estimates (gamma) for contextual effects of the uranium per household.\n\nSee Gelman and Hill (2006) for details on the example, or https://docs.pymc.io/notebooks/multilevel_modeling.html by Chris Fonnesbeck for details on this implementation.\n\nremote: http://ndownloader.figshare.com/files/24067472 source"},{"id":346,"pagetitle":"API","title":"ArviZExampleData.load_example_data","ref":"/ArviZExampleData/stable/api/#ArviZExampleData.load_example_data","content":" ArviZExampleData.load_example_data — Function load_example_data(name; kwargs...) -> InferenceObjects.InferenceData\nload_example_data() -> Dict{String,AbstractFileMetadata} Load a local or remote pre-made dataset. kwargs are forwarded to InferenceObjects.from_netcdf . Pass no parameters to get a Dict listing all available datasets. Data files are handled by DataDeps.jl. A file is downloaded only when it is requested and then cached for future use. Examples julia> keys(load_example_data())\nKeySet for a OrderedCollections.OrderedDict{String, ArviZExampleData.AbstractFileMetadata} with 9 entries. Keys:\n \"centered_eight\"\n \"non_centered_eight\"\n \"radon\"\n \"rugby\"\n \"regression1d\"\n \"regression10d\"\n \"classification1d\"\n \"classification10d\"\n \"glycan_torsion_angles\"\n\njulia> load_example_data(\"centered_eight\")\nInferenceData with groups:\n > posterior\n > posterior_predictive\n > log_likelihood\n > sample_stats\n > prior\n > prior_predictive\n > observed_data\n > constant_data source"},{"id":349,"pagetitle":"Datasets","title":"Datasets","ref":"/ArviZExampleData/stable/datasets/#Datasets","content":" Datasets The following shows the currently available example datasets: using ArviZExampleData\n\nprintln(describe_example_data()) centered_eight\n==============\n\nA centered parameterization of the eight schools model. Provided as an example of a model that NUTS has trouble fitting. Compare to `non_centered_eight`.\n\nThe eight schools model is a hierarchical model used for an analysis of the effectiveness of classes that were designed to improve students' performance on the Scholastic Aptitude Test.\n\nSee Bayesian Data Analysis (Gelman et. al.) for more details.\n\nlocal: /home/runner/.julia/artifacts/1a48fb48ab2b35cdeeb84e0dcdcda134e24a1c20/arviz_example_data-0.1.1/data/centered_eight.nc\n\nnon_centered_eight\n==================\n\nA non-centered parameterization of the eight schools model. This is a hierarchical model where sampling problems may be fixed by a non-centered parametrization. Compare to `centered_eight`.\n\nThe eight schools model is a hierarchical model used for an analysis of the effectiveness of classes that were designed to improve students' performance on the Scholastic Aptitude Test.\n\nSee Bayesian Data Analysis (Gelman et. al.) for more details.\n\nlocal: /home/runner/.julia/artifacts/1a48fb48ab2b35cdeeb84e0dcdcda134e24a1c20/arviz_example_data-0.1.1/data/non_centered_eight.nc\n\nradon\n=====\n\nRadon is a radioactive gas that enters homes through contact points with the ground. It is a carcinogen that is the primary cause of lung cancer in non-smokers. Radon levels vary greatly from household to household.\n\nThis example uses an EPA study of radon levels in houses in Minnesota to construct a model with a hierarchy over households within a county. The model includes estimates (gamma) for contextual effects of the uranium per household.\n\nSee Gelman and Hill (2006) for details on the example, or https://docs.pymc.io/notebooks/multilevel_modeling.html by Chris Fonnesbeck for details on this implementation.\n\nremote: http://ndownloader.figshare.com/files/24067472\n\nrugby\n=====\n\nThe Six Nations Championship is a yearly rugby competition between Italy, Ireland, Scotland, England, France and Wales. Fifteen games are played each year, representing all combinations of the six teams.\n\nThis example uses and includes results from 2014 - 2017, comprising 60 total games. It models latent parameters for each team's attack and defense, as well as a parameter for home team advantage.\n\nSee https://docs.pymc.io/notebooks/rugby_analytics.html by Peader Coyle for more details and references.\n\nremote: http://ndownloader.figshare.com/files/16254359\n\nregression1d\n============\n\nA synthetic one dimensional linear regression dataset with latent slope, intercept, and noise (\"eps\"). One hundred data points, fit with PyMC3.\n\nTrue slope and intercept are included as deterministic variables.\n\nremote: http://ndownloader.figshare.com/files/16254899\n\nregression10d\n=============\n\nA synthetic multi-dimensional (10 dimensions) linear regression dataset with latent weights (\"w\"), intercept, and noise (\"eps\"). Five hundred data points, fit with PyMC3.\n\nTrue weights and intercept are included as deterministic variables.\n\nremote: http://ndownloader.figshare.com/files/16255736\n\nclassification1d\n================\n\nA synthetic one dimensional logistic regression dataset with latent slope and intercept, passed into a Bernoulli random variable. One hundred data points, fit with PyMC3.\n\nTrue slope and intercept are included as deterministic variables.\n\nremote: http://ndownloader.figshare.com/files/16256678\n\nclassification10d\n=================\n\nA synthetic multi dimensional (10 dimensions) logistic regression dataset with latent weights (\"w\") and intercept, passed into a Bernoulli random variable. Five hundred data points, fit with PyMC3.\n\nTrue weights and intercept are included as deterministic variables.\n\nremote: http://ndownloader.figshare.com/files/16256681\n\nglycan_torsion_angles\n=====================\n\nTorsion angles phi and psi are critical for determining the three dimensional structure of bio-molecules. Combinations of phi and psi torsion angles that produce clashes between atoms in the bio-molecule result in high energy, unlikely structures.\n\nThis model uses a Von Mises distribution to propose torsion angles for the structure of a glycan molecule (pdb id: 2LIQ), and a Potential to estimate the proposed structure's energy. Said Potential is bound by Boltzman's law.\n\nremote: http://ndownloader.figshare.com/files/22882652"},{"id":352,"pagetitle":"For developers","title":"For developers","ref":"/ArviZExampleData/stable/for_developers/#For-developers","content":" For developers This package has arviz_example_data as a data dependency, which is included as an artifact . When arviz_example_data is updated, and a new release is made, Artifacts.toml should be updated to point to the new tarball corresponding to the release: julia> using ArtifactUtils\n\njulia> version = v\"0.1.0\";\n\njulia> tarball_url = \"https://github.com/arviz-devs/arviz_example_data/archive/refs/tags/v$version.tar.gz\";\n\njulia> add_artifact!(\"Artifacts.toml\", \"arviz_example_data\", tarball_url; force=true);"},{"id":357,"pagetitle":"DimensionalData.jl","title":"DimensionalData ¤","ref":"/DimensionalData/stable/#dimensionaldata","content":" DimensionalData ¤ DimensionalData.jl provides tools and abstractions for working with datasets that have named dimensions, and optionally a lookup index. DimensionalData is a pluggable, generalised version of AxisArrays.jl with a cleaner syntax, and additional functionality found in NamedDims.jl. It has similar goals to pythons xarray , and is primarily written for use with spatial data in Rasters.jl ."},{"id":358,"pagetitle":"DimensionalData.jl","title":"Goals ¤","ref":"/DimensionalData/stable/#goals","content":" Goals ¤ Clean, readable syntax. Minimise required parentheses, minimise of exported Zero-cost dimensional indexing a[Y(4), X(5)] of a single value. methods, and instead extend Base methods whenever possible. Plotting is easy: data should plot sensibly and correctly with useful labels, by default. Least surprise: everything works the same as in Base, but with named dims. If a method accepts numeric indices or dims=X in base, you should be able to use DimensionalData.jl dims. Minimal interface: implementing a dimension-aware type should be easy. Maximum extensibility: always use method dispatch. Regular types over special syntax. Recursion over @generated. Always dispatch on abstract types. Type stability: dimensional methods should be type stable more often than Base methods Functional style: structs are always rebuilt, and other than the array data, fields are not mutated in place."},{"id":359,"pagetitle":"DimensionalData.jl","title":"For package developers ¤","ref":"/DimensionalData/stable/#for-package-developers","content":" For package developers ¤"},{"id":360,"pagetitle":"DimensionalData.jl","title":"Data types and the interface ¤","ref":"/DimensionalData/stable/#data-types-and-the-interface","content":" Data types and the interface ¤ DimensionalData.jl provides the concrete DimArray type. But its behaviours are intended to be easily applied to other array types. more The main requirement for extending DimensionalData.jl is to define a dims method\nthat returns a Tuple of Dimension that matches the dimension order\nand axis values of your data. Define rebuild and base methods for similar \nand parent if you want the metadata to persist through transformations (see\nthe DimArray and AbstractDimArray types). A refdims method\nreturns the lost dimensions of a previous transformation, passed in to the\n rebuild method. refdims can be discarded, the main loss being plot labels\nand ability to reconstruct dimensions in cat . Inheriting from AbstractDimArray in this way will give nearly all the functionality\nof using DimArray ."},{"id":361,"pagetitle":"DimensionalData.jl","title":"LookupArrays and Dimensions ¤","ref":"/DimensionalData/stable/#lookuparrays-and-dimensions","content":" LookupArrays and Dimensions ¤ Sub modules LookupArrays and Dimensions define the behviour of dimensions and their lookup index. LookupArrays and Dimensions"},{"id":364,"pagetitle":"Crash course - DimensionalData.jl","title":"Dimensions and DimArrays ¤","ref":"/DimensionalData/stable/crash/generated/course/course/#dimensions-and-dimarrays","content":" Dimensions and DimArrays ¤ The core type of DimensionalData.jl is the Dimension and the types that inherit from it, such as Ti , X , Y , Z , the generic Dim{:x} , or others that you define manually using the @dim macro. Dimension s are primarily used in DimArray , other AbstractDimArray . We can use dimensions without a value index - these simply label the axis. A DimArray with labelled dimensions is constructed by: using DimensionalData \n A = rand ( X ( 5 ), Y ( 5 )) \n 5×5 DimArray{Float64,2} with dimensions: X, Y\n 0.0257194 0.0545864 0.668622 0.990097 0.652228\n 0.44662 0.762548 0.954042 0.497596 0.000702532\n 0.980668 0.583562 0.190779 0.233336 0.298915\n 0.313727 0.392187 0.54035 0.644368 0.940491\n 0.723664 0.83586 0.834754 0.0447846 0.45741\n get value A [ Y ( 1 ), X ( 2 )] \n 0.44661950368409176\n As shown above, Dimension s can be used to construct arrays in rand , ones , zeros and fill with either a range for a lookup index or a number for the dimension length. Or we can use the Dim{X} dims by using Symbol s, and indexing with keywords: A = DimArray ( rand ( 5 , 5 ), ( :a , :b )) \n 5×5 DimArray{Float64,2} with dimensions: Dim{:a}, Dim{:b}\n 0.262882 0.664631 0.533606 0.734399 0.832567\n 0.760415 0.700901 0.331099 0.768394 0.23546\n 0.81808 0.436833 0.769763 0.867433 0.0349366\n 0.157131 0.589521 0.798718 0.463894 0.188219\n 0.486978 0.486446 0.437844 0.816005 0.460578\n get value A [ a = 3 , b = 5 ] \n 0.03493658137331457\n Often, we want to provide a lookup index for the dimension: using Dates \n t = DateTime ( 2001 ) : Month ( 1 ) : DateTime ( 2001 , 12 ) \n x = 10 : 10 : 100 \n A = rand ( X ( x ), Ti ( t )) \n 10×12 DimArray{Float64,2} with dimensions: \n X Sampled{Int64} 10:10:100 ForwardOrdered Regular Points,\n Ti Sampled{DateTime} DateTime(\"2001-01-01T00:00:00\"):Month(1):DateTime(\"2001-12-01T00:00:00\") ForwardOrdered Regular Points\n 2001-01-01T00:00:00 … 2001-12-01T00:00:00\n 10 0.220572 0.272713\n 20 0.383863 0.308758\n 30 0.0220933 0.211049\n 40 0.475009 0.835277\n 50 0.733425 … 0.991225\n 60 0.713087 0.0849085\n 70 0.38453 0.558929\n 80 0.523681 0.277764\n 90 0.767148 0.848079\n 100 0.125821 … 0.598359\n Here both X and Ti are dimensions from DimensionalData . The currently exported dimensions are X, Y, Z, Ti ( Ti is shortening of Time ). The length of each dimension index has to match the size of the corresponding array axis. This can also be done with Symbol , using Dim{X} : A2 = DimArray ( rand ( 12 , 10 ), ( time = t , distance = x )) \n 12×10 DimArray{Float64,2} with dimensions: \n Dim{:time} Sampled{DateTime} DateTime(\"2001-01-01T00:00:00\"):Month(1):DateTime(\"2001-12-01T00:00:00\") ForwardOrdered Regular Points,\n Dim{:distance} Sampled{Int64} 10:10:100 ForwardOrdered Regular Points\n … 80 90 100\n 2001-01-01T00:00:00 0.776826 0.446688 0.758554\n 2001-02-01T00:00:00 0.380958 0.696744 0.905861\n 2001-03-01T00:00:00 0.864697 0.318554 0.441301\n 2001-04-01T00:00:00 0.618603 0.753646 0.0732071\n 2001-05-01T00:00:00 … 0.698003 0.106475 0.611565\n 2001-06-01T00:00:00 0.487678 0.394129 0.878072\n 2001-07-01T00:00:00 0.102116 0.476639 0.895151\n 2001-08-01T00:00:00 0.659545 0.144719 0.792332\n 2001-09-01T00:00:00 0.433718 0.0994015 0.614477\n 2001-10-01T00:00:00 … 0.668483 0.796421 0.179683\n 2001-11-01T00:00:00 0.686543 0.935012 0.663855\n 2001-12-01T00:00:00 0.436568 0.745237 0.87978\n Symbols can be more convenient to use than defining custom dims with @dim , but have some downsides. They don't inherit from a specific Dimension type, so plots will not know what axis to put them on. They also cannot use the basic constructor methods like rand or zeros , as we cannot dispatch on Symbol for Base methods without \"type-piracy\"."},{"id":365,"pagetitle":"Crash course - DimensionalData.jl","title":"Indexing the array by name and index ¤","ref":"/DimensionalData/stable/crash/generated/course/course/#indexing-the-array-by-name-and-index","content":" Indexing the array by name and index ¤ Dimensions can be used to index the array by name, without having to worry about the order of the dimensions. The simplest case is to select a dimension by index. Let's say every 2nd point of the Ti dimension and every 3rd point of the X dimension. This is done with the simple Ti(range) syntax like so: A [ X ( 1 : 3 : 11 ), Ti ( 1 : 2 : 11 )] \n 4×6 DimArray{Float64,2} with dimensions: \n X Sampled{Int64} 10:30:100 ForwardOrdered Regular Points,\n Ti Sampled{DateTime} DateTime(\"2001-01-01T00:00:00\"):Month(2):DateTime(\"2001-11-01T00:00:00\") ForwardOrdered Regular Points\n 2001-01-01T00:00:00 … 2001-11-01T00:00:00\n 10 0.220572 0.435993\n 40 0.475009 0.446399\n 70 0.38453 0.863633\n 100 0.125821 0.639194\n When specifying only one dimension, all elements of the other dimensions are assumed to be included: A [ X ( 1 : 3 : 10 )] \n 4×12 DimArray{Float64,2} with dimensions: \n X Sampled{Int64} 10:30:100 ForwardOrdered Regular Points,\n Ti Sampled{DateTime} DateTime(\"2001-01-01T00:00:00\"):Month(1):DateTime(\"2001-12-01T00:00:00\") ForwardOrdered Regular Points\n 2001-01-01T00:00:00 … 2001-12-01T00:00:00\n 10 0.220572 0.272713\n 40 0.475009 0.835277\n 70 0.38453 0.558929\n 100 0.125821 0.598359\n Indexing Indexing AbstractDimArray s works with getindex , setindex! and view . The result is still an AbstracDimArray , unless using all single Int or Selector s that resolve to Int . Dimension s can be used to construct arrays in rand , ones , zeros and fill with either a range for a lookup index or a number for the dimension length. using DimensionalData \n A1 = ones ( X ( 1 : 40 ), Y ( 50 )) \n 40×50 DimArray{Float64,2} with dimensions: \n X Sampled{Int64} 1:40 ForwardOrdered Regular Points,\n Y\n 1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 … 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n 2 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n 3 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n 4 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n 5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n 6 1.0 1.0 1.0 1.0 1.0 1.0 1.0 … 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n ⋮ ⋮ ⋱ ⋮ ⋮ \n 35 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n 36 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n 37 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n 38 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n 39 1.0 1.0 1.0 1.0 1.0 1.0 1.0 … 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n 40 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n We can also use dim wrappers for indexing, so that the dimension order in the underlying array does not need to be known: A1 [ Y ( 1 ), X ( 1 : 10 )] \n 10-element DimArray{Float64,1} with dimensions: \n X Sampled{Int64} 1:10 ForwardOrdered Regular Points\nand reference dimensions: Y\n 1 1.0\n 2 1.0\n 3 1.0\n 4 1.0\n 5 1.0\n 6 1.0\n 7 1.0\n 8 1.0\n 9 1.0\n 10 1.0\n"},{"id":366,"pagetitle":"Crash course - DimensionalData.jl","title":"Indexing Performance ¤","ref":"/DimensionalData/stable/crash/generated/course/course/#indexing-performance","content":" Indexing Performance ¤ Indexing with Dimension has no runtime cost: A2 = ones ( X ( 3 ), Y ( 3 )) \n 3×3 DimArray{Float64,2} with dimensions: X, Y\n 1.0 1.0 1.0\n 1.0 1.0 1.0\n 1.0 1.0 1.0\n time ? using BenchmarkTools \n\n println ( @btime $ A2 [ X ( 1 ), Y ( 2 )]) \n 43.920 ns (0 allocations: 0 bytes)\n1.0\n and println ( @btime parent ( $ A2 )[ 1 , 2 ]) \n 3.095 ns (0 allocations: 0 bytes)\n1.0\n"},{"id":367,"pagetitle":"Crash course - DimensionalData.jl","title":"Specifying dims keyword arguments with Dimension ¤","ref":"/DimensionalData/stable/crash/generated/course/course/#specifying-dims-keyword-arguments-with-dimension","content":" Specifying dims keyword arguments with Dimension ¤ In many Julia functions like size or sum , you can specify the dimension along which to perform the operation as an Int . It is also possible to do this using Dimension types with AbstractDimArray : A3 = rand ( X ( 3 ), Y ( 4 ), Ti ( 5 )); \n sum ( A3 ; dims = Ti ) \n 3×4×1 DimArray{Float64,3} with dimensions: X, Y, Ti\n[:, :, 1]\n 2.86333 3.42363 2.38244 1.3045\n 1.47257 2.43555 2.6565 2.27314\n 3.24374 2.10504 2.27636 2.93816\n This also works in methods from Statistics : using Statistics \n mean ( A3 ; dims = Ti ) \n 3×4×1 DimArray{Float64,3} with dimensions: X, Y, Ti\n[:, :, 1]\n 0.572667 0.684727 0.476489 0.2609\n 0.294513 0.48711 0.5313 0.454629\n 0.648749 0.421008 0.455273 0.587633\n"},{"id":368,"pagetitle":"Crash course - DimensionalData.jl","title":"Methods where dims, dim types, or Symbol s can be used to indicate the array dimension: ¤","ref":"/DimensionalData/stable/crash/generated/course/course/#methods-where-dims-dim-types-or-symbols-can-be-used-to-indicate-the-array-dimension","content":" Methods where dims, dim types, or Symbol s can be used to indicate the array dimension: ¤ size , axes , firstindex , lastindex cat , reverse , dropdims reduce , mapreduce sum , prod , maximum , minimum , mean , median , extrema , std , var , cor , cov permutedims , adjoint , transpose , Transpose mapslices , eachslice"},{"id":369,"pagetitle":"Crash course - DimensionalData.jl","title":"LookupArrays and Selectors ¤","ref":"/DimensionalData/stable/crash/generated/course/course/#lookuparrays-and-selectors","content":" LookupArrays and Selectors ¤ Indexing by value in DimensionalData is done with Selectors . IntervalSets.jl is now used for selecting ranges of values (formerly Between ). Selector Description At(x) get the index exactly matching the passed in value(s) Near(x) get the closest index to the passed in value(s) Contains(x) get indices where the value x falls within an interval Where(f) filter the array axis by a function of the dimension index values. [ Not(x) ] get all indices not selected by x , which can be another selector. [ a..b ] get all indices between two values, inclusively. [ OpenInterval(a, b) ] get all indices between a and b , exclusively. [ Interval{A,B}(a, b) ] get all indices between a and b , as :closed or :open . Selectors find indices in the LookupArray , for each dimension. Here we use an Interval to select a range between integers and DateTime : A [ X ( 12 .. 35 ), Ti ( Date ( 2001 , 5 ) .. Date ( 2001 , 7 ))] \n 2×3 DimArray{Float64,2} with dimensions: \n X Sampled{Int64} 20:10:30 ForwardOrdered Regular Points,\n Ti Sampled{DateTime} DateTime(\"2001-05-01T00:00:00\"):Month(1):DateTime(\"2001-07-01T00:00:00\") ForwardOrdered Regular Points\n 2001-05-01T00:00:00 … 2001-07-01T00:00:00\n 20 0.57611 0.535862\n 30 0.642167 0.457967\n To select intervals in DimArrays (e.g. A2 ) you need to specify dimname=a .. b : A2 [ distance = 12 .. 35 , time = Date ( 2001 , 5 ) .. Date ( 2001 , 7 )] \n 3×3 DimArray{Float64,2} with dimensions: X, Y\n 1.0 1.0 1.0\n 1.0 1.0 1.0\n 1.0 1.0 1.0\n Selectors can be used in getindex , setindex! and view to select indices matching the passed in value(s) We can use selectors inside dim wrappers, here selecting values from DateTime and Int : using Dates \n timespan = DateTime ( 2001 , 1 ) : Month ( 1 ) : DateTime ( 2001 , 12 ) \n A4 = rand ( Ti ( timespan ), X ( 10 : 10 : 100 )) \n A4 [ X ( Near ( 35 )), Ti ( At ( DateTime ( 2001 , 5 )))] \n 0.9138958993339432\n Without dim wrappers selectors must be in the right order, and specify all axes: using Unitful \n A5 = rand ( Y (( 1 : 10 : 100 ) u \"m\" ), Ti (( 1 : 5 : 100 ) u \"s\" )); \n A5 [ 10.5 u \"m\" .. 50.5 u \"m\" , Near ( 23 u \"s\" )] \n 4-element DimArray{Float64,1} with dimensions: \n Y Sampled{Quantity{Int64, 𝐋, Unitful.FreeUnits{(m,), 𝐋, nothing}}} (11:10:41) m ForwardOrdered Regular Points\nand reference dimensions: \n Ti Sampled{Quantity{Int64, 𝐓, Unitful.FreeUnits{(s,), 𝐓, nothing}}} (21:5:21) s ForwardOrdered Regular Points\n 11 m 0.270118\n 21 m 0.191835\n 31 m 0.767381\n 41 m 0.117902\n We can also use Linear indices as in standard Array : A5 [ 1 : 5 ] \n 5-element Vector{Float64}:\n 0.4403938161748643\n 0.116883355447569\n 0.18929453007416674\n 0.33024233140041537\n 0.6230648314878906\n But unless the DimArray is one dimensional, this will return a regular Array . It is not possible to keep the LookupArray or even Dimension s after linear indexing is used."},{"id":370,"pagetitle":"Crash course - DimensionalData.jl","title":"LookupArrays and traits ¤","ref":"/DimensionalData/stable/crash/generated/course/course/#lookuparrays-and-traits","content":" LookupArrays and traits ¤ Using a regular range or Vector as a lookup index has a number of downsides. We cannot use searchsorted for fast searches without knowing the order of the array, and this is slow to compute at runtime. It also means reverse or rotations cannot be used while keeping the DimArray wrapper. Step sizes are also a problem. Some ranges like LinRange lose their step size with a length of 1 . Often, instead of a range, multi-dimensional data formats provide a Vector of evenly spaced values for a lookup, with a step size specified separately. Converting to a range introduces floating point errors that means points may not be selected with At without setting tolerances. This means using a lookup wrapper with traits is more generally robust and versatile than simply using a range or vector. DimensionalData provides types for specifying details about the dimension index, in the LookupArrays sub-module: using DimensionalData \n using . LookupArrays \n The main LookupArray are : Sampled Categorical , NoLookup Each comes with specific traits that are either fixed or variable, depending on the contained index. These enable optimisations with Selector s, and modified behaviours, such as: Selection of Intervals or Points , which will give slightly different results for selectors like .. - as whole intervals are selected, and have different bounds values. Tracking of lookup order. A reverse order is labelled ReverseOrdered and will still work with searchsorted , and for plots to always be the right way up when either the index or the array is backwards. Reversing a DimArray will reverse the LookupArray for that dimension, swapping ReverseOrdered to ForwardOrdered . Sampled Intervals can have index located at a Locus of: Start , Center End Which specifies the point of the interval represented in the index, to match different data standards, e.g. GeoTIFF ( Start ) and NetCDF ( Center ). A Span specifies the gap between Points or the size of Intervals . This may be: Regular , in the case of a range and equally spaced vector, Irregular for unequally spaced vectors Explicit for the case where all interval start and end points are specified explicitly - as is common in the NetCDF standard. These traits all for subtypes of Aligned . Unaligned also exists to handle dimensions with an index that is rotated or otherwise transformed in relation to the underlying array, such as Transformed ."},{"id":371,"pagetitle":"Crash course - DimensionalData.jl","title":"LookupArray detection ¤","ref":"/DimensionalData/stable/crash/generated/course/course/#lookuparray-detection","content":" LookupArray detection ¤ Aligned types will be detected automatically if not specified - which usually isn't required. An empty Dimension or a Type or Symbol will be assigned NoLookup - this behaves as a simple named dimension without a lookup index. A Dimension containing and index of String , Char , Symbol or mixed types will be given the Categorical mode, A range will be assigned Sampled , defaulting to Regular , Points Other AbstractVector will be assigned Sampled Irregular Points . In all cases the Order of ForwardOrdered or ReverseOrdered will be be detected, otherwise Unordered for an unsorted Array . See the LookupArray API docs for more detail."},{"id":372,"pagetitle":"Crash course - DimensionalData.jl","title":"Referenced dimensions ¤","ref":"/DimensionalData/stable/crash/generated/course/course/#referenced-dimensions","content":" Referenced dimensions ¤ The reference dimensions record the previous dimensions that an array was selected from. These can be use for plot labelling, and tracking array changes so that cat can reconstruct the lookup array from previous dimensions that have been sliced."},{"id":373,"pagetitle":"Crash course - DimensionalData.jl","title":"Warnings ¤","ref":"/DimensionalData/stable/crash/generated/course/course/#warnings","content":" Warnings ¤ Indexing with unordered or reverse-ordered arrays has undefined behaviour. It will trash the dimension index, break searchsorted and nothing will make sense any more. So do it at you own risk. However, indexing with sorted vectors of Int can be useful, so it's allowed. But it may do strange things to interval sizes for Intervals that are not Explicit . This selects the first 5 entries of the underlying array. In the case that A has only one dimension, it will be retained. Multidimensional AbstracDimArray indexed this way will return a regular array. This page was generated using Literate.jl ."},{"id":376,"pagetitle":"Reference - DimensionalData.jl","title":"API ¤","ref":"/DimensionalData/stable/reference/#api","content":" API ¤"},{"id":377,"pagetitle":"Reference - DimensionalData.jl","title":"Arrays ¤","ref":"/DimensionalData/stable/reference/#arrays","content":" Arrays ¤ # DimensionalData.AbstractDimArray — Type . AbstractDimArray <: AbstractArray \n Abstract supertype for all \"dim\" arrays. These arrays return a Tuple of Dimension from a dims method, and can be rebuilt using rebuild . parent must return the source array. They should have metadata , name and refdims methods, although these are optional. A rebuild method for AbstractDimArray must accept data , dims , refdims , name , metadata arguments. Indexing AbstractDimArray with non-range AbstractArray has undefined effects on the Dimension index. Use forward-ordered arrays only\" source # DimensionalData.DimArray — Type . DimArray <: AbstractDimArray \n\n DimArray ( data , dims , refdims , name , metadata ) \n DimArray ( data , dims :: Tuple ; refdims = (), name = NoName (), metadata = NoMetadata ()) \n The main concrete subtype of AbstractDimArray . DimArray maintains and updates its Dimension s through transformations and moves dimensions to reference dimension refdims after reducing operations (like e.g. mean ). Arguments data : An AbstractArray . dims : A Tuple of Dimension name : A string name for the array. Shows in plots and tables. refdims : refence dimensions. Usually set programmatically to track past slices and reductions of dimension for labelling and reconstruction. metadata : Dict or Metadata object, or NoMetadata() Indexing can be done with all regular indices, or with Dimension s and/or Selector s. Indexing AbstractDimArray with non-range AbstractArray has undefined effects on the Dimension index. Use forward-ordered arrays only\" Example: using Dates , DimensionalData \n\n ti = ( Ti ( DateTime ( 2001 ) : Month ( 1 ) : DateTime ( 2001 , 12 )), \n x = X ( 10 : 10 : 100 )) \n A = DimArray ( rand ( 12 , 10 ), ( ti , x ), \"example\" ) \n\n julia > A [ X ( Near ([ 12 , 35 ])), Ti ( At ( DateTime ( 2001 , 5 )))]; \n\n julia > A [ Near ( DateTime ( 2001 , 5 , 4 )), Between ( 20 , 50 )]; \n source"},{"id":378,"pagetitle":"Reference - DimensionalData.jl","title":"Multi-array datasets ¤","ref":"/DimensionalData/stable/reference/#multi-array-datasets","content":" Multi-array datasets ¤ # DimensionalData.AbstractDimStack — Type . AbstractDimStack \n Abstract supertype for dimensional stacks. These have multiple layers of data, but share dimensions. Notably, their behaviour lies somewhere between a DimArray and a NamedTuple : indexing with a Symbol as in dimstack[:symbol] returns a DimArray layer. iteration amd map are apply over array layers, as indexed with a Symbol . getindex and many base methods are applied as for DimArray - to avoid the need to allways use map . This design gives very succinct code when working with many-layered, mixed-dimension objects. But it may be jarring initially - the most surprising outcome is that dimstack[1] will return a NamedTuple of values for the first index in all layers, while first(dimstack) will return the first value of the iterator - the DimArray for the first layer. See DimStack for the concrete implementation. Most methods are defined on the abstract type. To extend AbstractDimStack , implement argument and keyword version of rebuild and also rebuild_from_arrays . The constructor of an AbstractDimStack must accept a NamedTuple . source # DimensionalData.DimStack — Type . DimStack <: AbstractDimStack \n\n DimStack ( data :: AbstractDimArray ... ) \n DimStack ( data :: Tuple { Vararg { AbstractDimArray }}) \n DimStack ( data :: NamedTuple { Keys , Vararg { AbstractDimArray }}) \n DimStack ( data :: NamedTuple , dims :: DimTuple ; metadata = NoMetadata ()) \n DimStack holds multiple objects sharing some dimensions, in a NamedTuple . Notably, their behaviour lies somewhere between a DimArray and a NamedTuple : indexing with a Symbol as in dimstack[:symbol] returns a DimArray layer. iteration amd map are apply over array layers, as indexed with a Symbol . getindex or view with Int , Dimension s or Selector s that resolve to Int will return a NamedTuple of values from each layer in the stack. This has very good performace, and avoids the need to always use map . getindex or view with a Vector or Colon will return another DimStack where all data layers have been sliced. setindex! must pass a Tuple or NamedTuple maching the layers. many base and Statistics methods ( sum , mean etc) will work as for a DimArray again removing the need to use map . For example, here we take the mean over the time dimension for all layers : mean ( mydimstack ; dims = Ti ) \n And this equivalent to: map ( A -> mean ( A ; dims = Ti ), mydimstack ) \n This design gives succinct code when working with many-layered, mixed-dimension objects. But it may be jarring initially - the most surprising outcome is that dimstack[1] will return a NamedTuple of values for the first index in all layers, while first(dimstack) will return the first value of the iterator - the DimArray for the first layer. DimStack can be constructed from multiple AbstractDimArray or a NamedTuple of AbstractArray and a matching dims tuple. Most Base and Statistics methods that apply to AbstractArray can be used on all layers of the stack simulataneously. The result is a DimStack , or a NamedTuple if methods like mean are used without dims arguments, and return a single non-array value. Example julia> using DimensionalData \n\n julia> A = [ 1.0 2.0 3.0 ; 4.0 5.0 6.0 ]; \n\n julia> dimz = ( X ([ :a , :b ]), Y ( 10.0 : 10.0 : 30.0 )) \n X Symbol[:a, :b], \n Y 10.0:10.0:30.0 \n\n julia> da1 = DimArray ( 1 A , dimz ; name = :one ); \n\n julia> da2 = DimArray ( 2 A , dimz ; name = :two ); \n\n julia> da3 = DimArray ( 3 A , dimz ; name = :three ); \n\n julia> s = DimStack ( da1 , da2 , da3 ); \n\n julia> s [ At ( :b ), At ( 10.0 )] \n (one = 4.0, two = 8.0, three = 12.0) \n\n julia> s [ X ( At ( :a ))] isa DimStack \n true \n source"},{"id":379,"pagetitle":"Reference - DimensionalData.jl","title":"Dimension indices generators ¤","ref":"/DimensionalData/stable/reference/#dimension-indices-generators","content":" Dimension indices generators ¤ # DimensionalData.DimIndices — Type . DimIndices <: AbstractArray \n\n DimIndices ( x ) \n DimIndices ( dims :: Tuple ) \n DimIndices ( dims :: Dimension ) \n Like CartesianIndices , but for Dimension s. Behaves as an Array of Tuple of Dimension(i) for all combinations of the axis indices of dims . This can be used to view/index into arbitrary dimensions over an array, and is especially useful when combined with otherdims , to iterate over the indices of unknown dimension. source # DimensionalData.DimKeys — Type . DimKeys <: AbstractArray \n\n DimKeys ( x ) \n DimKeys ( dims :: Tuple ) \n DimKeys ( dims :: Dimension ) \n Like CartesianIndices , but for the lookup values of Dimensions. Behaves as an Array of Tuple of Dimension(At(lookupvalue)) for all combinations of the lookup values of dims . source # DimensionalData.DimPoints — Type . DimPoints <: AbstractArray \n\n DimPoints ( x ; order ) \n DimPoints ( dims :: Tuple ; order ) \n DimPoints ( dims :: Dimension ; order ) \n Like CartesianIndices , but for the point values of the dimension index. Behaves as an Array of Tuple lookup values (whatever they are) for all combinations of the lookup values of dims . Either a Dimension , a Tuple of Dimension or an object that defines a dims method can be passed in. Keywords order : determines the order of the points, the same as the order of dims by default. source"},{"id":380,"pagetitle":"Reference - DimensionalData.jl","title":"Tables.jl/TableTraits.jl interface ¤","ref":"/DimensionalData/stable/reference/#tablesjltabletraitsjl-interface","content":" Tables.jl/TableTraits.jl interface ¤ # DimensionalData.AbstractDimTable — Type . AbstractDimTable <: Tables . AbstractColumns \n Abstract supertype for dim tables source # DimensionalData.DimTable — Type . DimTable <: AbstractDimTable \n\n DimTable ( s :: AbstractDimStack ; mergedims = nothing ) \n DimTable ( x :: AbstractDimArray ; layersfrom = nothing , mergedims = nothing ) \n DimTable ( xs :: Vararg { AbstractDimArray }; layernames = nothing , mergedims = nothing ) \n Construct a Tables.jl/TableTraits.jl compatible object out of an AbstractDimArray or AbstractDimStack . This table will have columns for the array data and columns for each Dimension index, as a [ DimColumn ]. These are lazy, and generated as required. Column names are converted from the dimension types using DimensionalData.dim2key . This means type Ti becomes the column name :Ti , and Dim{:custom} becomes :custom . To get dimension columns, you can index with Dimension ( X() ) or Dimension type ( X ) as well as the regular Int or Symbol . Keywords mergedims : Combine two or more dimensions into a new dimension. layersfrom : Treat a dimension of an AbstractDimArray as layers of an AbstractDimStack . Example julia> a = DimArray ( rand ( 32 , 32 , 3 ), ( X , Y , Dim { :band })); \n\n julia> DimTable ( a , layersfrom = Dim { :band }, mergedims = ( X , Y ) =>: geometry ) \n DimTable with 1024 rows, 4 columns, and schema: \n :geometry Tuple{Int64, Int64} \n :band_1 Float64 \n :band_2 Float64 \n :band_3 Float64 \n source # DimensionalData.DimColumn — Type . DimColumn { T , D <: Dimension } <: AbstractVector { T } \n\n DimColumn ( dim :: Dimension , dims :: Tuple { Vararg { DimTuple }}) \n DimColumn ( dim :: DimColumn , length :: Int , dimstride :: Int ) \n A table column based on a Dimension and it's relationship with other Dimension s in dims . length is the product of all dim lengths (usually the length of the corresponding array data), while stride is the product of the preceding dimension lengths, which may or may not be the real stride of the corresponding array depending on the data type. For A isa Array , the dimstride will match the stride . When the second argument is a Tuple of Dimension , the length and dimstride fields are calculated from the dimensions, relative to the column dimension dim . This object will be returned as a column of DimTable . source"},{"id":381,"pagetitle":"Reference - DimensionalData.jl","title":"Common methods ¤","ref":"/DimensionalData/stable/reference/#common-methods","content":" Common methods ¤ Common functions for obtaining information from objects: # DimensionalData.Dimensions.dims — Function . dims ( x , [ dims :: Tuple ]) => Tuple { Vararg { Dimension }} \n dims ( x , dim ) => Dimension \n Return a tuple of Dimension s for an object, in the order that matches the axes or columns of the underlying data. dims can be Dimension , Dimension types, or Symbols for Dim{Symbol} . The default is to return nothing . source # DimensionalData.Dimensions.refdims — Function . refdims ( x , [ dims :: Tuple ]) => Tuple { Vararg { Dimension }} \n refdims ( x , dim ) => Dimension \n Reference dimensions for an array that is a slice or view of another array with more dimensions. slicedims(a, dims) returns a tuple containing the current new dimensions and the new reference dimensions. Refdims can be stored in a field or disgarded, as it is mostly to give context to plots. Ignoring refdims will simply leave some captions empty. The default is to return an empty Tuple () . source # DimensionalData.Dimensions.LookupArrays.metadata — Function . metadata ( x ) => ( object metadata ) \n metadata ( x , dims :: Tuple ) => Tuple ( Dimension metadata ) \n metadata ( xs :: Tuple ) => Tuple \n Returns the metadata for an object or for the specified dimension(s) Second argument dims can be Dimension s, Dimension types, or Symbols for Dim{Symbol} . source # DimensionalData.Dimensions.name — Function . name ( x ) => Symbol \n name ( xs : Tuple ) => NTuple { N , Symbol } \n name ( x , dims :: Tuple ) => NTuple { N , Symbol } \n name ( x , dim ) => Symbol \n Get the name of an array or Dimension, or a tuple of of either as a Symbol. Second argument dims can be Dimension s, Dimension types, or Symbols for Dim{Symbol} . source Utility methods for transforming DimensionalData objects: # DimensionalData.Dimensions.LookupArrays.set — Function . set ( x , val ) \n set ( x , args :: Pairs ... ) => x with updated field / s \n set ( x , args ... ; kw ... ) => x with updated field / s \n set ( x , args :: Tuple { Vararg { Dimension }}; kw ... ) => x with updated field / s \n\n set ( dim :: Dimension , index :: AbstractArray ) => Dimension \n set ( dim :: Dimension , lookup :: LookupArray ) => Dimension \n set ( dim :: Dimension , lookupcomponent :: LookupArrayTrait ) => Dimension \n set ( dim :: Dimension , metadata :: AbstractMetadata ) => Dimension \n Set the properties of an object, its internal data or the traits of its dimensions and lookup index. As DimensionalData is so strongly typed you do not need to specify what field of a LookupArray to set - there is no ambiguity. To set fields of a LookupArray you need to specify the dimension. This can be done using X => val pairs, X = val keyword arguments, or X(val) wrapped arguments. When a Dimension or LookupArray is passed to set to replace the existing ones, fields that are not set will keep their original values. Notes: Changing a lookup index range/vector will also update the step size and order where applicable. Setting the Order like ForwardOrdered will not reverse the array or dimension to match. Use reverse and reorder to do this. Examples julia> using DimensionalData ; const DD = DimensionalData \n DimensionalData \n\n julia> da = DimArray ( zeros ( 3 , 4 ), ( custom = 10.0 : 010.0 : 30.0 , Z =- 20 : 010.0 : 10.0 )); \n\n julia> set ( da , ones ( 3 , 4 )) \n 3×4 DimArray{Float64,2} with dimensions: \n Dim{:custom} Sampled{Float64} 10.0:10.0:30.0 ForwardOrdered Regular Points, \n Z Sampled{Float64} -20.0:10.0:10.0 ForwardOrdered Regular Points \n -20.0 -10.0 0.0 10.0 \n 10.0 1.0 1.0 1.0 1.0 \n 20.0 1.0 1.0 1.0 1.0 \n 30.0 1.0 1.0 1.0 1.0 \n Change the Dimension wrapper type: julia> set ( da , :Z => Ti , :custom => Z ) \n 3×4 DimArray{Float64,2} with dimensions: \n Z Sampled{Float64} 10.0:10.0:30.0 ForwardOrdered Regular Points, \n Ti Sampled{Float64} -20.0:10.0:10.0 ForwardOrdered Regular Points \n -20.0 -10.0 0.0 10.0 \n 10.0 0.0 0.0 0.0 0.0 \n 20.0 0.0 0.0 0.0 0.0 \n 30.0 0.0 0.0 0.0 0.0 \n Change the lookup Vector : julia> set ( da , Z => [ :a , :b , :c , :d ], :custom => [ 4 , 5 , 6 ]) \n 3×4 DimArray{Float64,2} with dimensions: \n Dim{:custom} Sampled{Int64} Int64[4, 5, 6] ForwardOrdered Regular Points, \n Z Sampled{Symbol} Symbol[:a, :b, :c, :d] ForwardOrdered Regular Points \n :a :b :c :d \n 4 0.0 0.0 0.0 0.0 \n 5 0.0 0.0 0.0 0.0 \n 6 0.0 0.0 0.0 0.0 \n Change the LookupArray type: julia> set ( da , Z = DD . NoLookup (), custom = DD . Sampled ()) \n 3×4 DimArray{Float64,2} with dimensions: \n Dim{:custom} Sampled{Float64} 10.0:10.0:30.0 ForwardOrdered Regular Points, \n Z \n 10.0 0.0 0.0 0.0 0.0 \n 20.0 0.0 0.0 0.0 0.0 \n 30.0 0.0 0.0 0.0 0.0 \n Change the Sampling trait: julia> set ( da , :custom => DD . Irregular ( 10 , 12 ), Z => DD . Regular ( 9.9 )) \n 3×4 DimArray{Float64,2} with dimensions: \n Dim{:custom} Sampled{Float64} 10.0:10.0:30.0 ForwardOrdered Irregular Points, \n Z Sampled{Float64} -20.0:10.0:10.0 ForwardOrdered Regular Points \n -20.0 -10.0 0.0 10.0 \n 10.0 0.0 0.0 0.0 0.0 \n 20.0 0.0 0.0 0.0 0.0 \n 30.0 0.0 0.0 0.0 0.0 \n source # DimensionalData.Dimensions.LookupArrays.rebuild — Function . rebuild ( x , args ... ) \n rebuild ( x ; kw ... ) \n Rebuild an object struct with updated field values. x can be a AbstractDimArray , a Dimension , LookupArray or other custom types. This is an abstraction that alows inbuilt and custom types to be rebuilt to update their fields, as most objects in DimensionalData.jl are immutable. The arguments version can be concise but depends on a fixed order defined for some DimensionalData objects. It should be defined based on the object type in DimensionalData, adding the fields specific to your object. The keyword version ignores order, and is mostly automated using ConstructionBase.setproperties . It should only be defined if your object has missing fields or fields with different names to DimensionalData objects. The arguments required are defined for the abstract type that has a rebuild method. source # DimensionalData.modify — Function . modify ( f , A :: AbstractDimArray ) => AbstractDimArray \n modify ( f , s :: AbstractDimStack ) => AbstractDimStack \n modify ( f , dim :: Dimension ) => Dimension \n modify ( f , x , lookupdim :: Dimension ) => typeof ( x ) \n Modify the parent data, rebuilding the object wrapper without change. f must return a AbstractArray of the same size as the original. This method is mostly useful as a way of swapping the parent array type of an object. Example If we have a previously-defined DimArray , we can copy it to an Nvidia GPU with: A = DimArray ( rand ( 100 , 100 ), ( X , Y )) \n modify ( CuArray , A ) \n This also works for all the data layers in a DimStack . source # DimensionalData.broadcast_dims — Function . broadcast_dims ( f , sources :: AbstractDimArray ... ) => AbstractDimArray \n Broadcast function f over the AbstractDimArray s in sources , permuting and reshaping dimensions to match where required. The result will contain all the dimensions in all passed in arrays in the order in which they are found. Arguments sources : AbstractDimArrays to broadcast over with f . This is like broadcasting over every slice of A if it is sliced by the dimensions of B . source # DimensionalData.broadcast_dims! — Function . broadcast_dims! ( f , dest :: AbstractDimArray , sources :: AbstractDimArray ... ) => dest \n Broadcast function f over the AbstractDimArray s in sources , writing to dest . sources are permuting and reshaping dimensions to match where required. The result will contain all the dimensions in all passed in arrays, in the order in which they are found. Arguments dest : AbstractDimArray to update. sources : AbstractDimArrays to broadcast over with f . source # DimensionalData.mergedims — Function . mergedims ( old_dims => new_dim ) => Dimension \n Return a dimension new_dim whose indices are a MergedLookup of the indices of old_dims . source mergedims(dims, old_dims => new_dim, others::Pair...) => dims_new\n If dimensions old_dims , new_dim , etc. are found in dims , then return new dims_new where all dims in old_dims have been combined into a single dim new_dim . The returned dimension will keep only the name of new_dim . Its coords will be a MergedLookup of the coords of the dims in old_dims . New dimensions are always placed at the end of dims_new . others contains other dimension pairs to be merged. Example julia> ds = ( X ( 0 : 0.1 : 0.4 ), Y ( 10 : 10 : 100 ), Ti ([ 0 , 3 , 4 ])); \n julia> mergedims ( ds , Ti => :time , ( X , Y ) => :space ) \n Dim{:time} MergedLookup{Tuple{Int64}} Tuple{Int64}[(0,), (3,), (4,)] Ti, \n Dim{:space} MergedLookup{Tuple{Float64, Int64}} Tuple{Float64, Int64}[(0.0, 10), (0.1, 10), …, (0.3, 100), (0.4, 100)] X, Y \n source mergedims(A::AbstractDimArray, dim_pairs::Pair...) => AbstractDimArray\nmergedims(A::AbstractDimStack, dim_pairs::Pair...) => AbstractDimStack\n Return a new array or stack whose dimensions are the result of mergedims(dims(A), dim_pairs) . source # DimensionalData.unmergedims — Function . unmergedims ( merged_dims :: Tuple { Vararg { Dimension }}) => Tuple { Vararg { Dimension }} \n Return the unmerged dimensions from a tuple of merged dimensions. However, the order of the original dimensions are not necessarily preserved. source unmergedims(A::AbstractDimArray, original_dims) => AbstractDimArray\nunmergedims(A::AbstractDimStack, original_dims) => AbstractDimStack\n Return a new array or stack whose dimensions are restored to their original prior to calling mergedims(A, dim_pairs) . source # DimensionalData.reorder — Function . reorder ( A :: Union { AbstractDimArray , AbstractDimStack }, order :: Pair ... ) \n reorder ( A :: Union { AbstractDimArray , AbstractDimStack }, order ) \n reorder ( A :: Dimension , order :: Order ) \n Reorder every dims index/array to order , or reorder index for the the given dimension(s) in order . order can be an Order , Dimension => Order pairs. A Tuple of Dimensions or any object that defines dims can be used in which case dimensions are If no axis reversal is required the same objects will be returned, without allocation. Example **Create a DimArray**\n\nda = DimArray([1 2 3; 4 5 6], (X(10:10:20), Y(300:-100:100)))\n\n**Reverse it**\n\nrev = reverse(da, dims=Y)\n\n**using `da` in reorder will return it to the original order**\n\nreorder(rev, da) == da\n\n**output**\n\ntrue\n\n\nsource
        \n\n#\n**`Base.cat`** — *Function*.\n\n\n\n```julia\nBase.cat(stacks::AbstractDimStack...; [keys=keys(stacks[1])], dims)\n Concatenate all or a subset of layers for all passed in stacks. Keywords keys : Tuple of Symbol for the stack keys to concatenate. dims : Dimension of child array to concatenate on. Example Concatenate the :sea surface temp and :humidity layers in the time dimension: cat ( stacks ... ; keys = ( :sea_surface_temp , :humidity ), dims = Ti ) \n source # Base.map — Function . Base . map ( f , stacks :: AbstractDimStack ... ) \n Apply function f to each layer of the stacks . If f returns DimArray s the result will be another DimStack . Other values will be returned in a NamedTuple . source # Base.copy! — Function . Base . copy! ( dst :: AbstractArray , src :: AbstractGimStack , key :: Key ) \n Copy the stack layer key to dst , which can be any AbstractArray . Example Copy the :humidity layer from stack to array . copy! ( array , stack , :humidity ) \n source Base.copy!(dst::AbstractDimStack, src::AbstractDimStack, [keys=keys(dst)])\n Copy all or a subset of layers from one stack to another. Example Copy just the :sea_surface_temp and :humidity layers from src to dst . copy! ( dst :: AbstractDimStack , src :: AbstractDimStack , keys = ( :sea_surface_temp , :humidity )) \n source # Base.eachslice — Function . Base . eachslice ( stack :: AbstractDimStack ; dims ) \n Create a generator that iterates over dimensions dims of stack , returning stacks that select all the data from the other dimensions in stack using views. The generator has size and axes equivalent to those of the provided dims . Examples julia > ds = DimStack (( \n x = DimArray ( randn ( 2 , 3 , 4 ), ( X ([ :x1 , :x2 ]), Y ( 1 : 3 ), Z )), \n y = DimArray ( randn ( 2 , 3 , 5 ), ( X ([ :x1 , :x2 ]), Y ( 1 : 3 ), Ti )) \n )); \n\n julia > slices = eachslice ( ds ; dims = ( Z , X )); \n\n julia > size ( slices ) \n ( 4 , 2 ) \n\n julia > map ( dims , axes ( slices )) \n Z , \n X Categorical { Symbol } Symbol [ x1 , x2 ] ForwardOrdered \n\n julia > first ( slices ) \n DimStack with dimensions : \n Y Sampled { Int64 } 1 : 3 ForwardOrdered Regular Points , \n Ti \n and 2 layers : \n :x Float64 dims : Y ( 3 ) \n :y Float64 dims : Y , Ti ( 3 × 5 ) \n source Most base methods work as expected, using Dimension wherever a dims keyword is used. They are not allspecifically documented here. Shorthand constructors: # Base.fill — Function . Base . fill ( x , dims :: Dimension ... ; kw ... ) => DimArray \n Base . fill ( x , dims :: Tuple { Vararg { Dimension }}; kw ... ) => DimArray \n Create a DimArray with a fill value of x . There are two kinds of Dimension value acepted: A Dimension holding an AbstractVector will set the dimension index to that AbstractVector , and detect the dimension lookup. A Dimension holding an Integer will set the length of the axis, and set the dimension lookup to NoLookup . Keywords are the same as for DimArray . Example ```@doctest\njulia> using DimensionalData julia> rand(Bool, X(2), Y(4))\n2×4 DimArray{Bool,2} with dimensions: X, Y\n 1 0 0 1\n 1 0 1 1\n source
        \n\n#\n**`Base.rand`** — *Function*.\n\n\n\n```julia\nBase.rand(x, dims::Dimension...; kw...) => DimArray\nBase.rand(x, dims::Tuple{Vararg{Dimension}}; kw...) => DimArray\nBase.rand(r::AbstractRNG, x, dims::Tuple{Vararg{Dimension}}; kw...) => DimArray\nBase.rand(r::AbstractRNG, x, dims::Dimension...; kw...) => DimArray\n Create a DimArray of random values. There are two kinds of Dimension value acepted: A Dimension holding an AbstractVector will set the dimension index to that AbstractVector , and detect the dimension lookup. A Dimension holding an Integer will set the length of the axis, and set the dimension lookup to NoLookup . Keywords are the same as for DimArray . Example julia > using DimensionalData \n\n julia > rand ( Bool , X ( 2 ), Y ( 4 )) \n 2 × 4 DimArray { Bool , 2 } with dimensions : X , Y \n 1 0 0 1 \n 1 0 1 1 \n\n julia > rand ( X ([ :a , :b , :c ]), Y ( 100.0 : 50 : 200.0 )) \n 3 × 3 DimArray { Float64 , 2 } with dimensions : \n X : Symbol [ a , b , c ] Categorical : Unordered , \n Y : 100.0 : 50.0 : 200.0 Sampled : Ordered Regular Points \n 0.43204 0.835111 0.624231 \n 0.752868 0.471638 0.193652 \n 0.484558 0.846559 0.455256 \n source # Base.zeros — Function . Base . zeros ( x , dims :: Dimension ... ; kw ... ) => DimArray \n Base . zeros ( x , dims :: Tuple { Vararg { Dimension }}; kw ... ) => DimArray \n Create a DimArray of zeros. There are two kinds of Dimension value acepted: A Dimension holding an AbstractVector will set the dimension index to that AbstractVector , and detect the dimension lookup. A Dimension holding an Integer will set the length of the axis, and set the dimension lookup to NoLookup . Keywords are the same as for DimArray . Example ```@doctest\njulia> using DimensionalData julia> zeros(Bool, X(2), Y(4))\n2×4 DimArray{Bool,2} with dimensions: X, Y\n 0 0 0 0\n 0 0 0 0 julia> zeros(X([:a, :b, :c]), Y(100.0:50:200.0))\n3×3 DimArray{Float64,2} with dimensions:\n X: Symbol[a, b, c] Categorical: Unordered,\n Y: 100.0:50.0:200.0 Sampled: Ordered Regular Points\n 0.0 0.0 0.0\n 0.0 0.0 0.0\n 0.0 0.0 0.0\n source
        \n\n#\n**`Base.ones`** — *Function*.\n\n\n\n```julia\nBase.ones(x, dims::Dimension...; kw...) => DimArray\nBase.ones(x, dims::Tuple{Vararg{Dimension}}; kw...) => DimArray\n Create a DimArray of ones. There are two kinds of Dimension value acepted: A Dimension holding an AbstractVector will set the dimension index to that AbstractVector , and detect the dimension lookup. A Dimension holding an Integer will set the length of the axis, and set the dimension lookup to NoLookup . Keywords are the same as for DimArray . Example ```@doctest\njulia> using DimensionalData julia> ones(Bool, X(2), Y(4))\n2×4 DimArray{Bool,2} with dimensions: X, Y\n 1 1 1 1\n 1 1 1 1 julia> ones(X([:a, :b, :c]), Y(100.0:50:200.0))\n3×3 DimArray{Float64,2} with dimensions:\n X: Symbol[a, b, c] Categorical: Unordered,\n Y: 100.0:50.0:200.0 Sampled: Ordered Regular Points\n 1.0 1.0 1.0\n 1.0 1.0 1.0\n 1.0 1.0 1.0\n source
        \n\n\n\n\n\n\n# Dimensions\n\n\nHandling of Dimensions is kept in a sub-module `Dimensions`.\n\n#\n**`DimensionalData.Dimensions`** — *Module*.\n\n\n\nDimensions\n\nSub-module for [`Dimension`](reference.md#DimensionalData.Dimensions.Dimension)s wrappers, and operations on them used in DimensionalData.jl.\n\nTo load `Dimensions` types and methods into scope:\n\n```julia\nusing DimensionalData\nusing DimensionalData.Dimensions\n source Dimensions have a type-heirarchy that organises plotting and dimension matching. # DimensionalData.Dimensions.Dimension — Type . Dimension \n Abstract supertype of all dimension types. Example concrete implementations are X , Y , Z , Ti (Time), and the custom [ Dim ]@ref) dimension. Dimension s label the axes of an AbstractDimArray , or other dimensional objects, and are used to index into the array. They may also provide an alternate index to lookup for each array axis. This may be any AbstractVector matching the array axis length, or a Val holding a tuple for compile-time index lookups. Dimension s also have lookup and metadata fields. lookup gives more details about the dimension, such as that it is Categorical or Sampled as Points or Intervals along some transect. DimensionalData will attempt to guess the lookup from the passed-in index value. Example: using DimensionalData , Dates \n\n x = X ( 2 : 2 : 10 ) \n y = Y ([ 'a' , 'b' , 'c' ]) \n ti = Ti ( DateTime ( 2021 , 1 ) : Month ( 1 ) : DateTime ( 2021 , 12 )) \n\n A = DimArray ( zeros ( 3 , 5 , 12 ), ( y , x , ti )) \n\n # output \n\n 3 × 5 × 12 DimArray { Float64 , 3 } with dimensions : \n Y Categorical { Char } Char [ 'a' , 'b' , 'c' ] ForwardOrdered , \n X Sampled { Int64 } 2 : 2 : 10 ForwardOrdered Regular Points , \n Ti Sampled { DateTime } DateTime ( \"2021-01-01T00:00:00\" ) : Month ( 1 ) : DateTime ( \"2021-12-01T00:00:00\" ) ForwardOrdered Regular Points \n [ : , : , 1 ] \n 2 4 6 8 10 \n 'a' 0.0 0.0 0.0 0.0 0.0 \n 'b' 0.0 0.0 0.0 0.0 0.0 \n 'c' 0.0 0.0 0.0 0.0 0.0 \n [ and 11 more slices ... ] \n For simplicity, the same Dimension types are also used as wrappers in getindex , like: x = A [ X ( 2 ), Y ( 3 )] \n\n # output \n\n 12 - element DimArray { Float64 , 1 } with dimensions : \n Ti Sampled { DateTime } DateTime ( \"2021-01-01T00:00:00\" ) : Month ( 1 ) : DateTime ( \"2021-12-01T00:00:00\" ) ForwardOrdered Regular Points \n and reference dimensions : \n Y Categorical { Char } Char [ 'c' ] ForwardOrdered , \n X Sampled { Int64 } 4 : 2 : 4 ForwardOrdered Regular Points \n 2021 - 01 - 01 T00 : 00 : 00 0.0 \n 2021 - 02 - 01 T00 : 00 : 00 0.0 \n 2021 - 03 - 01 T00 : 00 : 00 0.0 \n 2021 - 04 - 01 T00 : 00 : 00 0.0 \n ⋮ \n 2021 - 10 - 01 T00 : 00 : 00 0.0 \n 2021 - 11 - 01 T00 : 00 : 00 0.0 \n 2021 - 12 - 01 T00 : 00 : 00 0.0 \n A Dimension can also wrap Selector . x = A [ X ( Between ( 3 , 4 )), Y ( At ( 'b' ))] \n\n # output \n\n 1 × 12 DimArray { Float64 , 2 } with dimensions : \n X Sampled { Int64 } 4 : 2 : 4 ForwardOrdered Regular Points , \n Ti Sampled { DateTime } DateTime ( \"2021-01-01T00:00:00\" ) : Month ( 1 ) : DateTime ( \"2021-12-01T00:00:00\" ) ForwardOrdered Regular Points \n and reference dimensions : \n Y Categorical { Char } Char [ 'b' ] ForwardOrdered \n 2021 - 01 - 01 T00 : 00 : 00 … 2021 - 12 - 01 T00 : 00 : 00 \n 4 0.0 0.0 \n Dimension objects may have lookup and metadata fields to track additional information about the data and the index, and their relationship. source # DimensionalData.Dimensions.DependentDim — Type . DependentDim <: Dimension \n Abstract supertype for Dependent dimensions. These will plot on the Y axis. source # DimensionalData.Dimensions.IndependentDim — Type . IndependentDim <: Dimension \n Abstract supertype for independent dimensions. Thise will plot on the X axis. source # DimensionalData.Dimensions.XDim — Type . XDim <: IndependentDim \n Abstract supertype for all X dimensions. source # DimensionalData.Dimensions.YDim — Type . YDim <: DependentDim \n Abstract supertype for all Y dimensions. source # DimensionalData.Dimensions.ZDim — Type . ZDim <: DependentDim \n Abstract supertype for all Z dimensions. source # DimensionalData.Dimensions.TimeDim — Type . TimeDim <: IndependentDim \n Abstract supertype for all time dimensions. In a TimeDime with Interval sampling the locus will automatically be set to Start() . Dates and times generally refer to the start of a month, hour, second etc., not the central point as is more common with spatial data. ` source # DimensionalData.Dimensions.X — Type . X <: XDim \n\n X ( val =: ) \n X Dimension . X <: XDim <: IndependentDim Example: xdim = X ( 2 : 2 : 10 ) \n # Or \n val = A [ X ( 1 )] \n # Or \n mean ( A ; dims = X ) \n source # DimensionalData.Dimensions.Y — Type . Y <: YDim \n\n Y ( val =: ) \n Y Dimension . Y <: YDim <: DependentDim Example: ydim = Y ([ 'a' , 'b' , 'c' ]) \n # Or \n val = A [ Y ( 1 )] \n # Or \n mean ( A ; dims = Y ) \n source # DimensionalData.Dimensions.Z — Type . Z <: ZDim \n\n Z ( val =: ) \n Z Dimension . Z <: ZDim <: Dimension Example: zdim = Z ( 10 : 10 : 100 ) \n # Or \n val = A [ Z ( 1 )] \n # Or \n mean ( A ; dims = Z ) \n source # DimensionalData.Dimensions.Ti — Type . m Ti <: TimeDim Ti(val=:)\n Time Dimension . Ti <: TimeDim <: IndependentDim Time is already used by Dates, and T is a common type parameter, We use Ti to avoid clashes. Example: timedim = Ti ( DateTime ( 2021 , 1 ) : Month ( 1 ) : DateTime ( 2021 , 12 )) \n # Or \n val = A [ Ti ( 1 )] \n # Or \n mean ( A ; dims = Ti ) \n source # DimensionalData.Dimensions.Dim — Type . Dim { S }( val =: ) \n A generic dimension. For use when custom dims are required when loading data from a file. Can be used as keyword arguments for indexing. Dimension types take precedence over same named Dim types when indexing with symbols, or e.g. creating Tables.jl keys. using DimensionalData \n\n dim = Dim { :custom }([ 'a' , 'b' , 'c' ]) \n\n # output \n\n Dim { :custom } Char [ 'a' , 'b' , 'c' ] \n source # DimensionalData.Dimensions.Coord — Type . Coord <: Dimension \n A coordinate dimension itself holds dimensions. This allows combining point data with other dimensions, such as time. Example julia > using DimensionalData \n\n julia > dim = Coord ([( 1.0 , 1.0 , 1.0 ), ( 1.0 , 2.0 , 2.0 ), ( 3.0 , 4.0 , 4.0 ), ( 1.0 , 3.0 , 4.0 )], ( X (), Y (), Z ())) \n Coord :: \n val : Tuple { Float64 , Float64 , Float64 }[( 1.0 , 1.0 , 1.0 ), ( 1.0 , 2.0 , 2.0 ), ( 3.0 , 4.0 , 4.0 ), ( 1.0 , 3.0 , \n 4.0 )] \n lookup : MergedLookup \n Coord { Vector { Tuple { Float64 , Float64 , Float64 }}, DimensionalData . MergedLookup { Tuple { X { Colon , AutoLookup { Auto \n Order }, NoMetadata }, Y { Colon , AutoLookup { AutoOrder }, NoMetadata }, Z { Colon , AutoLookup { AutoOrder }, NoMetada \n ta }}}, NoMetadata } \n\n julia > da = DimArray ( 0.1 : 0.1 : 0.4 , dim ) \n 4 - element DimArray { Float64 , 1 } with dimensions : \n Coord () : Tuple { Float64 , Float64 , Float64 }[( 1.0 , 1.0 , 1.0 ), ( 1.0 , 2.0 , 2.0 ), ( 3.0 , 4.0 , 4.0 ), ( 1.0 , \n 3.0 , 4.0 )] \n MergedLookup \n 0.1 \n 0.2 \n 0.3 \n 0.4 \n\n julia > da [ Coord ( Z ( At ( 1.0 )), Y ( Between ( 1 , 3 )))] \n 1 - element DimArray { Float64 , 1 } with dimensions : \n Coord () : Tuple { Float64 , Float64 , Float64 }[( 1.0 , 1.0 , 1.0 )] MergedLookup \n 0.1 \n\n julia > da [ Coord ( 4 )] == 0.4 \n true \n\n julia > da [ Coord ( Between ( 1 , 5 ), : , At ( 4.0 ))] \n 2 - element DimArray { Float64 , 1 } with dimensions : \n Coord () : Tuple { Float64 , Float64 , Float64 }[( 3.0 , 4.0 , 4.0 ), ( 1.0 , 3.0 , 4.0 )] MergedLookup \n 0.3 \n 0.4 \n source # DimensionalData.Dimensions.AnonDim — Type . AnonDim <: Dimension \n\n AnonDim () \n Anonymous dimension. Used when extra dimensions are created, such as during transpose of a vector. source # DimensionalData.Dimensions.@dim — Macro . @dim typ [ supertype = Dimension ] [ name :: String = string ( typ )] \n Macro to easily define new dimensions. The supertype will be inserted into the type of the dim. The default is simply YourDim <: Dimension . Making a Dimesion inherit from XDim , YDim , ZDim or TimeDim will affect automatic plot layout and other methods that dispatch on these types. <: YDim are plotted on the Y axis, <: XDim on the X axis, etc. Example: using DimensionalData \n using DimensionalData : @dim , YDim , XDim \n @dim Lat YDim \"latitude\" \n @dim Lon XDim \"Longitude\" \n # output \n source"},{"id":382,"pagetitle":"Reference - DimensionalData.jl","title":"Exported methods ¤","ref":"/DimensionalData/stable/reference/#exported-methods","content":" Exported methods ¤ # DimensionalData.Dimensions.hasdim — Function . hasdim ([ f ], x , query :: Tuple ) => NTUple { Bool } \n hasdim ([ f ], x , query ... ) => NTUple { Bool } \n hasdim ([ f ], x , query ) => Bool \n Check if an object x has dimensions that match or inherit from the query dimensions. Arguments x : any object with a dims method, a Tuple of Dimension or a single Dimension . query : Tuple or single Dimension or dimension Type . f : <: by default, but can be >: to match abstract types to concrete types. Check if an object or tuple contains an Dimension , or a tuple of dimensions. Example julia> using DimensionalData \n\n julia> A = DimArray ( ones ( 10 , 10 , 10 ), ( X , Y , Z )); \n\n julia> hasdim ( A , X ) \n true \n\n julia> hasdim ( A , ( Z , X , Y )) \n (true, true, true) \n\n julia> hasdim ( A , Ti ) \n false \n source # DimensionalData.Dimensions.dimnum — Function . dimnum ( x , query :: Tuple ) => NTuple { Int } \n dimnum ( x , query ) => Int \n Get the number(s) of Dimension (s) as ordered in the dimensions of an object. Arguments x : any object with a dims method, a Tuple of Dimension or a single Dimension . query : Tuple, Array or single Dimension or dimension Type . The return type will be a Tuple of Int or a single Int , depending on wether query is a Tuple or single Dimension . Example julia> using DimensionalData \n\n julia> A = DimArray ( ones ( 10 , 10 , 10 ), ( X , Y , Z )); \n\n julia> dimnum ( A , ( Z , X , Y )) \n (3, 1, 2) \n\n julia> dimnum ( A , Y ) \n 2 \n source"},{"id":383,"pagetitle":"Reference - DimensionalData.jl","title":"Non-exported methods ¤","ref":"/DimensionalData/stable/reference/#non-exported-methods","content":" Non-exported methods ¤ # DimensionalData.Dimensions.lookup — Function . lookup ( x :: Dimension ) => LookupArray \n lookup ( x , [ dims :: Tuple ]) => Tuple { Vararg { LookupArray }} \n lookup ( x :: Tuple ) => Tuple { Vararg { LookupArray }} \n lookup ( x , dim ) => LookupArray \n Returns the LookupArray of a dimension. This dictates properties of the dimension such as array axis and index order, and sampling properties. dims can be a Dimension , a dimension type, or a tuple of either. source # DimensionalData.Dimensions.label — Function . label ( x ) => String \n label ( x , dims :: Tuple ) => NTuple { N , String } \n label ( x , dim ) => String \n label ( xs :: Tuple ) => NTuple { N , String } \n Get a plot label for data or a dimension. This will include the name and units if they exist, and anything else that should be shown on a plot. Second argument dims can be Dimension s, Dimension types, or Symbols for Dim{Symbol} . source # DimensionalData.Dimensions.dim2key — Function . dim2key ( dim :: Dimension ) => Symbol \n dim2key ( dims :: Type { <: Dimension }) => Symbol \n dim2key ( dims :: Tuple ) => Tuple { Symbol , Vararg } \n Convert a dimension object to a simbol. X() , Y() , Ti() etc will be converted. to :X , :Y , :Ti , as with any other dims generated with the @dim macro. All other Dim{S}() dimensions will generate Symbol s S . source # DimensionalData.Dimensions.key2dim — Function . key2dim ( s :: Symbol ) => Dimension \n key2dim ( dims ... ) => Tuple { Dimension , Vararg } \n key2dim ( dims :: Tuple ) => Tuple { Dimension , Vararg } \n Convert a symbol to a dimension object. :X , :Y , :Ti etc will be converted. to X() , Y() , Ti() , as with any other dims generated with the @dim macro. All other Symbol s S will generate Dim{S}() dimensions. source # DimensionalData.Dimensions.dims2indices — Function . dims2indices ( dim :: Dimension , I ) => NTuple { Union { Colon , AbstractArray , Int }} \n Convert a Dimension or Selector I to indices of Int , AbstractArray or Colon . source # DimensionalData.Dimensions.LookupArrays.selectindices — Function . selectindices ( lookups , selectors ) \n Converts Selector to regular indices. source # DimensionalData.Dimensions.format — Function . format ( dims , x ) => Tuple { Vararg { Dimension , N }} \n Format the passed-in dimension(s) dims to match the object x . Errors are thrown if dims don't match the array dims or size, and any fields holding Auto- objects are filled with guessed objects. If a LookupArray hasn't been specified, a lookup is chosen based on the type and element type of the index. source # DimensionalData.Dimensions.reducedims — Function . reducedims ( x , dimstoreduce ) => Tuple { Vararg { Dimension }} \n Replace the specified dimensions with an index of length 1. This is usually to match a new array size where an axis has been reduced with a method like mean or reduce to a length of 1, but the number of dimensions has not changed. LookupArray traits are also updated to correspond to the change in cell step, sampling type and order. source # DimensionalData.Dimensions.swapdims — Function . swapdims ( x :: T , newdims ) => T \n swapdims ( dims :: Tuple , newdims ) => Tuple { Vararg { Dimension }} \n Swap dimensions for the passed in dimensions, in the order passed. Passing in the Dimension types rewraps the dimension index, keeping the index values and metadata, while constructed Dimension objectes replace the original dimension. nothing leaves the original dimension as-is. Arguments x : any object with a dims method or a Tuple of Dimension . newdim : Tuple of Dimension or dimension Type . Example using DimensionalData \n A = ones ( X ( 2 ), Y ( 4 ), Z ( 2 )) \n Dimensions . swapdims ( A , ( Dim { :a }, Dim { :b }, Dim { :c })) \n\n # output \n 2 × 4 × 2 DimArray { Float64 , 3 } with dimensions : Dim { :a }, Dim { :b }, Dim { :c } \n [ : , : , 1 ] \n 1.0 1.0 1.0 1.0 \n 1.0 1.0 1.0 1.0 \n [ and 1 more slices ... ] \n source # DimensionalData.Dimensions.slicedims — Function . slicedims ( x , I ) => Tuple { Tuple , Tuple } \n slicedims ( f , x , I ) => Tuple { Tuple , Tuple } \n Slice the dimensions to match the axis values of the new array. All methods return a tuple conatining two tuples: the new dimensions, and the reference dimensions. The ref dimensions are no longer used in the new struct but are useful to give context to plots. Called at the array level the returned tuple will also include the previous reference dims attached to the array. Arguments f : a function getindex , view or dotview . This will be used for slicing getindex is the default if f is not included. x : An AbstractDimArray , Tuple of Dimension , or Dimension I : A tuple of Integer , Colon or AbstractArray source # DimensionalData.Dimensions.comparedims — Function . comparedims ( A :: AbstractDimArray ... ; kw ... ) \n comparedims ( A :: Tuple ... ; kw ... ) \n comparedims ( A :: Dimension ... ; kw ... ) \n comparedims ( :: Type { Bool }, args ... ; kw ... ) \n Check that dimensions or tuples of dimensions passed as each argument are the same, and return the first valid dimension. If AbstractDimArray s are passed as arguments their dimensions are compared. Empty tuples and nothing dimension values are ignored, returning the Dimension value if it exists. Passing Bool as the first argument means true / false will be returned, rather than throwing an error. Keywords These are all Bool flags: type : compare dimension type, true by default. valtype : compare wrapped value type, false by default. val : compare wrapped values, false by default. order : compare order, false by default. length : compare lengths, true by default. ignore_length_one : ignore length 1 in comparisons, and return whichever dimension is not length 1, if any. This is useful in e.g. broadcasting comparisons. false by default. warn : a String or nothing . Used only for Bool methods, to give a warning for false values and include warn in the warning text. source # DimensionalData.Dimensions.combinedims — Function . combinedims ( xs ; check = true ) \n Combine the dimensions of each object in xs , in the order they are found. source # DimensionalData.Dimensions.otherdims — Function . otherdims ( x , query ) => Tuple { Vararg { Dimension , N }} \n Get the dimensions of an object not in query . Arguments x : any object with a dims method, a Tuple of Dimension . query : Tuple or single Dimension or dimension Type . f : <: by default, but can be >: to match abstract types to concrete types. A tuple holding the unmatched dimensions is always returned. Example julia> using DimensionalData , DimensionalData . Dimensions \n\n julia> A = DimArray ( ones ( 10 , 10 , 10 ), ( X , Y , Z )); \n\n julia> otherdims ( A , X ) \n Y, Z \n\n julia> otherdims ( A , ( Y , Z )) \n X \n source # DimensionalData.Dimensions.commondims — Function . commondims ([ f ], x , query ) => Tuple { Vararg { Dimension }} \n This is basically dims(x, query) where the order of the original is kept, unlike dims where the query tuple determines the order Also unlike dims , commondims always returns a Tuple , no matter the input. No errors are thrown if dims are absent from either x or query . f is <: by default, but can be >: to sort abstract types by concrete types. julia> using DimensionalData , . Dimensions \n\n julia> A = DimArray ( ones ( 10 , 10 , 10 ), ( X , Y , Z )); \n\n julia> commondims ( A , X ) \n X \n\n julia> commondims ( A , ( X , Z )) \n X, Z \n\n julia> commondims ( A , Ti ) \n () \n source # DimensionalData.Dimensions.sortdims — Function . sortdims ([ f ], tosort , order ) => Tuple \n Sort dimensions tosort by order . Dimensions in order but missing from tosort are replaced with nothing . tosort and order can be Tuple s or Vector s or Dimension or dimension type. Abstract supertypes like TimeDim can be used in order . f is <: by default, but can be >: to sort abstract types by concrete types. source # DimensionalData.Dimensions.LookupArrays.basetypeof — Function . basetypeof ( x ) => Type \n Get the \"base\" type of an object - the minimum required to define the object without it's fields. By default this is the full UnionAll for the type. But custom basetypeof methods can be defined for types with free type parameters. In DimensionalData this is primariliy used for comparing Dimension s, where Dim{:x} is different from Dim{:y} . source # DimensionalData.Dimensions.setdims — Function . setdims ( X , newdims ) => AbstractArray \n setdims ( :: Tuple , newdims ) => Tuple { Vararg { Dimension , N }} \n Replaces the first dim matching <: basetypeof(newdim) with newdim, and returns a new object or tuple with the dimension updated. Arguments x : any object with a dims method, a Tuple of Dimension or a single Dimension . newdim : Tuple or single Dimension , Type or Symbol . Example using DimensionalData , DimensionalData . Dimensions , DimensionalData . LookupArrays \n A = ones ( X ( 10 ), Y ( 10 : 10 : 100 )) \n B = setdims ( A , Y ( Categorical ( 'a' : 'j' ; order = ForwardOrdered ()))) \n lookup ( B , Y ) \n # output \n Categorical { Char } ForwardOrdered \n wrapping : 'a' : 1 : 'j' \n source # DimensionalData.Dimensions.dimsmatch — Function . dimsmatch ([ f ], dim , query ) => Bool \n dimsmatch ([ f ], dims :: Tuple , query :: Tuple ) => Bool \n Compare 2 dimensions or Tuple of Dimension are of the same base type, or are at least rotations/transformations of the same type. f is <: by default, but can be >: to match abstract types to concrete types. source # DimensionalData.Dimensions.dimstride — Function . dimstride ( x , dim ) => Int \n Get the stride of the dimension relative to the other dimensions. This may or may not be equal to the stride of the related array, although it will be for Array . Arguments x is any object with a dims method, or a Tuple of Dimension . dim is a Dimension , Dimension type, or and Int . Using an Int is not type-stable. source # DimensionalData.refdims_title — Function . refdims_title ( A :: AbstractDimArray ) \n refdims_title ( refdims :: Tuple ) \n refdims_title ( refdim :: Dimension ) \n Generate a title string based on reference dimension values. source # DimensionalData.rebuild_from_arrays — Function . rebuild_from_arrays ( s :: AbstractDimStack , das :: NamedTuple { <: Any , <: Tuple { Vararg { AbstractDimArray }}}; kw ... ) \n Rebuild an AbstractDimStack from a Tuple or NamedTuple of AbstractDimArray and an existing stack. Keywords Keywords are simply the fields of the stack object: data dims refdims metadata layerdims layermetadata source"},{"id":384,"pagetitle":"Reference - DimensionalData.jl","title":"LookupArrays ¤","ref":"/DimensionalData/stable/reference/#lookuparrays","content":" LookupArrays ¤ # DimensionalData.Dimensions.LookupArrays — Module . LookupArrays \n Module for LookupArrays and [ Selector ]s used in DimensionalData.jl LookupArrays defines traits and AbstractArray wrappers that give specific behaviours for a lookup index when indexed with Selector . For example, these allow tracking over array order so fast indexing works evne when the array is reversed. To load LookupArrays types and methods into scope: using DimensionalData \n using DimensionalData . LookupArrays \n source"},{"id":385,"pagetitle":"Reference - DimensionalData.jl","title":"Selectors ¤","ref":"/DimensionalData/stable/reference/#selectors","content":" Selectors ¤ # DimensionalData.Dimensions.LookupArrays.Selector — Type . Selector \n Abstract supertype for all selectors. Selectors are wrappers that indicate that passed values are not the array indices, but values to be selected from the dimension index, such as DateTime objects for a Ti dimension. Selectors provided in DimensionalData are: At Between Touches Near Where Contains source # DimensionalData.Dimensions.LookupArrays.IntSelector — Type . IntSelector <: Selector \n Abstract supertype for Selector s that return a single Int index. IntSelectors provided by DimensionalData are: At Contains Near source # DimensionalData.Dimensions.LookupArrays.ArraySelector — Type . ArraySelector <: Selector \n Abstract supertype for Selector s that return an AbstractArray . ArraySelectors provided by DimensionalData are: Between Touches Where source # DimensionalData.Dimensions.LookupArrays.At — Type . At <: IntSelector \n\n At ( x , atol , rtol ) \n At ( x ; atol = nothing , rtol = nothing ) \n Selector that exactly matches the value on the passed-in dimensions, or throws an error. For ranges and arrays, every intermediate value must match an existing value - not just the end points. x can be any value or Vector of values. atol and rtol are passed to isapprox . For Number rtol will be set to Base.rtoldefault , otherwise nothing , and wont be used. Example using DimensionalData \n\n A = DimArray ([ 1 2 3 ; 4 5 6 ], ( X ( 10 : 10 : 20 ), Y ( 5 : 7 ))) \n A [ X ( At ( 20 )), Y ( At ( 6 ))] \n\n # output \n\n 5 \n source # DimensionalData.Dimensions.LookupArrays.Near — Type . Near <: IntSelector \n\n Near ( x ) \n Selector that selects the nearest index to x . With Points this is simply the index values nearest to the x , however with Intervals it is the interval center nearest to x . This will be offset from the index value for Start and End loci. Example using DimensionalData \n\n A = DimArray ([ 1 2 3 ; 4 5 6 ], ( X ( 10 : 10 : 20 ), Y ( 5 : 7 ))) \n A [ X ( Near ( 23 )), Y ( Near ( 5.1 ))] \n\n # output \n 4 \n source # DimensionalData.Dimensions.LookupArrays.Between — Type . Between <: ArraySelector \n\n Between ( a , b ) \n Depreciated: use a..b instead of Between(a, b) . Other Interval objects from IntervalSets.jl, like `OpenInterval(a, b) will also work, giving the correct open/closed boundaries. Between will e removed in furture to avoid clashes with DataFrames.Between . Selector that retreive all indices located between 2 values, evaluated with >= for the lower value, and < for the upper value. This means the same value will not be counted twice in 2 adjacent Between selections. For Intervals the whole interval must be lie between the values. For Points the points must fall between the values. Different Sampling types may give different results with the same input - this is the intended behaviour. Between for Irregular intervals is a little complicated. The interval is the distance between a value and the next (for Start locus) or previous (for End locus) value. For Center , we take the mid point between two index values as the start and end of each interval. This may or may not make sense for the values in your indes, so use Between with Irregular Intervals(Center()) with caution. Example using DimensionalData \n\n A = DimArray ([ 1 2 3 ; 4 5 6 ], ( X ( 10 : 10 : 20 ), Y ( 5 : 7 ))) \n A [ X ( Between ( 15 , 25 )), Y ( Between ( 4 , 6.5 ))] \n\n # output \n\n 1 × 2 DimArray { Int64 , 2 } with dimensions : \n X Sampled { Int64 } 20 : 10 : 20 ForwardOrdered Regular Points , \n Y Sampled { Int64 } 5 : 6 ForwardOrdered Regular Points \n 5 6 \n 20 4 5 \n source # DimensionalData.Dimensions.LookupArrays.Touches — Type . Touches <: ArraySelector \n\n Touches ( a , b ) \n Selector that retreives all indices touching the closed interval 2 values, for the maximum possible area that could interact with the supplied range. This can be better than .. when e.g. subsetting an area to rasterize, as you may wish to include pixels that just touch the area, rather than those that fall within it. Touches is different to using closed intervals when the lookups also contain intervals - if any of the intervals touch, they are included. With .. they are discarded unless the whole cell interval falls inside the selector interval. Example using DimensionalData \n\n A = DimArray ([ 1 2 3 ; 4 5 6 ], ( X ( 10 : 10 : 20 ), Y ( 5 : 7 ))) \n A [ X ( Touches ( 15 , 25 )), Y ( Touches ( 4 , 6.5 ))] \n\n # output \n 1 × 2 DimArray { Int64 , 2 } with dimensions : \n X Sampled { Int64 } 20 : 10 : 20 ForwardOrdered Regular Points , \n Y Sampled { Int64 } 5 : 6 ForwardOrdered Regular Points \n 5 6 \n 20 4 5 \n source # DimensionalData.Dimensions.LookupArrays.Contains — Type . Contains <: IntSelector \n\n Contains ( x ) \n Selector that selects the interval the value is contained by. If the interval is not present in the index, an error will be thrown. Can only be used for Intervals or Categorical . For Categorical it falls back to using At . Contains should not be confused with Base.contains - use Where(contains(x)) to check for if values are contain in categorical values like strings. Example using DimensionalData ; const DD = DimensionalData \n dims_ = X ( 10 : 10 : 20 ; sampling = DD . Intervals ( DD . Center ())), \n Y ( 5 : 7 ; sampling = DD . Intervals ( DD . Center ())) \n A = DimArray ([ 1 2 3 ; 4 5 6 ], dims_ ) \n A [ X ( Contains ( 8 )), Y ( Contains ( 6.8 ))] \n\n # output \n 3 \n source # DimensionalData.Dimensions.LookupArrays.Where — Type . Where <: ArraySelector \n\n Where ( f :: Function ) \n Selector that filters a dimension lookup by any function that accepts a single value and returns a Bool . Example using DimensionalData \n\n A = DimArray ([ 1 2 3 ; 4 5 6 ], ( X ( 10 : 10 : 20 ), Y ( 19 : 21 ))) \n A [ X ( Where ( x -> x > 15 )), Y ( Where ( x -> x in ( 19 , 21 )))] \n\n # output \n\n 1 × 2 DimArray { Int64 , 2 } with dimensions : \n X Sampled { Int64 } Int64 [ 20 ] ForwardOrdered Regular Points , \n Y Sampled { Int64 } Int64 [ 19 , 21 ] ForwardOrdered Regular Points \n 19 21 \n 20 4 6 \n source # DimensionalData.Dimensions.LookupArrays.All — Type . All <: Selector \n\n All ( selectors :: Selector ... ) \n Selector that combines the results of other selectors. The indices used will be the union of all result sorted in ascending order. Example using DimensionalData , Unitful \n\n dimz = X ( 10.0 : 20 : 200.0 ), Ti ( 1 u \"s\" : 5 u \"s\" : 100 u \"s\" ) \n A = DimArray (( 1 : 10 ) * ( 1 : 20 ) ' , dimz ) \n A [ X = All ( At ( 10.0 ), At ( 50.0 )), Ti = All ( 1 u \"s\" .. 10 u \"s\" , 90 u \"s\" .. 100 u \"s\" )] \n\n # output \n\n 2 × 4 DimArray { Int64 , 2 } with dimensions : \n X Sampled { Float64 } Float64 [ 10.0 , 50.0 ] ForwardOrdered Regular Points , \n Ti Sampled { Quantity { Int64 , 𝐓 , Unitful . FreeUnits {( s ,), 𝐓 , nothing }}} Quantity { Int64 , 𝐓 , Unitful . FreeUnits {( s ,), 𝐓 , nothing }}[ 1 s , 6 s , 91 s , 96 s ] ForwardOrdered Regular Points \n 1 s 6 s 91 s 96 s \n 10.0 1 2 19 20 \n 50.0 3 6 57 60 \n source Lookup properties: # DimensionalData.Dimensions.LookupArrays.bounds — Function . bounds ( xs , [ dims :: Tuple ]) => Tuple { Vararg { Tuple { T , T }}} \n bounds ( xs :: Tuple ) => Tuple { Vararg { Tuple { T , T }}} \n bounds ( x , dim ) => Tuple { T , T } \n bounds ( dim :: Union { Dimension , LookupArray }) => Tuple { T , T } \n Return the bounds of all dimensions of an object, of a specific dimension, or of a tuple of dimensions. If bounds are not known, one or both values may be nothing . dims can be a Dimension , a dimension type, or a tuple of either. source # DimensionalData.Dimensions.LookupArrays.val — Function . val ( x ) \n val ( dims :: Tuple ) => Tuple \n Return the contained value of a wrapper object. dims can be Dimension , Dimension types, or Symbols for Dim{Symbol} . Objects that don't define a val method are returned unaltered. source # DimensionalData.Dimensions.LookupArrays.LookupArray — Type . LookupArray \n Types defining the behaviour of a lookup index, how it is plotted and how Selector s like Between work. A LookupArray may be NoLookup indicating that the index is just the underlying array axis, Categorical for ordered or unordered categories, or a Sampled index for Points or Intervals . source # DimensionalData.Dimensions.LookupArrays.Aligned — Type . Aligned <: LookupArray \n Abstract supertype for LookupArray s where the index is aligned with the array axes. This is by far the most common supertype for LookupArray . source # DimensionalData.Dimensions.LookupArrays.AbstractSampled — Type . AbstractSampled <: Aligned \n Abstract supertype for LookupArray s where the index is aligned with the array, and is independent of other dimensions. Sampled is provided by this package. AbstractSampled must have order , span and sampling fields, or a rebuild method that accpts them as keyword arguments. source # DimensionalData.Dimensions.LookupArrays.Sampled — Type . Sampled <: AbstractSampled \n\n Sampled ( data :: AbstractVector , order :: Order , span :: Span , sampling :: Sampling , metadata ) \n Sampled ( data = AutoIndex (); order = AutoOrder (), span = AutoSpan (), sampling = Points (), metadata = NoMetadata ()) \n A concrete implementation of the LookupArray AbstractSampled . It can be used to represent Points or Intervals . Sampled is capable of representing gridded data from a wide range of sources, allowing correct bounds and Selector s for points or intervals of regular, irregular, forward and reverse indexes. On AbstractDimArray construction, Sampled lookup is assigned for all lookups of AbstractRange not assigned to Categorical . Arguments data : An AbstractVector of index values, matching the length of the curresponding array axis. order : Order ) indicating the order of the index, AutoOrder by default, detected from the order of data to be ForwardOrdered , ReverseOrdered or Unordered . These can be provided explicitly if they are known and performance is important. span : indicates the size of intervals or distance between points, and will be set to Regular for AbstractRange and Irregular for AbstractArray , unless assigned manually. sampling : is assigned to Points , unless set to Intervals manually. Using Intervals will change the behaviour of bounds and Selectors s to take account for the full size of the interval, rather than the point alone. metadata : a Dict or Metadata wrapper that holds any metadata object adding more information about the array axis - useful for extending DimensionalData for specific contexts, like geospatial data in GeoData.jl. By default it is NoMetadata() . Example Create an array with [ Interval ] sampling, and Regular span for a vector with known spacing. We set the Locus of the Intervals to Start specifying that the index values are for the positions at the start of each interval. using DimensionalData , DimensionalData . LookupArrays \n\n x = X ( Sampled ( 100 :- 20 : 10 ; sampling = Intervals ( Start ()))) \n y = Y ( Sampled ([ 1 , 4 , 7 , 10 ]; span = Regular ( 3 ), sampling = Intervals ( Start ()))) \n A = ones ( x , y ) \n\n # output \n 5 × 4 DimArray { Float64 , 2 } with dimensions : \n X Sampled { Int64 } 100 :- 20 : 20 ReverseOrdered Regular Intervals , \n Y Sampled { Int64 } Int64 [ 1 , 4 , 7 , 10 ] ForwardOrdered Regular Intervals \n 1 4 7 10 \n 100 1.0 1.0 1.0 1.0 \n 80 1.0 1.0 1.0 1.0 \n 60 1.0 1.0 1.0 1.0 \n 40 1.0 1.0 1.0 1.0 \n 20 1.0 1.0 1.0 1.0 \n source # DimensionalData.Dimensions.LookupArrays.AbstractCyclic — Type . AbstractCyclic <: AbstractSampled end \n An abstract supertype for cyclic lookups. These are AbstractSampled lookups that are cyclic for Selectors . source # DimensionalData.Dimensions.LookupArrays.Cyclic — Type . Cyclic <: AbstractCyclic \n\n Cyclic ( data ; order = AutoOrder (), span = AutoSpan (), sampling = Points (), metadata = NoMetadata (), cycle ) \n A Cyclic lookup is similar to Sampled but out of range Selectors At , Near , Contains will cycle the values to typemin or typemax over the length of cycle . Where and .. work as for Sampled . This is useful when we are using mean annual datasets over a real time-span, or for wrapping longitudes so that -360 and 360 are the same. Arguments data : An AbstractVector of index values, matching the length of the curresponding array axis. order : Order ) indicating the order of the index, AutoOrder by default, detected from the order of data to be ForwardOrdered , ReverseOrdered or Unordered . These can be provided explicitly if they are known and performance is important. span : indicates the size of intervals or distance between points, and will be set to Regular for AbstractRange and Irregular for AbstractArray , unless assigned manually. sampling : is assigned to Points , unless set to Intervals manually. Using Intervals will change the behaviour of bounds and Selectors s to take account for the full size of the interval, rather than the point alone. metadata : a Dict or Metadata wrapper that holds any metadata object adding more information about the array axis - useful for extending DimensionalData for specific contexts, like geospatial data in GeoData.jl. By default it is NoMetadata() . cycle : the length of the cycle. This does not have to exactly match the data, the step size is Week(1) the cycle can be Years(1) . Notes If you use dates and e.g. cycle over a Year , every year will have the number and spacing of Week s and Day s as the cycle year. Using At may not be reliable in terms of exact dates, as it will be applied to the specified date plus or minus n years. Indexing into a Cycled with any AbstractArray or AbstractRange will return a Sampled as the full cycle is likely no longer available. .. or Between selectors do not work in a cycled way: they work as for Sampled . This may change in future to return cycled values, but there are problems with this, such as leap years breaking correct date cycling of a single year. If you actually need this behaviour, please make a GitHub issue. source # DimensionalData.Dimensions.LookupArrays.AbstractCategorical — Type . AbstractCategorical <: Aligned \n LookupArray s where the values are categories. Categorical is the provided concrete implementation. but this can easily be extended - all methods are defined for AbstractCategorical . All AbstractCategorical must provide a rebuild method with data , order and metadata keyword arguments. source # DimensionalData.Dimensions.LookupArrays.Categorical — Type . Categorical <: AbstractCategorical \n\n Categorical ( o :: Order ) \n Categorical (; order = Unordered ()) \n An LookupArray where the values are categories. This will be automatically assigned if the index contains AbstractString , Symbol or Char . Otherwise it can be assigned manually. Order will be determined automatically where possible. Arguments data : An AbstractVector of index values, matching the length of the curresponding array axis. order : Order ) indicating the order of the index, AutoOrder by default, detected from the order of data to be ForwardOrdered , ReverseOrdered or Unordered . Can be provided if this is known and performance is important. metadata : a Dict or Metadata wrapper that holds any metadata object adding more information about the array axis - useful for extending DimensionalData for specific contexts, like geospatial data in GeoData.jl. By default it is NoMetadata() . Example Create an array with [ Interval ] sampling. using DimensionalData \n\n ds = X ([ \"one\" , \"two\" , \"three\" ]), Y ([ :a , :b , :c , :d ]) \n A = DimArray ( rand ( 3 , 4 ), ds ) \n Dimensions . lookup ( A ) \n\n # output \n\n Categorical { String } String [ \"one\" , \"two\" , \"three\" ] Unordered , \n Categorical { Symbol } Symbol [ :a , :b , :c , :d ] ForwardOrdered \n source # DimensionalData.Dimensions.LookupArrays.Unaligned — Type . Unaligned <: LookupArray \n Abstract supertype for LookupArray where the index is not aligned to the grid. Indexing an Unaligned with Selector s must provide all other Unaligned dimensions. source # DimensionalData.Dimensions.LookupArrays.Transformed — Type . Transformed <: Unaligned \n\n Transformed ( f , dim :: Dimension ; metadata = NoMetadata ()) \n LookupArray that uses an affine transformation to convert dimensions from dims(lookup) to dims(array) . This can be useful when the dimensions are e.g. rotated from a more commonly used axis. Any function can be used to do the transformation, but transformations from CoordinateTransformations.jl may be useful. Arguments f : transformation function dim : a dimension to transform to. Keyword Arguments metdata : Example using DimensionalData , DimensionalData . LookupArrays , CoordinateTransformations \n\n m = LinearMap ([ 0.5 0.0 ; 0.0 0.5 ]) \n A = [ 1 2 3 4 \n 5 6 7 8 \n 9 10 11 12 ]; \n da = DimArray ( A , ( t1 = Transformed ( m , X ), t2 = Transformed ( m , Y ))) \n\n da [ X ( At ( 6 )), Y ( At ( 2 ))] \n\n # output \n 9 \n source # DimensionalData.Dimensions.MergedLookup — Type . MergedLookup <: LookupArray \n\n MergedLookup ( data , dims ; [ metadata ]) \n A LookupArray that holds multiple combined dimensions. MergedLookup can be indexed with Selector s like At , Between , and Where although Near has undefined meaning. Arguments data : A Vector of Tuple . dims : A Tuple of Dimension indicating the dimensions in the tuples in data . Keywords metadata : a Dict or Metadata object to attach dimension metadata. source # DimensionalData.Dimensions.LookupArrays.NoLookup — Type . NoLookup <: LookupArray \n\n NoLookup () \n A LookupArray that is identical to the array axis. Selector s can't be used on this lookup. Example Defining a DimArray without passing an index to the dimensions, it will be assigned NoLookup : using DimensionalData \n\n A = DimArray ( rand ( 3 , 3 ), ( X , Y )) \n Dimensions . lookup ( A ) \n\n # output \n\n NoLookup , NoLookup \n Which is identical to: using . LookupArrays \n A = DimArray ( rand ( 3 , 3 ), ( X ( NoLookup ()), Y ( NoLookup ()))) \n Dimensions . lookup ( A ) \n\n # output \n\n NoLookup , NoLookup \n source # DimensionalData.Dimensions.LookupArrays.AutoLookup — Type . AutoLookup <: LookupArray \n\n AutoLookup () \n AutoLookup ( index = AutoIndex (); kw ... ) \n Automatic LookupArray , the default lookup. It will be converted automatically to another LookupArray when it is possible to detect it from the index. Keywords will be used in the detected LookupArray constructor. source # DimensionalData.Dimensions.LookupArrays.AutoIndex — Type . AutoIndex \n Detect a LookupArray index from the context. This is used in NoLookup to simply use the array axis as the index when the array is constructed, and in set to change the LookupArray type without changing the index values. source"},{"id":386,"pagetitle":"Reference - DimensionalData.jl","title":"Metadata ¤","ref":"/DimensionalData/stable/reference/#metadata","content":" Metadata ¤ # DimensionalData.Dimensions.LookupArrays.AbstractMetadata — Type . AbstractMetadata { X , T } \n Abstract supertype for all metadata wrappers. Metadata wrappers allow tracking the contents and origin of metadata. This can facilitate conversion between metadata types (for saving a file to a differenet format) or simply saving data back to the same file type with identical metadata. Using a wrapper instead of Dict or NamedTuple also lets us pass metadata objects to set without ambiguity about where to put them. source # DimensionalData.Dimensions.LookupArrays.Metadata — Type . Metadata <: AbstractMetadata \n\n Metadata { X }( val :: Union { Dict , NamedTuple }) \n Metadata { X }( pairs :: Pair ... ) => Metadata { Dict } \n Metadata { X }(; kw ... ) => Metadata { NamedTuple } \n General Metadata object. The X type parameter categorises the metadata for method dispatch, if required. source # DimensionalData.Dimensions.LookupArrays.NoMetadata — Type . NoMetadata <: AbstractMetadata \n\n NoMetadata () \n Indicates an object has no metadata. But unlike using nothing , get , keys and haskey will still work on it, get always returning the fallback argument. keys returns () while haskey always returns false . source"},{"id":387,"pagetitle":"Reference - DimensionalData.jl","title":"LookupArray traits ¤","ref":"/DimensionalData/stable/reference/#lookuparray-traits","content":" LookupArray traits ¤ # DimensionalData.Dimensions.LookupArrays.LookupArrayTrait — Type . LookupArrayTrait \n Abstract supertype of all traits of a LookupArray . These modify the behaviour of the lookup index. The term \"Trait\" is used loosely - these may be fields of an object of traits hard-coded to specific types. source"},{"id":388,"pagetitle":"Reference - DimensionalData.jl","title":"Order ¤","ref":"/DimensionalData/stable/reference/#order","content":" Order ¤ # DimensionalData.Dimensions.LookupArrays.Order — Type . Order <: LookupArrayTrait \n Traits for the order of a LookupArray . These determine how searchsorted finds values in the index, and how objects are plotted. source # DimensionalData.Dimensions.LookupArrays.Ordered — Type . Ordered <: Order \n Supertype for the order of an ordered LookupArray , including ForwardOrdered and ReverseOrdered . source # DimensionalData.Dimensions.LookupArrays.ForwardOrdered — Type . ForwardOrdered <: Ordered \n\n ForwardOrdered () \n Indicates that the LookupArray index is in the normal forward order. source # DimensionalData.Dimensions.LookupArrays.ReverseOrdered — Type . ReverseOrdered <: Ordered \n\n ReverseOrdered () \n Indicates that the LookupArray index is in the reverse order. source # DimensionalData.Dimensions.LookupArrays.Unordered — Type . Unordered <: Order \n\n Unordered () \n Indicates that LookupArray is unordered. This means the index cannot be searched with searchsortedfirst or similar optimised methods - instead it will use findfirst . source # DimensionalData.Dimensions.LookupArrays.AutoOrder — Type . AutoOrder <: Order \n\n AutoOrder () \n Specifies that the Order of a LookupArray will be found automatically where possible. source"},{"id":389,"pagetitle":"Reference - DimensionalData.jl","title":"Span ¤","ref":"/DimensionalData/stable/reference/#span","content":" Span ¤ # DimensionalData.Dimensions.LookupArrays.Span — Type . Span <: LookupArrayTrait \n Defines the type of span used in a Sampling index. These are Regular or Irregular . source # DimensionalData.Dimensions.LookupArrays.Regular — Type . Regular <: Span \n\n Regular ( step = AutoStep ()) \n Points or Intervals that have a fixed, regular step. source # DimensionalData.Dimensions.LookupArrays.Irregular — Type . Irregular <: Span \n\n Irregular ( bounds :: Tuple ) \n Irregular ( lowerbound , upperbound ) \n Points or Intervals that have an Irrigular step size. To enable bounds tracking and accuract selectors, the starting bounds are provided as a 2 tuple, or 2 arguments. (nothing, nothing) is acceptable input, the bounds will be guessed from the index, but may be innaccurate. source # DimensionalData.Dimensions.LookupArrays.Explicit — Type . Explicit ( bounds :: AbstractMatix ) \n Intervals where the span is explicitly listed for every interval. This uses a matrix where with length 2 columns for each index value, holding the lower and upper bounds for that specific index. source # DimensionalData.Dimensions.LookupArrays.AutoSpan — Type . AutoSpan <: Span \n\n AutoSpan () \n The span will be guessed and replaced in format or set . source"},{"id":390,"pagetitle":"Reference - DimensionalData.jl","title":"Sampling ¤","ref":"/DimensionalData/stable/reference/#sampling","content":" Sampling ¤ # DimensionalData.Dimensions.LookupArrays.Sampling — Type . Sampling <: LookupArrayTrait \n Indicates the sampling method used by the index: Points or Intervals . source # DimensionalData.Dimensions.LookupArrays.Points — Type . Points <: Sampling \n\n Points () \n Sampling lookup where single samples at exact points. These are always plotted at the center of array cells. source # DimensionalData.Dimensions.LookupArrays.Intervals — Type . Intervals <: Sampling \n\n Intervals ( locus :: Locus ) \n Sampling specifying that sampled values are the mean (or similar) value over an interval , rather than at one specific point. Intervals require a Locus of Start , Center or End to define the location in the interval that the index values refer to. source"},{"id":391,"pagetitle":"Reference - DimensionalData.jl","title":"Loci ¤","ref":"/DimensionalData/stable/reference/#loci","content":" Loci ¤ # DimensionalData.Dimensions.LookupArrays.Locus — Type . Locus <: LookupArrayTrait Abstract supertype of types that indicate the position of index values where they represent Intervals . These allow for values array cells to align with the Start , Center , or End of values in the lookup index. This means they can be plotted with correct axis markers, and allows automatic converrsions to between formats with different standards (such as NetCDF and GeoTiff). source # DimensionalData.Dimensions.LookupArrays.Center — Type . Center <: Locus \n\n Center () \n Indicates a lookup value is for the center of its corresponding array cell. source # DimensionalData.Dimensions.LookupArrays.Start — Type . Start <: Locus \n\n Start () \n Indicates a lookup value is for the start of its corresponding array cell, in the direction of the lookup index order. source # DimensionalData.Dimensions.LookupArrays.End — Type . End <: Locus \n\n End () \n Indicates a lookup value is for the end of its corresponding array cell, in the direction of the lookup index order. source # DimensionalData.Dimensions.LookupArrays.AutoLocus — Type . AutoLocus <: Locus \n\n AutoLocus () \n Indicates a interval where the index position is not yet known. This will be filled with a default value on object construction. source"},{"id":392,"pagetitle":"Reference - DimensionalData.jl","title":"LookupArrays methods ¤","ref":"/DimensionalData/stable/reference/#lookuparrays-methods","content":" LookupArrays methods ¤ # DimensionalData.Dimensions.LookupArrays.hasselection — Function . hasselection ( x , selector ) => Bool \n hasselection ( x , selectors :: Tuple ) => Bool \n Check if indexing into x with selectors can be performed, where x is some object with a dims method, and selectors is a Selector or Dimension or a tuple of either. source # DimensionalData.Dimensions.LookupArrays.shiftlocus — Function . shiftlocus ( locus :: Locus , x ) \n Shift the index of x from the current locus to the new locus. We only shift Sampled , Regular or Explicit , Intervals . source # DimensionalData.Dimensions.LookupArrays.sampling — Function . sampling ( x , [ dims :: Tuple ]) => Tuple \n sampling ( x , dim ) => Sampling \n sampling ( xs :: Tuple ) => Tuple { Vararg { Sampling }} \n sampling ( x : Union { Dimension , LookupArray }) => Sampling \n Return the Sampling for each dimension. Second argument dims can be Dimension s, Dimension types, or Symbols for Dim{Symbol} . source # DimensionalData.Dimensions.LookupArrays.span — Function . span ( x , [ dims :: Tuple ]) => Tuple \n span ( x , dim ) => Span \n span ( xs :: Tuple ) => Tuple { Vararg { Span , N }} \n span ( x :: Union { Dimension , LookupArray }) => Span \n Return the Span for each dimension. Second argument dims can be Dimension s, Dimension types, or Symbols for Dim{Symbol} . source # DimensionalData.Dimensions.LookupArrays.order — Function . order ( x , [ dims :: Tuple ]) => Tuple \n order ( xs :: Tuple ) => Tuple \n order ( x :: Union { Dimension , LookupArray }) => Order \n Return the Ordering of the dimension index for each dimension: ForwardOrdered , ReverseOrdered , or Unordered Second argument dims can be Dimension s, Dimension types, or Symbols for Dim{Symbol} . source # DimensionalData.Dimensions.LookupArrays.index — Function . index ( x ) => Tuple { Vararg { AbstractArray }} \n index ( x , dims :: Tuple ) => Tuple { Vararg { AbstractArray }} \n index ( dims :: Tuple ) => Tuple { Vararg { AbstractArray }} } \n index ( x , dim ) => AbstractArray \n index ( dim :: Dimension ) => AbstractArray \n Return the contained index of a Dimension . Only valid when a Dimension contains an AbstractArray or a Val tuple like Val{(:a, :b)}() . The Val is unwrapped to return just the Tuple dims can be a Dimension , or a tuple of Dimension . source # DimensionalData.Dimensions.LookupArrays.locus — Function . locus ( x , [ dims :: Tuple ]) => Tuple \n locus ( x , dim ) => Locus \n locus ( xs :: Tuple ) => Tuple { Vararg { Locus , N }} \n locus ( x :: Union { Dimension , LookupArray }) => Locus \n Return the Locus for each dimension. Second argument dims can be Dimension s, Dimension types, or Symbols for Dim{Symbol} . source # DimensionalData.Dimensions.LookupArrays.units — Function . units ( x ) => Union { Nothing , Any } \n units ( xs : Tuple ) => Tuple \n unit ( A :: AbstractDimArray , dims :: Tuple ) => Tuple \n unit ( A :: AbstractDimArray , dim ) => Union { Nothing , Any } \n Get the units of an array or Dimension , or a tuple of of either. Units do not have a set field, and may or may not be included in metadata . This method is to facilitate use in labels and plots when units are available, not a guarantee that they will be. If not available, nothing is returned. Second argument dims can be Dimension s, Dimension types, or Symbols for Dim{Symbol} . source"},{"id":393,"pagetitle":"Reference - DimensionalData.jl","title":"Name ¤","ref":"/DimensionalData/stable/reference/#name","content":" Name ¤ # DimensionalData.AbstractName — Type . AbstractName \n Abstract supertype for name wrappers. source # DimensionalData.Name — Type . Name <: AbstractName \n\n Name ( name :: Union { Symbol , Name ) => Name \n Name ( name :: NoName ) => NoName \n Name wrapper. This lets arrays keep symbol names when the array wrapper neeeds to be `isbits, like for use on GPUs. It makes the name a property of the type. It's not necessary to use in normal use, a symbol is probably easier. source # DimensionalData.NoName — Type . NoName <: AbstractName \n\n NoName () \n NoName specifies an array is not named, and is the default name value for all AbstractDimArray s. source"}] \ No newline at end of file +[{"id":3,"pagetitle":"Home","title":"ArviZ.jl: Exploratory analysis of Bayesian models in Julia","ref":"/ArviZ/stable/#arvizjl","content":" ArviZ.jl: Exploratory analysis of Bayesian models in Julia ArviZ.jl is a Julia meta-package for exploratory analysis of Bayesian models. It is part of the ArviZ project , which also includes a related Python package . ArviZ consists of and re-exports the following subpackages, along with extensions integrating them with InferenceObjects: InferenceObjects.jl : a base package implementing the InferenceData type with utilities for building, saving, and working with it MCMCDiagnosticTools.jl : diagnostics for Markov Chain Monte Carlo methods PSIS.jl : Pareto-smoothed importance sampling PosteriorStats.jl : common statistical analyses for the Bayesian workflow Additional functionality can be loaded with the following packages: ArviZExampleData.jl : example InferenceData objects, useful for demonstration and testing ArviZPythonPlots.jl : Python ArviZ's library of plotting functions for Julia types See the navigation bar for more useful packages."},{"id":4,"pagetitle":"Home","title":"Installation","ref":"/ArviZ/stable/#installation","content":" Installation From the Julia REPL, type ] to enter the Pkg REPL mode and run pkg> add ArviZ"},{"id":5,"pagetitle":"Home","title":"Usage","ref":"/ArviZ/stable/#usage","content":" Usage See the Quickstart for example usage and the API Overview for description of functions."},{"id":6,"pagetitle":"Home","title":"Extending ArviZ.jl","ref":"/ArviZ/stable/#extendingarviz","content":" Extending ArviZ.jl To use a custom data type with ArviZ.jl, simply overload InferenceObjects.convert_to_inference_data to convert your input(s) to an InferenceObjects.InferenceData ."},{"id":9,"pagetitle":"API Overview","title":"API Overview","ref":"/ArviZ/stable/api/#api","content":" API Overview Data Dataset Diagnostics InferenceData Stats"},{"id":12,"pagetitle":"Data","title":"Data","ref":"/ArviZ/stable/api/data/#data-api","content":" Data ArviZ.from_mcmcchains ArviZ.from_samplechains InferenceObjects.from_netcdf InferenceObjects.to_netcdf"},{"id":13,"pagetitle":"Data","title":"Inference library converters","ref":"/ArviZ/stable/api/data/#Inference-library-converters","content":" Inference library converters"},{"id":14,"pagetitle":"Data","title":"ArviZ.from_mcmcchains","ref":"/ArviZ/stable/api/data/#ArviZ.from_mcmcchains","content":" ArviZ.from_mcmcchains — Function from_mcmcchains(posterior::MCMCChains.Chains; kwargs...) -> InferenceData\nfrom_mcmcchains(; kwargs...) -> InferenceData\nfrom_mcmcchains(\n posterior::MCMCChains.Chains,\n posterior_predictive,\n predictions,\n log_likelihood;\n kwargs...\n) -> InferenceData Convert data in an MCMCChains.Chains format into an InferenceData . Any keyword argument below without an an explicitly annotated type above is allowed, so long as it can be passed to convert_to_inference_data . Arguments posterior::MCMCChains.Chains : Draws from the posterior Keywords posterior_predictive::Any=nothing : Draws from the posterior predictive distribution or name(s) of predictive variables in posterior predictions : Out-of-sample predictions for the posterior. prior : Draws from the prior prior_predictive : Draws from the prior predictive distribution or name(s) of predictive variables in prior observed_data : Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values. constant_data : Model constants, data included in the model that are not modeled as random variables. Keys are parameter names. predictions_constant_data : Constants relevant to the model predictions (i.e. new x values in a linear regression). log_likelihood : Pointwise log-likelihood for the data. It is recommended to use this argument as a named tuple whose keys are observed variable names and whose values are log likelihood arrays. Alternatively, provide the name of variable in posterior containing log likelihoods. library=MCMCChains : Name of library that generated the chains coords : Map from named dimension to named indices dims : Map from variable name to names of its dimensions eltypes : Map from variable names to eltypes. This is primarily used to assign discrete eltypes to discrete variables that were stored in Chains as floats. Returns InferenceData : The data with groups corresponding to the provided data source"},{"id":15,"pagetitle":"Data","title":"ArviZ.from_samplechains","ref":"/ArviZ/stable/api/data/#ArviZ.from_samplechains","content":" ArviZ.from_samplechains — Function from_samplechains(\n posterior=nothing;\n prior=nothing,\n library=SampleChains,\n kwargs...,\n) -> InferenceData Convert SampleChains samples to an InferenceData . Either posterior or prior may be a SampleChains.AbstractChain or SampleChains.MultiChain object. For descriptions of remaining kwargs , see from_namedtuple . source"},{"id":16,"pagetitle":"Data","title":"IO / Conversion","ref":"/ArviZ/stable/api/data/#IO-/-Conversion","content":" IO / Conversion"},{"id":17,"pagetitle":"Data","title":"InferenceObjects.from_netcdf","ref":"/ArviZ/stable/api/data/#InferenceObjects.from_netcdf","content":" InferenceObjects.from_netcdf — Function from_netcdf(path::AbstractString; kwargs...) -> InferenceData Load an InferenceData from an unopened NetCDF file. Remaining kwargs are passed to NCDatasets.NCDataset . This method loads data eagerly. To instead load data lazily, pass an opened NCDataset to from_netcdf . Note This method requires that NCDatasets is loaded before it can be used. Examples julia> using InferenceObjects, NCDatasets\n\njulia> idata = from_netcdf(\"centered_eight.nc\")\nInferenceData with groups:\n > posterior\n > posterior_predictive\n > sample_stats\n > prior\n > observed_data from_netcdf(ds::NCDatasets.NCDataset; load_mode) -> InferenceData Load an InferenceData from an opened NetCDF file. load_mode defaults to :lazy , which avoids reading variables into memory. Operations on these arrays will be slow. load_mode can also be :eager , which copies all variables into memory. It is then safe to close ds . If load_mode is :lazy and ds is closed after constructing InferenceData , using the variable arrays will have undefined behavior. Examples Here is how we might load an InferenceData from an InferenceData lazily from a web-hosted NetCDF file. julia> using HTTP, InferenceObjects, NCDatasets\n\njulia> resp = HTTP.get(\"https://github.com/arviz-devs/arviz_example_data/blob/main/data/centered_eight.nc?raw=true\");\n\njulia> ds = NCDataset(\"centered_eight\", \"r\"; memory = resp.body);\n\njulia> idata = from_netcdf(ds)\nInferenceData with groups:\n > posterior\n > posterior_predictive\n > sample_stats\n > prior\n > observed_data\n\njulia> idata_copy = copy(idata); # disconnect from the loaded dataset\n\njulia> close(ds); source"},{"id":18,"pagetitle":"Data","title":"InferenceObjects.to_netcdf","ref":"/ArviZ/stable/api/data/#InferenceObjects.to_netcdf","content":" InferenceObjects.to_netcdf — Function to_netcdf(data, dest::AbstractString; group::Symbol=:posterior, kwargs...)\nto_netcdf(data, dest::NCDatasets.NCDataset; group::Symbol=:posterior) Write data to a NetCDF file. data is any type that can be converted to an InferenceData using convert_to_inference_data . If not an InferenceData , then group specifies which group the data represents. dest specifies either the path to the NetCDF file or an opened NetCDF file. If dest is a path, remaining kwargs are passed to NCDatasets.NCDataset . Note This method requires that NCDatasets is loaded before it can be used. Examples julia> using InferenceObjects, NCDatasets\n\njulia> idata = from_namedtuple((; x = randn(4, 100, 3), z = randn(4, 100)))\nInferenceData with groups:\n > posterior\n\njulia> to_netcdf(idata, \"data.nc\")\n\"data.nc\" source"},{"id":21,"pagetitle":"Dataset","title":"Dataset","ref":"/ArviZ/stable/api/dataset/#dataset-api","content":" Dataset InferenceObjects.Dataset InferenceObjects.convert_to_dataset InferenceObjects.namedtuple_to_dataset"},{"id":22,"pagetitle":"Dataset","title":"Type definition","ref":"/ArviZ/stable/api/dataset/#Type-definition","content":" Type definition"},{"id":23,"pagetitle":"Dataset","title":"InferenceObjects.Dataset","ref":"/ArviZ/stable/api/dataset/#InferenceObjects.Dataset","content":" InferenceObjects.Dataset — Type Dataset{L} <: DimensionalData.AbstractDimStack{L} Container of dimensional arrays sharing some dimensions. This type is an DimensionalData.AbstractDimStack that implements the same interface as DimensionalData.DimStack and has identical usage. When a Dataset is passed to Python, it is converted to an xarray.Dataset without copying the data. That is, the Python object shares the same memory as the Julia object. However, if an xarray.Dataset is passed to Julia, its data must be copied. Constructors Dataset(data::DimensionalData.AbstractDimArray...)\nDataset(data::Tuple{Vararg{<:DimensionalData.AbstractDimArray}})\nDataset(data::NamedTuple{Keys,Vararg{<:DimensionalData.AbstractDimArray}})\nDataset(\n data::NamedTuple,\n dims::Tuple{Vararg{DimensionalData.Dimension}};\n metadata=DimensionalData.NoMetadata(),\n) In most cases, use convert_to_dataset to create a Dataset instead of directly using a constructor. source"},{"id":24,"pagetitle":"Dataset","title":"General conversion","ref":"/ArviZ/stable/api/dataset/#General-conversion","content":" General conversion"},{"id":25,"pagetitle":"Dataset","title":"InferenceObjects.convert_to_dataset","ref":"/ArviZ/stable/api/dataset/#InferenceObjects.convert_to_dataset","content":" InferenceObjects.convert_to_dataset — Function convert_to_dataset(obj; group = :posterior, kwargs...) -> Dataset Convert a supported object to a Dataset . In most cases, this function calls convert_to_inference_data and returns the corresponding group . source"},{"id":26,"pagetitle":"Dataset","title":"InferenceObjects.namedtuple_to_dataset","ref":"/ArviZ/stable/api/dataset/#InferenceObjects.namedtuple_to_dataset","content":" InferenceObjects.namedtuple_to_dataset — Function namedtuple_to_dataset(data; kwargs...) -> Dataset Convert NamedTuple mapping variable names to arrays to a Dataset . Any non-array values will be converted to a 0-dimensional array. Keywords attrs::AbstractDict{<:AbstractString} : a collection of metadata to attach to the dataset, in addition to defaults. Values should be JSON serializable. library::Union{String,Module} : library used for performing inference. Will be attached to the attrs metadata. dims : a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are: Symbol : dimension name Type{<:DimensionsionalData.Dimension} : dimension type DimensionsionalData.Dimension : dimension, potentially with indices Nothing : no dimension name provided, dimension name is automatically generated coords : a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated. source"},{"id":27,"pagetitle":"Dataset","title":"DimensionalData","ref":"/ArviZ/stable/api/dataset/#DimensionalData","content":" DimensionalData As a DimensionalData.AbstractDimStack , Dataset also implements the AbstractDimStack API and can be used like a DimStack . See DimensionalData's documentation for example usage."},{"id":28,"pagetitle":"Dataset","title":"Tables inteface","ref":"/ArviZ/stable/api/dataset/#Tables-inteface","content":" Tables inteface Dataset implements the Tables interface. This allows Dataset s to be used as sources for any function that can accept a table. For example, it's straightforward to: write to CSV with CSV.jl flatten to a DataFrame with DataFrames.jl plot with StatsPlots.jl plot with AlgebraOfGraphics.jl"},{"id":31,"pagetitle":"Diagnostics","title":"Diagnostics","ref":"/ArviZ/stable/api/diagnostics/#diagnostics-api","content":" Diagnostics MCMCDiagnosticTools.AutocovMethod MCMCDiagnosticTools.BDAAutocovMethod MCMCDiagnosticTools.FFTAutocovMethod MCMCDiagnosticTools.bfmi MCMCDiagnosticTools.ess MCMCDiagnosticTools.ess_rhat MCMCDiagnosticTools.mcse MCMCDiagnosticTools.rhat MCMCDiagnosticTools.rstar"},{"id":32,"pagetitle":"Diagnostics","title":"Bayesian fraction of missing information","ref":"/ArviZ/stable/api/diagnostics/#bfmi","content":" Bayesian fraction of missing information"},{"id":33,"pagetitle":"Diagnostics","title":"MCMCDiagnosticTools.bfmi","ref":"/ArviZ/stable/api/diagnostics/#MCMCDiagnosticTools.bfmi","content":" MCMCDiagnosticTools.bfmi — Function bfmi(energy::AbstractVector{<:Real}) -> Real\nbfmi(energy::AbstractMatrix{<:Real}; dims::Int=1) -> AbstractVector{<:Real} Calculate the estimated Bayesian fraction of missing information (BFMI). When sampling with Hamiltonian Monte Carlo (HMC), BFMI quantifies how well momentum resampling matches the marginal energy distribution. The current advice is that values smaller than 0.3 indicate poor sampling. However, this threshold is provisional and may change. A BFMI value below the threshold often indicates poor adaptation of sampling parameters or that the target distribution has heavy tails that were not well explored by the Markov chain. For more information, see Section 6.1 of [Betancourt2018] or [Betancourt2016] for a complete account. energy is either a vector of Hamiltonian energies of draws or a matrix of energies of draws for multiple chains. dims indicates the dimension in energy that contains the draws. The default dims=1 assumes energy has the shape draws or (draws, chains) . If a different shape is provided, dims must be set accordingly. If energy is a vector, a single BFMI value is returned. Otherwise, a vector of BFMI values for each chain is returned. source"},{"id":34,"pagetitle":"Diagnostics","title":"Effective sample size and $\\widehat{R}$ diagnostic","ref":"/ArviZ/stable/api/diagnostics/#ess_rhat","content":" Effective sample size and $\\widehat{R}$ diagnostic"},{"id":35,"pagetitle":"Diagnostics","title":"MCMCDiagnosticTools.ess","ref":"/ArviZ/stable/api/diagnostics/#MCMCDiagnosticTools.ess","content":" MCMCDiagnosticTools.ess — Function ess(\n samples::AbstractArray{<:Union{Missing,Real}};\n kind=:bulk,\n relative::Bool=false,\n autocov_method=AutocovMethod(),\n split_chains::Int=2,\n maxlag::Int=250,\n kwargs...\n) Estimate the effective sample size (ESS) of the samples of shape (draws, [chains[, parameters...]]) with the autocov_method . Optionally, the kind of ESS estimate to be computed can be specified (see below). Some kind s accept additional kwargs . If relative is true , the relative ESS is returned, i.e. ess / (draws * chains) . split_chains indicates the number of chains each chain is split into. When split_chains > 1 , then the diagnostics check for within-chain convergence. When d = mod(draws, split_chains) > 0 , i.e. the chains cannot be evenly split, then 1 draw is discarded after each of the first d splits within each chain. There must be at least 3 draws in each chain after splitting. maxlag indicates the maximum lag for which autocovariance is computed and must be greater than 0. For a given estimand, it is recommended that the ESS is at least 100 * chains and that $\\widehat{R} < 1.01$ . [VehtariGelman2021] See also: AutocovMethod , FFTAutocovMethod , BDAAutocovMethod , rhat , ess_rhat , mcse Kinds of ESS estimates If kind isa a Symbol , it may take one of the following values: :bulk : basic ESS computed on rank-normalized draws. This kind diagnoses poor convergence in the bulk of the distribution due to trends or different locations of the chains. :tail : minimum of the quantile-ESS for the symmetric quantiles where tail_prob=0.1 is the probability in the tails. This kind diagnoses poor convergence in the tails of the distribution. If this kind is chosen, kwargs may contain a tail_prob keyword. :basic : basic ESS, equivalent to specifying kind=Statistics.mean . Note While Bulk-ESS is conceptually related to basic ESS, it is well-defined even if the chains do not have finite variance. [VehtariGelman2021] For each parameter, rank-normalization proceeds by first ranking the inputs using \"tied ranking\" and then transforming the ranks to normal quantiles so that the result is standard normally distributed. This transform is monotonic. Otherwise, kind specifies one of the following estimators, whose ESS is to be estimated: Statistics.mean Statistics.median Statistics.std StatsBase.mad Base.Fix2(Statistics.quantile, p::Real) source ess(data::InferenceData; kwargs...) -> Dataset\ness(data::Dataset; kwargs...) -> Dataset Calculate the effective sample size (ESS) for each parameter in the data. source"},{"id":36,"pagetitle":"Diagnostics","title":"MCMCDiagnosticTools.rhat","ref":"/ArviZ/stable/api/diagnostics/#MCMCDiagnosticTools.rhat","content":" MCMCDiagnosticTools.rhat — Function rhat(samples::AbstractArray{Union{Real,Missing}}; kind::Symbol=:rank, split_chains=2) Compute the $\\widehat{R}$ diagnostics for each parameter in samples of shape (draws, [chains[, parameters...]]) . [VehtariGelman2021] kind indicates the kind of $\\widehat{R}$ to compute (see below). split_chains indicates the number of chains each chain is split into. When split_chains > 1 , then the diagnostics check for within-chain convergence. When d = mod(draws, split_chains) > 0 , i.e. the chains cannot be evenly split, then 1 draw is discarded after each of the first d splits within each chain. See also ess , ess_rhat , rstar Kinds of $\\widehat{R}$ The following kind s are supported: :rank : maximum of $\\widehat{R}$ with kind=:bulk and kind=:tail . :bulk : basic $\\widehat{R}$ computed on rank-normalized draws. This kind diagnoses poor convergence in the bulk of the distribution due to trends or different locations of the chains. :tail : $\\widehat{R}$ computed on draws folded around the median and then rank-normalized. This kind diagnoses poor convergence in the tails of the distribution due to different scales of the chains. :basic : Classic $\\widehat{R}$ . source rhat(data::InferenceData; kwargs...) -> Dataset\nrhat(data::Dataset; kwargs...) -> Dataset Calculate the $\\widehat{R}$ diagnostic for each parameter in the data. source"},{"id":37,"pagetitle":"Diagnostics","title":"MCMCDiagnosticTools.ess_rhat","ref":"/ArviZ/stable/api/diagnostics/#MCMCDiagnosticTools.ess_rhat","content":" MCMCDiagnosticTools.ess_rhat — Function ess_rhat(\n samples::AbstractArray{<:Union{Missing,Real}};\n kind::Symbol=:rank,\n kwargs...,\n) -> NamedTuple{(:ess, :rhat)} Estimate the effective sample size and $\\widehat{R}$ of the samples of shape (draws, [chains[, parameters...]]) . When both ESS and $\\widehat{R}$ are needed, this method is often more efficient than calling ess and rhat separately. See rhat for a description of supported kind s and ess for a description of kwargs . source ess_rhat(data::InferenceData; kwargs...) -> Dataset\ness_rhat(data::Dataset; kwargs...) -> Dataset Calculate the effective sample size (ESS) and $\\widehat{R}$ diagnostic for each parameter in the data. source The following autocovariance methods are supported:"},{"id":38,"pagetitle":"Diagnostics","title":"MCMCDiagnosticTools.AutocovMethod","ref":"/ArviZ/stable/api/diagnostics/#MCMCDiagnosticTools.AutocovMethod","content":" MCMCDiagnosticTools.AutocovMethod — Type AutocovMethod <: AbstractAutocovMethod The AutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains. It is is based on the discussion by [VehtariGelman2021] and uses the biased estimator of the autocovariance, as discussed by [Geyer1992] . source"},{"id":39,"pagetitle":"Diagnostics","title":"MCMCDiagnosticTools.FFTAutocovMethod","ref":"/ArviZ/stable/api/diagnostics/#MCMCDiagnosticTools.FFTAutocovMethod","content":" MCMCDiagnosticTools.FFTAutocovMethod — Type FFTAutocovMethod <: AbstractAutocovMethod The FFTAutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains. The algorithm is the same as the one of AutocovMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation. Info To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl . source"},{"id":40,"pagetitle":"Diagnostics","title":"MCMCDiagnosticTools.BDAAutocovMethod","ref":"/ArviZ/stable/api/diagnostics/#MCMCDiagnosticTools.BDAAutocovMethod","content":" MCMCDiagnosticTools.BDAAutocovMethod — Type BDAAutocovMethod <: AbstractAutocovMethod The BDAAutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains. It is is based on the discussion by [VehtariGelman2021] . and uses the variogram estimator of the autocorrelation function discussed by [BDA3] . source"},{"id":41,"pagetitle":"Diagnostics","title":"Monte Carlo standard error","ref":"/ArviZ/stable/api/diagnostics/#mcse","content":" Monte Carlo standard error"},{"id":42,"pagetitle":"Diagnostics","title":"MCMCDiagnosticTools.mcse","ref":"/ArviZ/stable/api/diagnostics/#MCMCDiagnosticTools.mcse","content":" MCMCDiagnosticTools.mcse — Function mcse(samples::AbstractArray{<:Union{Missing,Real}}; kind=Statistics.mean, kwargs...) Estimate the Monte Carlo standard errors (MCSE) of the estimator kind applied to samples of shape (draws, [chains[, parameters...]]) . See also: ess Kinds of MCSE estimates The estimator whose MCSE should be estimated is specified with kind . kind must accept a vector of the same eltype as samples and return a real estimate. For the following estimators, the effective sample size ess and an estimate of the asymptotic variance are used to compute the MCSE, and kwargs are forwarded to ess : Statistics.mean Statistics.median Statistics.std Base.Fix2(Statistics.quantile, p::Real) For other estimators, the subsampling bootstrap method (SBM) [FlegalJones2011] [Flegal2012] is used as a fallback, and the only accepted kwargs are batch_size , which indicates the size of the overlapping batches used to estimate the MCSE, defaulting to floor(Int, sqrt(draws * chains)) . Note that SBM tends to underestimate the MCSE, especially for highly autocorrelated chains. One should verify that autocorrelation is low by checking the bulk- and tail-ESS values. source mcse(data::InferenceData; kwargs...) -> Dataset\nmcse(data::Dataset; kwargs...) -> Dataset Calculate the Monte Carlo standard error (MCSE) for each parameter in the data. source"},{"id":43,"pagetitle":"Diagnostics","title":"$R^*$ diagnostic","ref":"/ArviZ/stable/api/diagnostics/#rstar","content":" $R^*$ diagnostic"},{"id":44,"pagetitle":"Diagnostics","title":"MCMCDiagnosticTools.rstar","ref":"/ArviZ/stable/api/diagnostics/#MCMCDiagnosticTools.rstar","content":" MCMCDiagnosticTools.rstar — Function rstar(\n rng::Random.AbstractRNG=Random.default_rng(),\n classifier,\n samples,\n chain_indices::AbstractVector{Int};\n subset::Real=0.7,\n split_chains::Int=2,\n verbosity::Int=0,\n) Compute the $R^*$ convergence statistic of the table samples with the classifier . samples must be either an AbstractMatrix , an AbstractVector , or a table (i.e. implements the Tables.jl interface) whose rows are draws and whose columns are parameters. chain_indices indicates the chain ids of each row of samples . This method supports ragged chains, i.e. chains of nonequal lengths. source rstar(\n rng::Random.AbstractRNG=Random.default_rng(),\n classifier,\n samples::AbstractArray{<:Real};\n subset::Real=0.7,\n split_chains::Int=2,\n verbosity::Int=0,\n) Compute the $R^*$ convergence statistic of the samples with the classifier . samples is an array of draws with the shape (draws, [chains[, parameters...]]) .` This implementation is an adaption of algorithms 1 and 2 described by Lambert and Vehtari. The classifier has to be a supervised classifier of the MLJ framework (see the MLJ documentation for a list of supported models). It is trained with a subset of the samples from each chain. Each chain is split into split_chains separate chains to additionally check for within-chain convergence. The training of the classifier can be inspected by adjusting the verbosity level. If the classifier is deterministic, i.e., if it predicts a class, the value of the $R^*$ statistic is returned (algorithm 1). If the classifier is probabilistic, i.e., if it outputs probabilities of classes, the scaled Poisson-binomial distribution of the $R^*$ statistic is returned (algorithm 2). Note The correctness of the statistic depends on the convergence of the classifier used internally in the statistic. Examples julia> using MLJBase, MLJIteration, EvoTrees, Statistics, StatisticalMeasures\n\njulia> samples = fill(4.0, 100, 3, 2); One can compute the distribution of the $R^*$ statistic (algorithm 2) with a probabilistic classifier. For instance, we can use a gradient-boosted trees model with nrounds = 100 sequentially stacked trees and learning rate eta = 0.05 : julia> model = EvoTreeClassifier(; nrounds=100, eta=0.05);\n\njulia> distribution = rstar(model, samples);\n\njulia> round(mean(distribution); digits=2)\n1.0f0 Note, however, that it is recommended to determine nrounds based on early-stopping. With the MLJ framework, this can be achieved in the following way (see the MLJ documentation for additional explanations): julia> model = IteratedModel(;\n model=EvoTreeClassifier(; eta=0.05),\n iteration_parameter=:nrounds,\n resampling=Holdout(),\n measures=log_loss,\n controls=[Step(5), Patience(2), NumberLimit(100)],\n retrain=true,\n );\n\njulia> distribution = rstar(model, samples);\n\njulia> round(mean(distribution); digits=2)\n1.0f0 For deterministic classifiers, a single $R^*$ statistic (algorithm 1) is returned. Deterministic classifiers can also be derived from probabilistic classifiers by e.g. predicting the mode. In MLJ this corresponds to a pipeline of models. julia> evotree_deterministic = Pipeline(model; operation=predict_mode);\n\njulia> value = rstar(evotree_deterministic, samples);\n\njulia> round(value; digits=2)\n1.0 References Lambert, B., & Vehtari, A. (2020). $R^*$ : A robust MCMC convergence diagnostic with uncertainty using decision tree classifiers. source rstar(\n rng::Random.AbstractRNG=Random.default_rng(),\n classifier,\n data::Union{InferenceData,Dataset};\n kwargs...,\n) Calculate the $R^*$ diagnostic for the data. source Betancourt2018 Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME] Betancourt2016 Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME] VehtariGelman2021 Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008 VehtariGelman2021 Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008 VehtariGelman2021 Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008 Geyer1992 Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483. VehtariGelman2021 Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008 BDA3 Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press. FlegalJones2011 Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf Flegal2012 Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18"},{"id":47,"pagetitle":"InferenceData","title":"InferenceData","ref":"/ArviZ/stable/api/inference_data/#inferencedata-api","content":" InferenceData InferenceObjects.InferenceData Base.cat Base.getindex Base.getproperty Base.merge Base.propertynames Base.setindex InferenceObjects.convert_to_inference_data InferenceObjects.from_dict InferenceObjects.from_namedtuple"},{"id":48,"pagetitle":"InferenceData","title":"Type definition","ref":"/ArviZ/stable/api/inference_data/#Type-definition","content":" Type definition"},{"id":49,"pagetitle":"InferenceData","title":"InferenceObjects.InferenceData","ref":"/ArviZ/stable/api/inference_data/#InferenceObjects.InferenceData","content":" InferenceObjects.InferenceData — Type InferenceData{group_names,group_types} Container for inference data storage using DimensionalData. This object implements the InferenceData schema . Internally, groups are stored in a NamedTuple , which can be accessed using parent(::InferenceData) . Constructors InferenceData(groups::NamedTuple)\nInferenceData(; groups...) Construct an inference data from either a NamedTuple or keyword arguments of groups. Groups must be Dataset objects. Instead of directly creating an InferenceData , use the exported from_xyz functions or convert_to_inference_data . source"},{"id":50,"pagetitle":"InferenceData","title":"Property interface","ref":"/ArviZ/stable/api/inference_data/#Property-interface","content":" Property interface"},{"id":51,"pagetitle":"InferenceData","title":"Base.getproperty","ref":"/ArviZ/stable/api/inference_data/#Base.getproperty","content":" Base.getproperty — Function getproperty(data::InferenceData, name::Symbol) -> Dataset Get group with the specified name . source"},{"id":52,"pagetitle":"InferenceData","title":"Base.propertynames","ref":"/ArviZ/stable/api/inference_data/#Base.propertynames","content":" Base.propertynames — Function propertynames(data::InferenceData) -> Tuple{Symbol} Get names of groups source"},{"id":53,"pagetitle":"InferenceData","title":"Indexing interface","ref":"/ArviZ/stable/api/inference_data/#Indexing-interface","content":" Indexing interface"},{"id":54,"pagetitle":"InferenceData","title":"Base.getindex","ref":"/ArviZ/stable/api/inference_data/#Base.getindex","content":" Base.getindex — Function Base.getindex(data::InferenceData, groups::Symbol; coords...) -> Dataset\nBase.getindex(data::InferenceData, groups; coords...) -> InferenceData Return a new InferenceData containing the specified groups sliced to the specified coords. coords specifies a dimension name mapping to an index, a DimensionalData.Selector , or an IntervalSets.AbstractInterval . If one or more groups lack the specified dimension, a warning is raised but can be ignored. All groups that contain the dimension must also contain the specified indices, or an exception will be raised. Examples Select data from all groups for just the specified id values. julia> using InferenceObjects, DimensionalData\n\njulia> idata = from_namedtuple(\n (θ=randn(4, 100, 4), τ=randn(4, 100));\n prior=(θ=randn(4, 100, 4), τ=randn(4, 100)),\n observed_data=(y=randn(4),),\n dims=(θ=[:id], y=[:id]),\n coords=(id=[\"a\", \"b\", \"c\", \"d\"],),\n )\nInferenceData with groups:\n > posterior\n > prior\n > observed_data\n\njulia> idata.posterior\nDataset with dimensions:\n Dim{:chain} Sampled 1:4 ForwardOrdered Regular Points,\n Dim{:draw} Sampled 1:100 ForwardOrdered Regular Points,\n Dim{:id} Categorical String[a, b, c, d] ForwardOrdered\nand 2 layers:\n :θ Float64 dims: Dim{:chain}, Dim{:draw}, Dim{:id} (4×100×4)\n :τ Float64 dims: Dim{:chain}, Dim{:draw} (4×100)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2022-08-11T11:15:21.4\"\n\njulia> idata_sel = idata[id=At([\"a\", \"b\"])]\nInferenceData with groups:\n > posterior\n > prior\n > observed_data\n\njulia> idata_sel.posterior\nDataset with dimensions:\n Dim{:chain} Sampled 1:4 ForwardOrdered Regular Points,\n Dim{:draw} Sampled 1:100 ForwardOrdered Regular Points,\n Dim{:id} Categorical String[a, b] ForwardOrdered\nand 2 layers:\n :θ Float64 dims: Dim{:chain}, Dim{:draw}, Dim{:id} (4×100×2)\n :τ Float64 dims: Dim{:chain}, Dim{:draw} (4×100)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2022-08-11T11:15:21.4\" Select data from just the posterior, returning a Dataset if the indices index more than one element from any of the variables: julia> idata[:observed_data, id=At([\"a\"])]\nDataset with dimensions:\n Dim{:id} Categorical String[a] ForwardOrdered\nand 1 layer:\n :y Float64 dims: Dim{:id} (1)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2022-08-11T11:19:25.982\" Note that if a single index is provided, the behavior is still to slice so that the dimension is preserved. source"},{"id":55,"pagetitle":"InferenceData","title":"Base.setindex","ref":"/ArviZ/stable/api/inference_data/#Base.setindex","content":" Base.setindex — Function Base.setindex(data::InferenceData, group::Dataset, name::Symbol) -> InferenceData Create a new InferenceData containing the group with the specified name . If a group with name is already in data , it is replaced. source"},{"id":56,"pagetitle":"InferenceData","title":"Iteration interface","ref":"/ArviZ/stable/api/inference_data/#Iteration-interface","content":" Iteration interface InferenceData also implements the same iteration interface as its underlying NamedTuple . That is, iterating over an InferenceData iterates over its groups."},{"id":57,"pagetitle":"InferenceData","title":"General conversion","ref":"/ArviZ/stable/api/inference_data/#General-conversion","content":" General conversion"},{"id":58,"pagetitle":"InferenceData","title":"InferenceObjects.convert_to_inference_data","ref":"/ArviZ/stable/api/inference_data/#InferenceObjects.convert_to_inference_data","content":" InferenceObjects.convert_to_inference_data — Function convert_to_inference_data(obj; group, kwargs...) -> InferenceData Convert a supported object to an InferenceData object. If obj converts to a single dataset, group specifies which dataset in the resulting InferenceData that is. See convert_to_dataset Arguments obj can be many objects. Basic supported types are: InferenceData : return unchanged Dataset / DimensionalData.AbstractDimStack : add to InferenceData as the only group NamedTuple / AbstractDict : create a Dataset as the only group AbstractArray{<:Real} : create a Dataset as the only group, given an arbitrary name, if the name is not set More specific types may be documented separately. Keywords group::Symbol = :posterior : If obj converts to a single dataset, assign the resulting dataset to this group. dims : a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are: Symbol : dimension name Type{<:DimensionsionalData.Dimension} : dimension type DimensionsionalData.Dimension : dimension, potentially with indices Nothing : no dimension name provided, dimension name is automatically generated coords : a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated. kwargs : remaining keywords forwarded to converter functions source"},{"id":59,"pagetitle":"InferenceData","title":"InferenceObjects.from_dict","ref":"/ArviZ/stable/api/inference_data/#InferenceObjects.from_dict","content":" InferenceObjects.from_dict — Function from_dict(posterior::AbstractDict; kwargs...) -> InferenceData Convert a Dict to an InferenceData . Arguments posterior : The data to be converted. Its strings must be Symbol or AbstractString , and its values must be arrays. Keywords posterior_predictive::Any=nothing : Draws from the posterior predictive distribution sample_stats::Any=nothing : Statistics of the posterior sampling process predictions::Any=nothing : Out-of-sample predictions for the posterior. prior::Dict=nothing : Draws from the prior prior_predictive::Any=nothing : Draws from the prior predictive distribution sample_stats_prior::Any=nothing : Statistics of the prior sampling process observed_data::NamedTuple : Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values. constant_data::NamedTuple : Model constants, data included in the model which is not modeled as a random variable. Keys are parameter names and values. predictions_constant_data::NamedTuple : Constants relevant to the model predictions (i.e. new x values in a linear regression). log_likelihood : Pointwise log-likelihood for the data. It is recommended to use this argument as a NamedTuple whose keys are observed variable names and whose values are log likelihood arrays. library : Name of library that generated the draws coords : Map from named dimension to named indices dims : Map from variable name to names of its dimensions Returns InferenceData : The data with groups corresponding to the provided data Examples using InferenceObjects\nnchains = 2\nndraws = 100\n\ndata = Dict(\n :x => rand(ndraws, nchains),\n :y => randn(2, ndraws, nchains),\n :z => randn(3, 2, ndraws, nchains),\n)\nidata = from_dict(data) source"},{"id":60,"pagetitle":"InferenceData","title":"InferenceObjects.from_namedtuple","ref":"/ArviZ/stable/api/inference_data/#InferenceObjects.from_namedtuple","content":" InferenceObjects.from_namedtuple — Function from_namedtuple(posterior::NamedTuple; kwargs...) -> InferenceData\nfrom_namedtuple(posterior::Vector{Vector{<:NamedTuple}}; kwargs...) -> InferenceData\nfrom_namedtuple(\n posterior::NamedTuple,\n sample_stats::Any,\n posterior_predictive::Any,\n predictions::Any,\n log_likelihood::Any;\n kwargs...\n) -> InferenceData Convert a NamedTuple or container of NamedTuple s to an InferenceData . If containers are passed, they are flattened into a single NamedTuple with array elements whose first dimensions correspond to the dimensions of the containers. Arguments posterior : The data to be converted. It may be of the following types: ::NamedTuple : The keys are the variable names and the values are arrays with dimensions (ndraws, nchains[, sizes...]) . ::Vector{Vector{<:NamedTuple}} : A vector of length nchains whose elements have length ndraws . Keywords posterior_predictive::Any=nothing : Draws from the posterior predictive distribution sample_stats::Any=nothing : Statistics of the posterior sampling process predictions::Any=nothing : Out-of-sample predictions for the posterior. prior=nothing : Draws from the prior. Accepts the same types as posterior . prior_predictive::Any=nothing : Draws from the prior predictive distribution sample_stats_prior::Any=nothing : Statistics of the prior sampling process observed_data::NamedTuple : Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values. constant_data::NamedTuple : Model constants, data included in the model which is not modeled as a random variable. Keys are parameter names and values. predictions_constant_data::NamedTuple : Constants relevant to the model predictions (i.e. new x values in a linear regression). log_likelihood : Pointwise log-likelihood for the data. It is recommended to use this argument as a NamedTuple whose keys are observed variable names and whose values are log likelihood arrays. library : Name of library that generated the draws coords : Map from named dimension to named indices dims : Map from variable name to names of its dimensions Returns InferenceData : The data with groups corresponding to the provided data Note If a NamedTuple is provided for observed_data , constant_data , or predictions constant data`, any non-array values (e.g. integers) are converted to 0-dimensional arrays. Examples using InferenceObjects\nnchains = 2\nndraws = 100\n\ndata1 = (\n x=rand(ndraws, nchains), y=randn(ndraws, nchains, 2), z=randn(ndraws, nchains, 3, 2)\n)\nidata1 = from_namedtuple(data1)\n\ndata2 = [[(x=rand(), y=randn(2), z=randn(3, 2)) for _ in 1:ndraws] for _ in 1:nchains];\nidata2 = from_namedtuple(data2) source"},{"id":61,"pagetitle":"InferenceData","title":"General functions","ref":"/ArviZ/stable/api/inference_data/#General-functions","content":" General functions"},{"id":62,"pagetitle":"InferenceData","title":"Base.cat","ref":"/ArviZ/stable/api/inference_data/#Base.cat","content":" Base.cat — Function cat(data::InferenceData...; [groups=keys(data[1]),] dims) -> InferenceData Concatenate InferenceData objects along the specified dimension dims . Only the groups in groups are concatenated. Remaining groups are merge d into the new InferenceData object. Examples Here is how we can concatenate all groups of two InferenceData objects along the existing chain dimension: julia> coords = (; a_dim=[\"x\", \"y\", \"z\"]);\n\njulia> dims = dims=(; a=[:a_dim]);\n\njulia> data = Dict(:a => randn(100, 4, 3), :b => randn(100, 4));\n\njulia> idata = from_dict(data; coords=coords, dims=dims)\nInferenceData with groups:\n > posterior\n\njulia> idata_cat1 = cat(idata, idata; dims=:chain)\nInferenceData with groups:\n > posterior\n\njulia> idata_cat1.posterior\nDataset with dimensions:\n Dim{:draw},\n Dim{:chain},\n Dim{:a_dim} Categorical{String} String[\"x\", \"y\", \"z\"] ForwardOrdered\nand 2 layers:\n :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim} (100×8×3)\n :b Float64 dims: Dim{:draw}, Dim{:chain} (100×8)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-04-03T18:41:35.779\" Alternatively, we can concatenate along a new run dimension, which will be created. julia> idata_cat2 = cat(idata, idata; dims=:run)\nInferenceData with groups:\n > posterior\n\njulia> idata_cat2.posterior\nDataset with dimensions:\n Dim{:draw},\n Dim{:chain},\n Dim{:a_dim} Categorical{String} String[\"x\", \"y\", \"z\"] ForwardOrdered,\n Dim{:run}\nand 2 layers:\n :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim}, Dim{:run} (100×4×3×2)\n :b Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:run} (100×4×2)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-04-03T18:41:35.779\" We can also concatenate only a subset of groups and merge the rest, which is useful when some groups are present only in some of the InferenceData objects or will be identical in all of them: julia> observed_data = Dict(:y => randn(10));\n\njulia> idata2 = from_dict(data; observed_data=observed_data, coords=coords, dims=dims)\nInferenceData with groups:\n > posterior\n > observed_data\n\njulia> idata_cat3 = cat(idata, idata2; groups=(:posterior,), dims=:run)\nInferenceData with groups:\n > posterior\n > observed_data\n\njulia> idata_cat3.posterior\nDataset with dimensions:\n Dim{:draw},\n Dim{:chain},\n Dim{:a_dim} Categorical{String} String[\"x\", \"y\", \"z\"] ForwardOrdered,\n Dim{:run}\nand 2 layers:\n :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim}, Dim{:run} (100×4×3×2)\n :b Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:run} (100×4×2)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-04-03T18:41:35.779\"\n\njulia> idata_cat3.observed_data\nDataset with dimensions: Dim{:y_dim_1}\nand 1 layer:\n :y Float64 dims: Dim{:y_dim_1} (10)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-02-17T15:11:00.59\" source"},{"id":63,"pagetitle":"InferenceData","title":"Base.merge","ref":"/ArviZ/stable/api/inference_data/#Base.merge","content":" Base.merge — Function merge(data::InferenceData...) -> InferenceData Merge InferenceData objects. The result contains all groups in data and others . If a group appears more than once, the one that occurs last is kept. See also: cat Examples Here we merge an InferenceData containing only a posterior group with one containing only a prior group to create a new one containing both groups. julia> idata1 = from_dict(Dict(:a => randn(100, 4, 3), :b => randn(100, 4)))\nInferenceData with groups:\n > posterior\n\njulia> idata2 = from_dict(; prior=Dict(:a => randn(100, 1, 3), :c => randn(100, 1)))\nInferenceData with groups:\n > prior\n\njulia> idata_merged = merge(idata1, idata2)\nInferenceData with groups:\n > posterior\n > prior source"},{"id":66,"pagetitle":"Stats","title":"Stats","ref":"/ArviZ/stable/api/stats/#stats-api","content":" Stats PSIS.PSISResult PosteriorStats.AbstractELPDResult PosteriorStats.AbstractModelWeightsMethod PosteriorStats.BootstrappedPseudoBMA PosteriorStats.ModelComparisonResult PosteriorStats.PSISLOOResult PosteriorStats.PseudoBMA PosteriorStats.Stacking PosteriorStats.SummaryStats PosteriorStats.WAICResult PSIS.PSISPlots.paretoshapeplot PSIS.ess_is PSIS.psis PSIS.psis! PosteriorStats.compare PosteriorStats.default_diagnostics PosteriorStats.default_stats PosteriorStats.default_summary_stats PosteriorStats.elpd_estimates PosteriorStats.hdi PosteriorStats.hdi! PosteriorStats.information_criterion PosteriorStats.loo PosteriorStats.loo_pit PosteriorStats.model_weights PosteriorStats.r2_score PosteriorStats.smooth_data PosteriorStats.summarize PosteriorStats.waic StatsBase.summarystats"},{"id":67,"pagetitle":"Stats","title":"Summary statistics","ref":"/ArviZ/stable/api/stats/#Summary-statistics","content":" Summary statistics"},{"id":68,"pagetitle":"Stats","title":"PosteriorStats.SummaryStats","ref":"/ArviZ/stable/api/stats/#PosteriorStats.SummaryStats","content":" PosteriorStats.SummaryStats — Type A container for a column table of values computed by summarize . This object implements the Tables and TableTraits interfaces and has a custom show method. name : The name of the collection of summary statistics, used as the table title in display. data : The summary statistics for each parameter, with an optional first column parameter containing the parameter names. source"},{"id":69,"pagetitle":"Stats","title":"PosteriorStats.default_summary_stats","ref":"/ArviZ/stable/api/stats/#PosteriorStats.default_summary_stats","content":" PosteriorStats.default_summary_stats — Function default_summary_stats(focus=Statistics.mean; kwargs...) Combinatiton of default_stats and default_diagnostics to be used with summarize . source"},{"id":70,"pagetitle":"Stats","title":"PosteriorStats.default_stats","ref":"/ArviZ/stable/api/stats/#PosteriorStats.default_stats","content":" PosteriorStats.default_stats — Function default_stats(focus=Statistics.mean; prob_interval=0.94, kwargs...) Default statistics to be computed with summarize . The value of focus determines the statistics to be returned: Statistics.mean : mean , std , hdi_3% , hdi_97% Statistics.median : median , mad , eti_3% , eti_97% If prob_interval is set to a different value than the default, then different HDI and ETI statistics are computed accordingly. hdi refers to the highest-density interval, while eti refers to the equal-tailed interval (i.e. the credible interval computed from symmetric quantiles). See also: hdi source"},{"id":71,"pagetitle":"Stats","title":"PosteriorStats.default_diagnostics","ref":"/ArviZ/stable/api/stats/#PosteriorStats.default_diagnostics","content":" PosteriorStats.default_diagnostics — Function default_diagnostics(focus=Statistics.mean; kwargs...) Default diagnostics to be computed with summarize . The value of focus determines the diagnostics to be returned: Statistics.mean : mcse_mean , mcse_std , ess_tail , ess_bulk , rhat Statistics.median : mcse_median , ess_tail , ess_bulk , rhat source"},{"id":72,"pagetitle":"Stats","title":"PosteriorStats.summarize","ref":"/ArviZ/stable/api/stats/#PosteriorStats.summarize","content":" PosteriorStats.summarize — Function summarize(data, stats_funs...; name=\"SummaryStats\", [var_names]) -> SummaryStats Compute the summary statistics in stats_funs on each param in data . stats_funs is a collection of functions that reduces a matrix with shape (draws, chains) to a scalar or a collection of scalars. Alternatively, an item in stats_funs may be a Pair of the form name => fun specifying the name to be used for the statistic or of the form (name1, ...) => fun when the function returns a collection. When the function returns a collection, the names in this latter format must be provided. If no stats functions are provided, then those specified in default_summary_stats are computed. var_names specifies the names of the parameters in data . If not provided, the names are inferred from data . To support computing summary statistics from a custom object, overload this method specifying the type of data . See also SummaryStats , default_summary_stats , default_stats , default_diagnostics . Examples Compute mean , std and the Monte Carlo standard error (MCSE) of the mean estimate: julia> using Statistics, StatsBase\n\njulia> x = randn(1000, 4, 3) .+ reshape(0:10:20, 1, 1, :);\n\njulia> summarize(x, mean, std, :mcse_mean => sem; name=\"Mean/Std\")\nMean/Std\n mean std mcse_mean\n 1 0.0003 0.990 0.016\n 2 10.02 0.988 0.016\n 3 19.98 0.988 0.016 Avoid recomputing the mean by using mean_and_std , and provide parameter names: julia> summarize(x, (:mean, :std) => mean_and_std, mad; var_names=[:a, :b, :c])\nSummaryStats\n mean std mad\n a 0.000305 0.990 0.978\n b 10.0 0.988 0.995\n c 20.0 0.988 0.979 Note that when an estimator and its MCSE are both computed, the MCSE is used to determine the number of significant digits that will be displayed. julia> summarize(x; var_names=[:a, :b, :c])\nSummaryStats\n mean std hdi_3% hdi_97% mcse_mean mcse_std ess_tail ess_bulk r ⋯\n a 0.0003 0.99 -1.92 1.78 0.016 0.012 3567 3663 1 ⋯\n b 10.02 0.99 8.17 11.9 0.016 0.011 3841 3906 1 ⋯\n c 19.98 0.99 18.1 21.9 0.016 0.012 3892 3749 1 ⋯\n 1 column omitted Compute just the statistics with an 89% HDI on all parameters, and provide the parameter names: julia> summarize(x, default_stats(; prob_interval=0.89)...; var_names=[:a, :b, :c])\nSummaryStats\n mean std hdi_5.5% hdi_94.5%\n a 0.000305 0.990 -1.63 1.52\n b 10.0 0.988 8.53 11.6\n c 20.0 0.988 18.5 21.6 Compute the summary stats focusing on Statistics.median : julia> summarize(x, default_summary_stats(median)...; var_names=[:a, :b, :c])\nSummaryStats\n median mad eti_3% eti_97% mcse_median ess_tail ess_median rhat\n a 0.004 0.978 -1.83 1.89 0.020 3567 3336 1.00\n b 10.02 0.995 8.17 11.9 0.023 3841 3787 1.00\n c 19.99 0.979 18.1 21.9 0.020 3892 3829 1.00 source"},{"id":73,"pagetitle":"Stats","title":"StatsBase.summarystats","ref":"/ArviZ/stable/api/stats/#StatsBase.summarystats","content":" StatsBase.summarystats — Function summarystats(data::InferenceData; group=:posterior, kwargs...) -> SummaryStats\nsummarystats(data::Dataset; kwargs...) -> SummaryStats Compute default summary statistics for the data using summarize . source"},{"id":74,"pagetitle":"Stats","title":"General statistics","ref":"/ArviZ/stable/api/stats/#General-statistics","content":" General statistics"},{"id":75,"pagetitle":"Stats","title":"PosteriorStats.hdi","ref":"/ArviZ/stable/api/stats/#PosteriorStats.hdi","content":" PosteriorStats.hdi — Function hdi(data::InferenceData; kwargs...) -> Dataset\nhdi(data::Dataset; kwargs...) -> Dataset Calculate the highest density interval (HDI) for each parameter in the data. source hdi(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper) Estimate the unimodal highest density interval (HDI) of samples for the probability prob . The HDI is the minimum width Bayesian credible interval (BCI). That is, it is the smallest possible interval containing (100*prob) % of the probability mass. [Hyndman1996] samples is an array of shape (draws[, chains[, params...]]) . If multiple parameters are present, then lower and upper are arrays with the shape (params...,) , computed separately for each marginal. This implementation uses the algorithm of [ChenShao1999] . Note Any default value of prob is arbitrary. The default value of prob=0.94 instead of a more common default like prob=0.95 is chosen to reminder the user of this arbitrariness. Examples Here we calculate the 83% HDI for a normal random variable: julia> x = randn(2_000);\n\njulia> hdi(x; prob=0.83) |> pairs\npairs(::NamedTuple) with 2 entries:\n :lower => -1.38266\n :upper => 1.25982 We can also calculate the HDI for a 3-dimensional array of samples: julia> x = randn(1_000, 1, 1) .+ reshape(0:5:10, 1, 1, :);\n\njulia> hdi(x) |> pairs\npairs(::NamedTuple) with 2 entries:\n :lower => [-1.9674, 3.0326, 8.0326]\n :upper => [1.90028, 6.90028, 11.9003] source"},{"id":76,"pagetitle":"Stats","title":"PosteriorStats.hdi!","ref":"/ArviZ/stable/api/stats/#PosteriorStats.hdi!","content":" PosteriorStats.hdi! — Function hdi!(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper) A version of hdi that sorts samples in-place while computing the HDI. source"},{"id":77,"pagetitle":"Stats","title":"PosteriorStats.r2_score","ref":"/ArviZ/stable/api/stats/#PosteriorStats.r2_score","content":" PosteriorStats.r2_score — Function r2_score(idata::InferenceData; y_name, y_pred_name) -> (; r2, r2_std) Compute $R²$ from idata , automatically formatting the predictions to the correct shape. Keywords y_name : Name of observed data variable in idata.observed_data . If not provided, then the only observed data variable is used. y_pred_name : Name of posterior predictive variable in idata.posterior_predictive . If not provided, then y_name is used. Examples julia> using ArviZExampleData, PosteriorStats\n\njulia> idata = load_example_data(\"regression10d\");\n\njulia> r2_score(idata) |> pairs\npairs(::NamedTuple) with 2 entries:\n :r2 => 0.998385\n :r2_std => 0.000100621 source r2_score(y_true::AbstractVector, y_pred::AbstractVecOrMat) -> (; r2, r2_std) $R²$ for linear Bayesian regression models. [GelmanGoodrich2019] Arguments y_true : Observed data of length noutputs y_pred : Predicted data with size (ndraws[, nchains], noutputs) Examples julia> using ArviZExampleData\n\njulia> idata = load_example_data(\"regression1d\");\n\njulia> y_true = idata.observed_data.y;\n\njulia> y_pred = PermutedDimsArray(idata.posterior_predictive.y, (:draw, :chain, :y_dim_0));\n\njulia> r2_score(y_true, y_pred) |> pairs\npairs(::NamedTuple) with 2 entries:\n :r2 => 0.683197\n :r2_std => 0.0368838 source"},{"id":78,"pagetitle":"Stats","title":"Pareto-smoothed importance sampling","ref":"/ArviZ/stable/api/stats/#Pareto-smoothed-importance-sampling","content":" Pareto-smoothed importance sampling"},{"id":79,"pagetitle":"Stats","title":"PSIS.PSISResult","ref":"/ArviZ/stable/api/stats/#PSIS.PSISResult","content":" PSIS.PSISResult — Type PSISResult Result of Pareto-smoothed importance sampling (PSIS) using psis . Properties log_weights : un-normalized Pareto-smoothed log weights weights : normalized Pareto-smoothed weights (allocates a copy) pareto_shape : Pareto $k=ξ$ shape parameter nparams : number of parameters in log_weights ndraws : number of draws in log_weights nchains : number of chains in log_weights reff : the ratio of the effective sample size of the unsmoothed importance ratios and the actual sample size. ess : estimated effective sample size of estimate of mean using smoothed importance samples (see ess_is ) tail_length : length of the upper tail of log_weights that was smoothed tail_dist : the generalized Pareto distribution that was fit to the tail of log_weights . Note that the tail weights are scaled to have a maximum of 1, so tail_dist * exp(maximum(log_ratios)) is the corresponding fit directly to the tail of log_ratios . normalized::Bool :indicates whether log_weights are log-normalized along the sample dimensions. Diagnostic The pareto_shape parameter $k=ξ$ of the generalized Pareto distribution tail_dist can be used to diagnose reliability and convergence of estimates using the importance weights [VehtariSimpson2021] . if $k < \\frac{1}{3}$ , importance sampling is stable, and importance sampling (IS) and PSIS both are reliable. if $k ≤ \\frac{1}{2}$ , then the importance ratio distributon has finite variance, and the central limit theorem holds. As $k$ approaches the upper bound, IS becomes less reliable, while PSIS still works well but with a higher RMSE. if $\\frac{1}{2} < k ≤ 0.7$ , then the variance is infinite, and IS can behave quite poorly. However, PSIS works well in this regime. if $0.7 < k ≤ 1$ , then it quickly becomes impractical to collect enough importance weights to reliably compute estimates, and importance sampling is not recommended. if $k > 1$ , then neither the variance nor the mean of the raw importance ratios exists. The convergence rate is close to zero, and bias can be large with practical sample sizes. See PSISPlots.paretoshapeplot for a diagnostic plot. source"},{"id":80,"pagetitle":"Stats","title":"PSIS.ess_is","ref":"/ArviZ/stable/api/stats/#PSIS.ess_is","content":" PSIS.ess_is — Function ess_is(weights; reff=1) Estimate effective sample size (ESS) for importance sampling over the sample dimensions. Given normalized weights $w_{1:n}$ , the ESS is estimated using the L2-norm of the weights: \\[\\mathrm{ESS}(w_{1:n}) = \\frac{r_{\\mathrm{eff}}}{\\sum_{i=1}^n w_i^2}\\] where $r_{\\mathrm{eff}}$ is the relative efficiency of the log_weights . ess_is(result::PSISResult; bad_shape_nan=true) Estimate ESS for Pareto-smoothed importance sampling. Note ESS estimates for Pareto shape values $k > 0.7$ , which are unreliable and misleadingly high, are set to NaN . To avoid this, set bad_shape_nan=false . source"},{"id":81,"pagetitle":"Stats","title":"PSIS.PSISPlots.paretoshapeplot","ref":"/ArviZ/stable/api/stats/#PSIS.PSISPlots.paretoshapeplot","content":" PSIS.PSISPlots.paretoshapeplot — Function paretoshapeplot(values; showlines=false, ...)\nparetoshapeplot!(values; showlines=false, kwargs...) Plot shape parameters of fitted Pareto tail distributions for diagnosing convergence. values may be either a vector of Pareto shape parameters or a PSIS.PSISResult . If showlines==true , horizontal lines indicating relevant Pareto shape thresholds are drawn. See PSIS.PSISResult for an explanation of the thresholds. All remaining kwargs are forwarded to the plotting function. See psis , PSISResult . Examples using PSIS, Distributions, Plots\nproposal = Normal()\ntarget = TDist(7)\nx = rand(proposal, 1_000, 100)\nlog_ratios = logpdf.(target, x) .- logpdf.(proposal, x)\nresult = psis(log_ratios)\nparetoshapeplot(result) We can also plot the Pareto shape parameters directly: paretoshapeplot(result.pareto_shape) We can also use plot directly: plot(result.pareto_shape; showlines=true) source"},{"id":82,"pagetitle":"Stats","title":"PSIS.psis","ref":"/ArviZ/stable/api/stats/#PSIS.psis","content":" PSIS.psis — Function psis(log_ratios, reff = 1.0; kwargs...) -> PSISResult\npsis!(log_ratios, reff = 1.0; kwargs...) -> PSISResult Compute Pareto smoothed importance sampling (PSIS) log weights [VehtariSimpson2021] . While psis computes smoothed log weights out-of-place, psis! smooths them in-place. Arguments log_ratios : an array of logarithms of importance ratios, with size (draws, [chains, [parameters...]]) , where chains>1 would be used when chains are generated using Markov chain Monte Carlo. reff::Union{Real,AbstractArray} : the ratio(s) of effective sample size of log_ratios and the actual sample size reff = ess/(draws * chains) , used to account for autocorrelation, e.g. due to Markov chain Monte Carlo. If an array, it must have the size (parameters...,) to match log_ratios . Keywords warn=true : If true , warning messages are delivered normalize=true : If true , the log-weights will be log-normalized so that exp.(log_weights) sums to 1 along the sample dimensions. Returns result : a PSISResult object containing the results of the Pareto-smoothing. A warning is raised if the Pareto shape parameter $k ≥ 0.7$ . See PSISResult for details and PSISPlots.paretoshapeplot for a diagnostic plot. source"},{"id":83,"pagetitle":"Stats","title":"PSIS.psis!","ref":"/ArviZ/stable/api/stats/#PSIS.psis!","content":" PSIS.psis! — Function psis(log_ratios, reff = 1.0; kwargs...) -> PSISResult\npsis!(log_ratios, reff = 1.0; kwargs...) -> PSISResult Compute Pareto smoothed importance sampling (PSIS) log weights [VehtariSimpson2021] . While psis computes smoothed log weights out-of-place, psis! smooths them in-place. Arguments log_ratios : an array of logarithms of importance ratios, with size (draws, [chains, [parameters...]]) , where chains>1 would be used when chains are generated using Markov chain Monte Carlo. reff::Union{Real,AbstractArray} : the ratio(s) of effective sample size of log_ratios and the actual sample size reff = ess/(draws * chains) , used to account for autocorrelation, e.g. due to Markov chain Monte Carlo. If an array, it must have the size (parameters...,) to match log_ratios . Keywords warn=true : If true , warning messages are delivered normalize=true : If true , the log-weights will be log-normalized so that exp.(log_weights) sums to 1 along the sample dimensions. Returns result : a PSISResult object containing the results of the Pareto-smoothing. A warning is raised if the Pareto shape parameter $k ≥ 0.7$ . See PSISResult for details and PSISPlots.paretoshapeplot for a diagnostic plot. source"},{"id":84,"pagetitle":"Stats","title":"LOO and WAIC","ref":"/ArviZ/stable/api/stats/#LOO-and-WAIC","content":" LOO and WAIC"},{"id":85,"pagetitle":"Stats","title":"PosteriorStats.AbstractELPDResult","ref":"/ArviZ/stable/api/stats/#PosteriorStats.AbstractELPDResult","content":" PosteriorStats.AbstractELPDResult — Type abstract type AbstractELPDResult An abstract type representing the result of an ELPD computation. Every subtype stores estimates of both the expected log predictive density ( elpd ) and the effective number of parameters p , as well as standard errors and pointwise estimates of each, from which other relevant estimates can be computed. Subtypes implement the following functions: elpd_estimates information_criterion source"},{"id":86,"pagetitle":"Stats","title":"PosteriorStats.PSISLOOResult","ref":"/ArviZ/stable/api/stats/#PosteriorStats.PSISLOOResult","content":" PosteriorStats.PSISLOOResult — Type Results of Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO). See also: loo , AbstractELPDResult estimates : Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p) pointwise : Pointwise estimates psis_result : Pareto-smoothed importance sampling (PSIS) results source"},{"id":87,"pagetitle":"Stats","title":"PosteriorStats.WAICResult","ref":"/ArviZ/stable/api/stats/#PosteriorStats.WAICResult","content":" PosteriorStats.WAICResult — Type Results of computing the widely applicable information criterion (WAIC). See also: waic , AbstractELPDResult estimates : Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p) pointwise : Pointwise estimates source"},{"id":88,"pagetitle":"Stats","title":"PosteriorStats.elpd_estimates","ref":"/ArviZ/stable/api/stats/#PosteriorStats.elpd_estimates","content":" PosteriorStats.elpd_estimates — Function elpd_estimates(result::AbstractELPDResult; pointwise=false) -> (; elpd, elpd_mcse, lpd) Return the (E)LPD estimates from the result . source"},{"id":89,"pagetitle":"Stats","title":"PosteriorStats.information_criterion","ref":"/ArviZ/stable/api/stats/#PosteriorStats.information_criterion","content":" PosteriorStats.information_criterion — Function information_criterion(elpd, scale::Symbol) Compute the information criterion for the given scale from the elpd estimate. scale must be one of (:deviance, :log, :negative_log) . See also: loo , waic source information_criterion(result::AbstractELPDResult, scale::Symbol; pointwise=false) Compute information criterion for the given scale from the existing ELPD result . scale must be one of (:deviance, :log, :negative_log) . If pointwise=true , then pointwise estimates are returned. source"},{"id":90,"pagetitle":"Stats","title":"PosteriorStats.loo","ref":"/ArviZ/stable/api/stats/#PosteriorStats.loo","content":" PosteriorStats.loo — Function loo(data::Dataset; [var_name::Symbol,] kwargs...) -> PSISLOOResult{<:NamedTuple,<:Dataset}\nloo(data::InferenceData; [var_name::Symbol,] kwargs...) -> PSISLOOResult{<:NamedTuple,<:Dataset} Compute PSIS-LOO from log-likelihood values in data . If more than one log-likelihood variable is present, then var_name must be provided. Examples Calculate PSIS-LOO of a model: julia> using ArviZExampleData, PosteriorStats\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> loo(idata)\nPSISLOOResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.34\n\nand PSISResult with 500 draws, 4 chains, and 8 parameters\nPareto shape (k) diagnostic values:\n Count Min. ESS\n (-Inf, 0.5] good 6 (75.0%) 135\n (0.5, 0.7] okay 2 (25.0%) 421 source loo(log_likelihood; reff=nothing, kwargs...) -> PSISLOOResult{<:NamedTuple,<:NamedTuple} Compute the Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO). [Vehtari2017] [LOOFAQ] log_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]) . Keywords reff::Union{Real,AbstractArray{<:Real}} : The relative effective sample size(s) of the likelihood values. If an array, it must have the same data dimensions as the corresponding log-likelihood variable. If not provided, then this is estimated using MCMCDiagnosticTools.ess . kwargs : Remaining keywords are forwarded to [ PSIS.psis ]. See also: PSISLOOResult , waic Examples Manually compute $R_\\mathrm{eff}$ and calculate PSIS-LOO of a model: julia> using ArviZExampleData, MCMCDiagnosticTools\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> reff = ess(log_like; kind=:basic, split_chains=1, relative=true);\n\njulia> loo(log_like; reff)\nPSISLOOResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.34\n\nand PSISResult with 500 draws, 4 chains, and 8 parameters\nPareto shape (k) diagnostic values:\n Count Min. ESS\n (-Inf, 0.5] good 7 (87.5%) 151\n (0.5, 0.7] okay 1 (12.5%) 446 source"},{"id":91,"pagetitle":"Stats","title":"PosteriorStats.waic","ref":"/ArviZ/stable/api/stats/#PosteriorStats.waic","content":" PosteriorStats.waic — Function waic(data::Dataset; [var_name::Symbol]) -> WAICResult{<:NamedTuple,<:Dataset}\nwaic(data::InferenceData; [var_name::Symbol]) -> WAICResult{<:NamedTuple,<:Dataset} Compute WAIC from log-likelihood values in data . If more than one log-likelihood variable is present, then var_name must be provided. Examples Calculate WAIC of a model: julia> using ArviZExampleData, PosteriorStats\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> waic(idata)\nWAICResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.33 source waic(log_likelihood::AbstractArray) -> WAICResult{<:NamedTuple,<:NamedTuple} Compute the widely applicable information criterion (WAIC). [Watanabe2010] [Vehtari2017] [LOOFAQ] log_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]) . See also: WAICResult , loo Examples Calculate WAIC of a model: julia> using ArviZExampleData\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> waic(log_like)\nWAICResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.33 source"},{"id":92,"pagetitle":"Stats","title":"Model comparison","ref":"/ArviZ/stable/api/stats/#Model-comparison","content":" Model comparison"},{"id":93,"pagetitle":"Stats","title":"PosteriorStats.ModelComparisonResult","ref":"/ArviZ/stable/api/stats/#PosteriorStats.ModelComparisonResult","content":" PosteriorStats.ModelComparisonResult — Type ModelComparisonResult Result of model comparison using ELPD. This struct implements the Tables and TableTraits interfaces. Each field returns a collection of the corresponding entry for each model: name : Names of the models, if provided. rank : Ranks of the models (ordered by decreasing ELPD) elpd_diff : ELPD of a model subtracted from the largest ELPD of any model elpd_diff_mcse : Monte Carlo standard error of the ELPD difference weight : Model weights computed with weights_method elpd_result : AbstactELPDResult s for each model, which can be used to access useful stats like ELPD estimates, pointwise estimates, and Pareto shape values for PSIS-LOO weights_method : Method used to compute model weights with model_weights source"},{"id":94,"pagetitle":"Stats","title":"PosteriorStats.compare","ref":"/ArviZ/stable/api/stats/#PosteriorStats.compare","content":" PosteriorStats.compare — Function compare(models; kwargs...) -> ModelComparisonResult Compare models based on their expected log pointwise predictive density (ELPD). The ELPD is estimated either by Pareto smoothed importance sampling leave-one-out cross-validation (LOO) or using the widely applicable information criterion (WAIC). We recommend loo. Read more theory here - in a paper by some of the leading authorities on model comparison dx.doi.org/10.1111/1467-9868.00353 Arguments models : a Tuple , NamedTuple , or AbstractVector whose values are either AbstractELPDResult entries or any argument to elpd_method . Keywords weights_method::AbstractModelWeightsMethod=Stacking() : the method to be used to weight the models. See model_weights for details elpd_method=loo : a method that computes an AbstractELPDResult from an argument in models . sort::Bool=true : Whether to sort models by decreasing ELPD. Returns ModelComparisonResult : A container for the model comparison results. The fields contain a similar collection to models . Examples Compare the centered and non centered models of the eight school problem using the defaults: loo and Stacking weights. A custom myloo method formates the inputs as expected by loo . julia> using ArviZExampleData\n\njulia> models = (\n centered=load_example_data(\"centered_eight\"),\n non_centered=load_example_data(\"non_centered_eight\"),\n );\n\njulia> function myloo(idata)\n log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1))\n return loo(log_like)\n end;\n\njulia> mc = compare(models; elpd_method=myloo)\n┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.\n└ @ PSIS ~/.julia/packages/PSIS/...\nModelComparisonResult with Stacking weights\n rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯\n non_centered 1 -31 1.4 0 0.0 1.0 0.9 ⋯\n centered 2 -31 1.4 0.06 0.067 0.0 0.9 ⋯\n 1 column omitted\njulia> mc.weight |> pairs\npairs(::NamedTuple) with 2 entries:\n :non_centered => 1.0\n :centered => 5.34175e-19 Compare the same models from pre-computed PSIS-LOO results and computing BootstrappedPseudoBMA weights: julia> elpd_results = mc.elpd_result;\n\njulia> compare(elpd_results; weights_method=BootstrappedPseudoBMA())\nModelComparisonResult with BootstrappedPseudoBMA weights\n rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯\n non_centered 1 -31 1.4 0 0.0 0.52 0.9 ⋯\n centered 2 -31 1.4 0.06 0.067 0.48 0.9 ⋯\n 1 column omitted source"},{"id":95,"pagetitle":"Stats","title":"PosteriorStats.model_weights","ref":"/ArviZ/stable/api/stats/#PosteriorStats.model_weights","content":" PosteriorStats.model_weights — Function model_weights(elpd_results; method=Stacking())\nmodel_weights(method::AbstractModelWeightsMethod, elpd_results) Compute weights for each model in elpd_results using method . elpd_results is a Tuple , NamedTuple , or AbstractVector with AbstractELPDResult entries. The weights are returned in the same type of collection. Stacking is the recommended approach, as it performs well even when the true data generating process is not included among the candidate models. See [YaoVehtari2018] for details. See also: AbstractModelWeightsMethod , compare Examples Compute Stacking weights for two models: julia> using ArviZExampleData\n\njulia> models = (\n centered=load_example_data(\"centered_eight\"),\n non_centered=load_example_data(\"non_centered_eight\"),\n );\n\njulia> elpd_results = map(models) do idata\n log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1))\n return loo(log_like)\n end;\n┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.\n└ @ PSIS ~/.julia/packages/PSIS/...\n\njulia> model_weights(elpd_results; method=Stacking()) |> pairs\npairs(::NamedTuple) with 2 entries:\n :centered => 5.34175e-19\n :non_centered => 1.0 Now we compute BootstrappedPseudoBMA weights for the same models: julia> model_weights(elpd_results; method=BootstrappedPseudoBMA()) |> pairs\npairs(::NamedTuple) with 2 entries:\n :centered => 0.483723\n :non_centered => 0.516277 source The following model weighting methods are available"},{"id":96,"pagetitle":"Stats","title":"PosteriorStats.AbstractModelWeightsMethod","ref":"/ArviZ/stable/api/stats/#PosteriorStats.AbstractModelWeightsMethod","content":" PosteriorStats.AbstractModelWeightsMethod — Type abstract type AbstractModelWeightsMethod An abstract type representing methods for computing model weights. Subtypes implement model_weights (method, elpd_results) . source"},{"id":97,"pagetitle":"Stats","title":"PosteriorStats.BootstrappedPseudoBMA","ref":"/ArviZ/stable/api/stats/#PosteriorStats.BootstrappedPseudoBMA","content":" PosteriorStats.BootstrappedPseudoBMA — Type struct BootstrappedPseudoBMA{R<:Random.AbstractRNG, T<:Real} <: AbstractModelWeightsMethod Model weighting method using pseudo Bayesian Model Averaging using Akaike-type weighting with the Bayesian bootstrap (pseudo-BMA+) [YaoVehtari2018] . The Bayesian bootstrap stabilizes the model weights. BootstrappedPseudoBMA(; rng=Random.default_rng(), samples=1_000, alpha=1)\nBootstrappedPseudoBMA(rng, samples, alpha) Construct the method. rng::Random.AbstractRNG : The random number generator to use for the Bayesian bootstrap samples::Int64 : The number of samples to draw for bootstrapping alpha::Real : The shape parameter in the Dirichlet distribution used for the Bayesian bootstrap. The default (1) corresponds to a uniform distribution on the simplex. See also: Stacking source"},{"id":98,"pagetitle":"Stats","title":"PosteriorStats.PseudoBMA","ref":"/ArviZ/stable/api/stats/#PosteriorStats.PseudoBMA","content":" PosteriorStats.PseudoBMA — Type struct PseudoBMA <: AbstractModelWeightsMethod Model weighting method using pseudo Bayesian Model Averaging (pseudo-BMA) and Akaike-type weighting. PseudoBMA(; regularize=false)\nPseudoBMA(regularize) Construct the method with optional regularization of the weights using the standard error of the ELPD estimate. Note This approach is not recommended, as it produces unstable weight estimates. It is recommended to instead use BootstrappedPseudoBMA to stabilize the weights or Stacking . For details, see [YaoVehtari2018] . See also: Stacking source"},{"id":99,"pagetitle":"Stats","title":"PosteriorStats.Stacking","ref":"/ArviZ/stable/api/stats/#PosteriorStats.Stacking","content":" PosteriorStats.Stacking — Type struct Stacking{O<:Optim.AbstractOptimizer} <: AbstractModelWeightsMethod Model weighting using stacking of predictive distributions [YaoVehtari2018] . Stacking(; optimizer=Optim.LBFGS(), options=Optim.Options()\nStacking(optimizer[, options]) Construct the method, optionally customizing the optimization. optimizer::Optim.AbstractOptimizer : The optimizer to use for the optimization of the weights. The optimizer must support projected gradient optimization via a manifold field. options::Optim.Options : The Optim options to use for the optimization of the weights. See also: BootstrappedPseudoBMA source"},{"id":100,"pagetitle":"Stats","title":"Predictive checks","ref":"/ArviZ/stable/api/stats/#Predictive-checks","content":" Predictive checks"},{"id":101,"pagetitle":"Stats","title":"PosteriorStats.loo_pit","ref":"/ArviZ/stable/api/stats/#PosteriorStats.loo_pit","content":" PosteriorStats.loo_pit — Function loo_pit(idata::InferenceData, log_weights; kwargs...) -> DimArray Compute LOO-PIT values using existing normalized log LOO importance weights. Keywords y_name : Name of observed data variable in idata.observed_data . If not provided, then the only observed data variable is used. y_pred_name : Name of posterior predictive variable in idata.posterior_predictive . If not provided, then y_name is used. kwargs : Remaining keywords are forwarded to the base method of loo_pit . Examples Calculate LOO-PIT values using already computed log weights. julia> using ArviZExampleData, PosteriorStats\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> loo_result = loo(idata; var_name=:obs);\n\njulia> loo_pit(idata, loo_result.psis_result.log_weights; y_name=:obs)\n8-element DimArray{Float64,1} loo_pit_obs with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.943511\n \"Deerfield\" 0.63797\n \"Phillips Andover\" 0.316697\n \"Phillips Exeter\" 0.582252\n \"Hotchkiss\" 0.295321\n \"Lawrenceville\" 0.403318\n \"St. Paul's\" 0.902508\n \"Mt. Hermon\" 0.655275 source loo_pit(idata::InferenceData; kwargs...) -> DimArray Compute LOO-PIT from groups in idata using PSIS-LOO. Keywords y_name : Name of observed data variable in idata.observed_data . If not provided, then the only observed data variable is used. y_pred_name : Name of posterior predictive variable in idata.posterior_predictive . If not provided, then y_name is used. log_likelihood_name : Name of log-likelihood variable in idata.log_likelihood . If not provided, then y_name is used if idata has a log_likelihood group, otherwise the only variable is used. reff::Union{Real,AbstractArray{<:Real}} : The relative effective sample size(s) of the likelihood values. If an array, it must have the same data dimensions as the corresponding log-likelihood variable. If not provided, then this is estimated using ess . kwargs : Remaining keywords are forwarded to the base method of loo_pit . Examples Calculate LOO-PIT values using as test quantity the observed values themselves. julia> using ArviZExampleData, PosteriorStats\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> loo_pit(idata; y_name=:obs)\n8-element DimArray{Float64,1} loo_pit_obs with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.943511\n \"Deerfield\" 0.63797\n \"Phillips Andover\" 0.316697\n \"Phillips Exeter\" 0.582252\n \"Hotchkiss\" 0.295321\n \"Lawrenceville\" 0.403318\n \"St. Paul's\" 0.902508\n \"Mt. Hermon\" 0.655275 source loo_pit(y, y_pred, log_weights; kwargs...) -> Union{Real,AbstractArray} Compute leave-one-out probability integral transform (LOO-PIT) checks. Arguments y : array of observations with shape (params...,) y_pred : array of posterior predictive samples with shape (draws, chains, params...) . log_weights : array of normalized log LOO importance weights with shape (draws, chains, params...) . Keywords is_discrete : If not provided, then it is set to true iff elements of y and y_pred are all integer-valued. If true , then data are smoothed using smooth_data to make them non-discrete before estimating LOO-PIT values. kwargs : Remaining keywords are forwarded to smooth_data if data is discrete. Returns pitvals : LOO-PIT values with same size as y . If y is a scalar, then pitvals is a scalar. LOO-PIT is a marginal posterior predictive check. If $y_{-i}$ is the array $y$ of observations with the $i$ th observation left out, and $y_i^*$ is a posterior prediction of the $i$ th observation, then the LOO-PIT value for the $i$ th observation is defined as \\[P(y_i^* \\le y_i \\mid y_{-i}) = \\int_{-\\infty}^{y_i} p(y_i^* \\mid y_{-i}) \\mathrm{d} y_i^*\\] The LOO posterior predictions and the corresponding observations should have similar distributions, so if conditional predictive distributions are well-calibrated, then all LOO-PIT values should be approximately uniformly distributed on $[0, 1]$ . [Gabry2019] Examples Calculate LOO-PIT values using as test quantity the observed values themselves. julia> using ArviZExampleData\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> y = idata.observed_data.obs;\n\njulia> y_pred = PermutedDimsArray(idata.posterior_predictive.obs, (:draw, :chain, :school));\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> log_weights = loo(log_like).psis_result.log_weights;\n\njulia> loo_pit(y, y_pred, log_weights)\n8-element DimArray{Float64,1} with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.943511\n \"Deerfield\" 0.63797\n \"Phillips Andover\" 0.316697\n \"Phillips Exeter\" 0.582252\n \"Hotchkiss\" 0.295321\n \"Lawrenceville\" 0.403318\n \"St. Paul's\" 0.902508\n \"Mt. Hermon\" 0.655275 Calculate LOO-PIT values using as test quantity the square of the difference between each observation and mu . julia> using Statistics\n\njulia> mu = idata.posterior.mu;\n\njulia> T = y .- median(mu);\n\njulia> T_pred = y_pred .- mu;\n\njulia> loo_pit(T .^ 2, T_pred .^ 2, log_weights)\n8-element DimArray{Float64,1} with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.873577\n \"Deerfield\" 0.243686\n \"Phillips Andover\" 0.357563\n \"Phillips Exeter\" 0.149908\n \"Hotchkiss\" 0.435094\n \"Lawrenceville\" 0.220627\n \"St. Paul's\" 0.775086\n \"Mt. Hermon\" 0.296706 source"},{"id":102,"pagetitle":"Stats","title":"Utilities","ref":"/ArviZ/stable/api/stats/#Utilities","content":" Utilities"},{"id":103,"pagetitle":"Stats","title":"PosteriorStats.smooth_data","ref":"/ArviZ/stable/api/stats/#PosteriorStats.smooth_data","content":" PosteriorStats.smooth_data — Function smooth_data(y; dims=:, interp_method=CubicSpline, offset_frac=0.01) Smooth y along dims using interp_method . interp_method is a 2-argument callabale that takes the arguments y and x and returns a DataInterpolations.jl interpolation method, defaulting to a cubic spline interpolator. offset_frac is the fraction of the length of y to use as an offset when interpolating. source Hyndman1996 Rob J. Hyndman (1996) Computing and Graphing Highest Density Regions, Amer. Stat., 50(2): 120-6. DOI: 10.1080/00031305.1996.10474359 jstor . ChenShao1999 Ming-Hui Chen & Qi-Man Shao (1999) Monte Carlo Estimation of Bayesian Credible and HPD Intervals, J Comput. Graph. Stat., 8:1, 69-92. DOI: 10.1080/10618600.1999.10474802 jstor . GelmanGoodrich2019 Andrew Gelman, Ben Goodrich, Jonah Gabry & Aki Vehtari (2019) R-squared for Bayesian Regression Models, The American Statistician, 73:3, 307-9, DOI: 10.1080/00031305.2018.1549100 . VehtariSimpson2021 Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO] VehtariSimpson2021 Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO] VehtariSimpson2021 Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO] Vehtari2017 Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544 LOOFAQ Aki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html Watanabe2010 Watanabe, S. Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory. 11(116):3571−3594, 2010. https://jmlr.csail.mit.edu/papers/v11/watanabe10a.html Vehtari2017 Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544 LOOFAQ Aki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html YaoVehtari2018 Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030 YaoVehtari2018 Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030 YaoVehtari2018 Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030 YaoVehtari2018 Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030 Gabry2019 Gabry, J., Simpson, D., Vehtari, A., Betancourt, M. & Gelman, A. Visualization in Bayesian Workflow. J. R. Stat. Soc. Ser. A Stat. Soc. 182, 389–402 (2019). doi: 10.1111/rssa.12378 arXiv: 1709.01449"},{"id":106,"pagetitle":"Creating custom plots","title":"Environment","ref":"/ArviZ/stable/creating_custom_plots/#Environment","content":" Environment using Pkg, InteractiveUtils using PlutoUI with_terminal(Pkg.status; color=false) Status `~/work/ArviZ.jl/ArviZ.jl/docs/Project.toml`\n [cbdf2221] AlgebraOfGraphics v0.6.17\n [131c737c] ArviZ v0.10.3 `~/work/ArviZ.jl/ArviZ.jl`\n [2f96bb34] ArviZExampleData v0.1.8\n [4a6e88f0] ArviZPythonPlots v0.1.3\n [13f3f980] CairoMakie v0.11.4\n [a93c6f00] DataFrames v1.6.1\n⌃ [0703355e] DimensionalData v0.24.13\n [31c24e10] Distributions v0.25.104\n [e30172f5] Documenter v1.2.1\n [f6006082] EvoTrees v0.16.5\n [b5cf5a8d] InferenceObjects v0.3.14\n [be115224] MCMCDiagnosticTools v0.3.8\n [a7f614a8] MLJBase v1.0.1\n [614be32b] MLJIteration v0.6.0\n [ce719bf2] PSIS v0.9.4\n [359b1769] PlutoStaticHTML v6.0.18\n [7f904dfe] PlutoUI v0.7.54\n [7f36be82] PosteriorStats v0.1.4\n [c1514b29] StanSample v7.6.0\n [a19d573c] StatisticalMeasures v0.1.3\n [2913bbd2] StatsBase v0.34.2\n⌅ [fce5fe82] Turing v0.29.3\n [f43a241f] Downloads v1.6.0\n [37e2e46d] LinearAlgebra\n [10745b16] Statistics v1.9.0\nInfo Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated`\n with_terminal(versioninfo) Julia Version 1.9.4\nCommit 8e5136fa297 (2023-11-14 08:46 UTC)\nBuild Info:\n Official https://julialang.org/ release\nPlatform Info:\n OS: Linux (x86_64-linux-gnu)\n CPU: 4 × AMD EPYC 7763 64-Core Processor\n WORD_SIZE: 64\n LIBM: libopenlibm\n LLVM: libLLVM-14.0.6 (ORCJIT, znver3)\n Threads: 2 on 4 virtual cores\nEnvironment:\n JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager\n JULIA_PROJECT = /home/runner/work/ArviZ.jl/ArviZ.jl/docs/\n JULIA_DEPOT_PATH = /home/runner/.julia:/opt/hostedtoolcache/julia/1.9.4/x64/local/share/julia:/opt/hostedtoolcache/julia/1.9.4/x64/share/julia\n JULIA_NUM_THREADS = 2\n JULIA_LOAD_PATH = @:@v#.#:@stdlib\n JULIA_CMDSTAN_HOME = /home/runner/work/ArviZ.jl/ArviZ.jl/.cmdstan//cmdstan-2.33.1/\n JULIA_REVISE_WORKER_ONLY = 1\n"},{"id":111,"pagetitle":"Working with InferenceData","title":"Working with InferenceData","ref":"/ArviZ/stable/working_with_inference_data/#working-with-inference-data","content":" Working with InferenceData using ArviZ, ArviZExampleData, DimensionalData, Statistics Here we present a collection of common manipulations you can use while working with InferenceData . Let's load one of ArviZ's example datasets. posterior , posterior_predictive , etc are the groups stored in idata , and they are stored as Dataset s. In this HTML view, you can click a group name to expand a summary of the group. idata = load_example_data(\"centered_eight\") InferenceData posterior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" posterior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:41.460544\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" log_likelihood Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:37.487399\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" sample_stats Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 16 layers:\n :max_energy_error Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :energy_error Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :lp Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :index_in_trajectory Int64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :acceptance_rate Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :diverging Bool dims: Dim{:draw}, Dim{:chain} (500×4)\n :process_time_diff Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :n_steps Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :perf_counter_start Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :largest_eigval Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (500×4)\n :smallest_eigval Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (500×4)\n :step_size_bar Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :step_size Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :energy Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :tree_depth Int64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :perf_counter_diff Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.324929\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.602116\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.604969\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" observed_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :obs Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.606375\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" constant_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :scores Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.607471\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" Info Dataset s are DimensionalData.AbstractDimStack s and can be used identically. The variables a Dataset contains are called \"layers\", and dimensions of the same name that appear in more than one layer within a Dataset must have the same indices. InferenceData behaves like a NamedTuple and can be used similarly. Note that unlike a NamedTuple , the groups always appear in a specific order. length(idata) # number of groups 8 keys(idata) # group names (:posterior, :posterior_predictive, :log_likelihood, :sample_stats, :prior, :prior_predictive, :observed_data, :constant_data)"},{"id":112,"pagetitle":"Working with InferenceData","title":"Get the dataset corresponding to a single group","ref":"/ArviZ/stable/working_with_inference_data/#Get-the-dataset-corresponding-to-a-single-group","content":" Get the dataset corresponding to a single group Group datasets can be accessed both as properties or as indexed items. post = idata.posterior Dataset with dimensions: \n Dim{ :draw } Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{ :chain } Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{ :school } Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n and 3 layers:\n :mu Float64 dims: Dim{ :draw } , Dim{ :chain } (500×4)\n :theta Float64 dims: Dim{ :school } , Dim{ :draw } , Dim{ :chain } (8×500×4)\n :tau Float64 dims: Dim{ :draw } , Dim{ :chain } (500×4)\n\n with metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" post is the dataset itself, so this is a non-allocating operation. idata[:posterior] === post true InferenceData supports a more advanced indexing syntax, which we'll see later."},{"id":113,"pagetitle":"Working with InferenceData","title":"Getting a new InferenceData with a subset of groups","ref":"/ArviZ/stable/working_with_inference_data/#Getting-a-new-InferenceData-with-a-subset-of-groups","content":" Getting a new InferenceData with a subset of groups We can index by a collection of group names to get a new InferenceData with just those groups. This is also non-allocating. idata_sub = idata[(:posterior, :posterior_predictive)] InferenceData posterior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" posterior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:41.460544\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\""},{"id":114,"pagetitle":"Working with InferenceData","title":"Adding groups to an InferenceData","ref":"/ArviZ/stable/working_with_inference_data/#Adding-groups-to-an-InferenceData","content":" Adding groups to an InferenceData InferenceData is immutable, so to add or replace groups we use merge to create a new object. merge(idata_sub, idata[(:observed_data, :prior)]) InferenceData posterior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" posterior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:41.460544\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.602116\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" observed_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :obs Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.606375\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" We can also use Base.setindex to out-of-place add or replace a single group. Base.setindex(idata_sub, idata.prior, :prior) InferenceData posterior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" posterior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:41.460544\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.602116\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\""},{"id":115,"pagetitle":"Working with InferenceData","title":"Add a new variable","ref":"/ArviZ/stable/working_with_inference_data/#Add-a-new-variable","content":" Add a new variable Dataset is also immutable. So while the values within the underlying data arrays can be mutated, layers cannot be added or removed from Dataset s, and groups cannot be added/removed from InferenceData . Instead, we do this out-of-place also using merge . merge(post, (log_tau=log.(post[:tau]),)) Dataset with dimensions: \n Dim{ :draw } Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{ :chain } Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{ :school } Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n and 4 layers:\n :mu Float64 dims: Dim{ :draw } , Dim{ :chain } (500×4)\n :theta Float64 dims: Dim{ :school } , Dim{ :draw } , Dim{ :chain } (8×500×4)\n :tau Float64 dims: Dim{ :draw } , Dim{ :chain } (500×4)\n :log_tau Float64 dims: Dim{ :draw } , Dim{ :chain } (500×4)\n\n with metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\""},{"id":116,"pagetitle":"Working with InferenceData","title":"Obtain an array for a given parameter","ref":"/ArviZ/stable/working_with_inference_data/#Obtain-an-array-for-a-given-parameter","content":" Obtain an array for a given parameter Let’s say we want to get the values for mu as an array. Parameters can be accessed with either property or index syntax. post.tau 500×4 DimArray{Float64,2} tau with dimensions: \n Dim{ :draw } Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{ :chain } Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\n 0 1 2 3 \n 0 4.72574 1.97083 3.50128 6.07326\n 1 3.90899 2.04903 2.89324 3.77187\n 2 4.84403 2.12376 4.27329 3.17054\n 3 1.8567 3.39183 11.8965 6.00193\n 4 4.74841 4.84368 7.11325 3.28632\n ⋮ \n 494 8.15827 1.61268 4.96249 3.13966\n 495 7.56498 1.61268 3.56495 2.78607\n 496 2.24702 1.84816 2.55959 4.28196\n 497 1.89384 2.17459 4.08978 2.74061\n 498 5.92006 1.32755 2.72017 2.93238\n 499 4.3259 1.21199 1.91701 4.46125 post[:tau] === post.tau true To remove the dimensions, just use parent to retrieve the underlying array. parent(post.tau) 500×4 Matrix{Float64}:\n 4.72574 1.97083 3.50128 6.07326\n 3.90899 2.04903 2.89324 3.77187\n 4.84403 2.12376 4.27329 3.17054\n 1.8567 3.39183 11.8965 6.00193\n 4.74841 4.84368 7.11325 3.28632\n 3.51387 10.8872 7.18892 2.16314\n 4.20898 4.01889 9.0977 7.68505\n 2.6834 4.28584 7.84286 4.08612\n 1.16889 3.70403 17.1548 5.1157\n 1.21052 3.15829 16.7573 4.86939\n ⋮ \n 2.05742 1.09087 10.8168 5.08507\n 2.72536 1.09087 2.16788 6.1552\n 5.97049 1.67101 5.19169 8.23756\n 8.15827 1.61268 4.96249 3.13966\n 7.56498 1.61268 3.56495 2.78607\n 2.24702 1.84816 2.55959 4.28196\n 1.89384 2.17459 4.08978 2.74061\n 5.92006 1.32755 2.72017 2.93238\n 4.3259 1.21199 1.91701 4.46125"},{"id":117,"pagetitle":"Working with InferenceData","title":"Get the dimension lengths","ref":"/ArviZ/stable/working_with_inference_data/#Get-the-dimension-lengths","content":" Get the dimension lengths Let’s check how many groups are in our hierarchical model. size(idata.observed_data, :school) 8"},{"id":118,"pagetitle":"Working with InferenceData","title":"Get coordinate/index values","ref":"/ArviZ/stable/working_with_inference_data/#Get-coordinate/index-values","content":" Get coordinate/index values What are the names of the groups in our hierarchical model? You can access them from the coordinate name school in this case. DimensionalData.index(idata.observed_data, :school) 8-element Vector{String}:\n \"Choate\"\n \"Deerfield\"\n \"Phillips Andover\"\n \"Phillips Exeter\"\n \"Hotchkiss\"\n \"Lawrenceville\"\n \"St. Paul's\"\n \"Mt. Hermon\""},{"id":119,"pagetitle":"Working with InferenceData","title":"Get a subset of chains","ref":"/ArviZ/stable/working_with_inference_data/#Get-a-subset-of-chains","content":" Get a subset of chains Let’s keep only chain 0 here. For the subset to take effect on all relevant InferenceData groups – posterior , sample_stats , log_likelihood , and posterior_predictive – we will index InferenceData instead of Dataset . Here we use DimensionalData's At selector. Its other selectors are also supported. idata[chain=At(0)] InferenceData posterior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" posterior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:41.460544\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" log_likelihood Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:37.487399\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" sample_stats Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points\nand 16 layers:\n :max_energy_error Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :energy_error Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :lp Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :index_in_trajectory Int64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :acceptance_rate Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :diverging Bool dims: Dim{:draw}, Dim{:chain} (500×1)\n :process_time_diff Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :n_steps Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :perf_counter_start Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :largest_eigval Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (500×1)\n :smallest_eigval Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (500×1)\n :step_size_bar Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :step_size Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :energy Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :tree_depth Int64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :perf_counter_diff Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.324929\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.602116\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.604969\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" observed_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :obs Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.606375\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" constant_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :scores Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.607471\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" Note that in this case, prior only has a chain of 0. If it also had the other chains, we could have passed chain=At([0, 2]) to subset by chains 0 and 2. Warning If we used idata[chain=[0, 2]] without the At selector, this is equivalent to idata[chain=DimensionalData.index(idata.posterior, :chain)[0, 2]] , that is, [0, 2] indexes an array of dimension indices, which here would error. But if we had requested idata[chain=[1, 2]] we would not hit an error, but we would index the wrong chains. So it's important to always use a selector to index by values of dimension indices."},{"id":120,"pagetitle":"Working with InferenceData","title":"Remove the first $n$ draws (burn-in)","ref":"/ArviZ/stable/working_with_inference_data/#Remove-the-first-n-draws-(burn-in)","content":" Remove the first $n$ draws (burn-in) Let’s say we want to remove the first 100 draws from all the chains and all InferenceData groups with draws. To do this we use the .. syntax from IntervalSets.jl, which is exported by DimensionalData. idata[draw=100 .. Inf] InferenceData posterior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[100, 101, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×400×4)\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" posterior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[100, 101, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×400×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:41.460544\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" log_likelihood Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[100, 101, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×400×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:37.487399\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" sample_stats Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[100, 101, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 16 layers:\n :max_energy_error Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :energy_error Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :lp Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :index_in_trajectory Int64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :acceptance_rate Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :diverging Bool dims: Dim{:draw}, Dim{:chain} (400×4)\n :process_time_diff Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :n_steps Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :perf_counter_start Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :largest_eigval Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (400×4)\n :smallest_eigval Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (400×4)\n :step_size_bar Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :step_size Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :energy Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :tree_depth Int64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :perf_counter_diff Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.324929\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[100, 101, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (400×1)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×400×1)\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (400×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.602116\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[100, 101, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×400×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.604969\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" observed_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :obs Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.606375\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" constant_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :scores Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.607471\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" If you check the object you will see that the groups posterior , posterior_predictive , prior , and sample_stats have 400 draws compared to idata , which has 500. The group observed_data has not been affected because it does not have the draw dimension. Alternatively, you can change a subset of groups by combining indexing styles with merge . Here we use this to build a new InferenceData where we have discarded the first 100 draws only from posterior . merge(idata, idata[(:posterior,), draw=100 .. Inf]) InferenceData posterior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[100, 101, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×400×4)\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (400×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" posterior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:41.460544\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" log_likelihood Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:37.487399\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" sample_stats Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 16 layers:\n :max_energy_error Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :energy_error Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :lp Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :index_in_trajectory Int64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :acceptance_rate Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :diverging Bool dims: Dim{:draw}, Dim{:chain} (500×4)\n :process_time_diff Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :n_steps Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :perf_counter_start Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :largest_eigval Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (500×4)\n :smallest_eigval Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (500×4)\n :step_size_bar Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :step_size Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :energy Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :tree_depth Int64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :perf_counter_diff Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.324929\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.602116\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.604969\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" observed_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :obs Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.606375\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" constant_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :scores Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.607471\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\""},{"id":121,"pagetitle":"Working with InferenceData","title":"Compute posterior mean values along draw and chain dimensions","ref":"/ArviZ/stable/working_with_inference_data/#Compute-posterior-mean-values-along-draw-and-chain-dimensions","content":" Compute posterior mean values along draw and chain dimensions To compute the mean value of the posterior samples, do the following: mean(post) (mu = 4.485933103402338,\n theta = 4.911515591394205,\n tau = 4.124222787491913,) This computes the mean along all dimensions, discarding all dimensions and returning the result as a NamedTuple . This may be what you wanted for mu and tau , which have only two dimensions ( chain and draw ), but maybe not what you expected for theta , which has one more dimension school . You can specify along which dimension you want to compute the mean (or other functions), which instead returns a Dataset . mean(post; dims=(:chain, :draw)) Dataset with dimensions: \n Dim{ :draw } Sampled{Float64} Float64[249.5] ForwardOrdered Irregular Points,\n Dim{ :chain } Sampled{Float64} Float64[1.5] ForwardOrdered Irregular Points,\n Dim{ :school } Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n and 3 layers:\n :mu Float64 dims: Dim{ :draw } , Dim{ :chain } (1×1)\n :theta Float64 dims: Dim{ :school } , Dim{ :draw } , Dim{ :chain } (8×1×1)\n :tau Float64 dims: Dim{ :draw } , Dim{ :chain } (1×1)\n\n with metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" The singleton dimensions of chain and draw now contain meaningless indices, so you may want to discard them, which you can do with dropdims . dropdims(mean(post; dims=(:chain, :draw)); dims=(:chain, :draw)) Dataset with dimensions: \n Dim{ :school } Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n and 3 layers:\n :mu Float64 dims: \n :theta Float64 dims: Dim{ :school } (8)\n :tau Float64 dims: \n\n with metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\""},{"id":122,"pagetitle":"Working with InferenceData","title":"Renaming a dimension","ref":"/ArviZ/stable/working_with_inference_data/#Renaming-a-dimension","content":" Renaming a dimension We can rename a dimension in a Dataset using DimensionalData's set method: theta_bis = set(post.theta; school=:school_bis) 8×500×4 DimArray{Float64,3} theta with dimensions: \n Dim{ :school_bis } Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{ :draw } Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{ :chain } Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\n[:, :, 1]\n 0 … 497 498 499 \n \"Choate\" 12.3207 -0.213828 10.4025 6.66131\n \"Deerfield\" 9.90537 1.35515 6.90741 7.41377\n \"Phillips Andover\" 14.9516 6.98269 -4.96414 -9.3226\n \"Phillips Exeter\" 11.0115 3.71681 3.13584 2.69192\n \"Hotchkiss\" 5.5796 … 5.32446 -2.2243 -0.502331\n \"Lawrenceville\" 16.9018 6.96589 -2.83504 -4.25487\n \"St. Paul's\" 13.1981 4.9302 5.39106 7.56657\n \"Mt. Hermon\" 15.0614 3.0586 6.38124 9.98762\n [and 3 more slices...] We can use this, for example, to broadcast functions across multiple arrays, automatically matching up shared dimensions, using DimensionalData.broadcast_dims . theta_school_diff = broadcast_dims(-, post.theta, theta_bis) 8×500×4×8 DimArray{Float64,4} theta with dimensions: \n Dim{ :school } Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{ :draw } Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{ :chain } Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{ :school_bis } Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n[:, :, 1, 1]\n 0 … 497 498 499 \n \"Choate\" 0.0 0.0 0.0 0.0\n \"Deerfield\" -2.41532 1.56898 -3.49509 0.752459\n \"Phillips Andover\" 2.63093 7.19652 -15.3666 -15.9839\n \"Phillips Exeter\" -1.3092 3.93064 -7.26666 -3.96939\n \"Hotchkiss\" -6.74108 … 5.53829 -12.6268 -7.16364\n \"Lawrenceville\" 4.58111 7.17972 -13.2375 -10.9162\n \"St. Paul's\" 0.877374 5.14403 -5.01144 0.905263\n \"Mt. Hermon\" 2.74068 3.27243 -4.02126 3.32631\n [and 31 more slices...]"},{"id":123,"pagetitle":"Working with InferenceData","title":"Compute and store posterior pushforward quantities","ref":"/ArviZ/stable/working_with_inference_data/#Compute-and-store-posterior-pushforward-quantities","content":" Compute and store posterior pushforward quantities We use “posterior pushfoward quantities” to refer to quantities that are not variables in the posterior but deterministic computations using posterior variables. You can compute these pushforward operations and store them as a new variable in a copy of the posterior group. Here we'll create a new InferenceData with theta_school_diff in the posterior: idata_new = Base.setindex(idata, merge(post, (; theta_school_diff)), :posterior) InferenceData posterior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:school_bis} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 4 layers:\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :theta_school_diff Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain}, Dim{:school_bis} (8×500×4×8)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" posterior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:41.460544\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" log_likelihood Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×4)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:37.487399\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" sample_stats Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points\nand 16 layers:\n :max_energy_error Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :energy_error Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :lp Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :index_in_trajectory Int64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :acceptance_rate Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :diverging Bool dims: Dim{:draw}, Dim{:chain} (500×4)\n :process_time_diff Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :n_steps Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :perf_counter_start Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :largest_eigval Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (500×4)\n :smallest_eigval Union{Missing, Float64} dims: Dim{:draw}, Dim{:chain} (500×4)\n :step_size_bar Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :step_size Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :energy Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :tree_depth Int64 dims: Dim{:draw}, Dim{:chain} (500×4)\n :perf_counter_diff Float64 dims: Dim{:draw}, Dim{:chain} (500×4)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.324929\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.602116\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" prior_predictive Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0] ForwardOrdered Irregular Points\nand 1 layer:\n :obs Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×1)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.604969\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" observed_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :obs Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.606375\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" constant_data Dataset with dimensions: \n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 1 layer:\n :scores Float64 dims: Dim{:school} (8)\n\nwith metadata Dict{String, Any} with 4 entries:\n \"created_at\" => \"2022-10-13T14:37:26.607471\"\n \"inference_library_version\" => \"4.2.2\"\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" Once you have these pushforward quantities in an InferenceData , you’ll then be able to plot them with ArviZ functions, calculate stats and diagnostics on them, or save and share the InferenceData object with the pushforward quantities included. Here we compute the mcse of theta_school_diff : mcse(idata_new.posterior).theta_school_diff 8×8 DimArray{Float64,2} theta_school_diff with dimensions: \n Dim{ :school } Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered,\n Dim{ :school_bis } Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" … \"St. Paul's\" \"Mt. Hermon\" \n \"Choate\" NaN 0.117476 0.219695\n \"Deerfield\" 0.191463 0.16484 0.189386\n \"Phillips Andover\" 0.255636 0.258001 0.160477\n \"Phillips Exeter\" 0.162782 0.156724 0.144923\n \"Hotchkiss\" 0.282881 … 0.283969 0.189015\n \"Lawrenceville\" 0.259065 0.251988 0.178094\n \"St. Paul's\" 0.117476 NaN 0.222054\n \"Mt. Hermon\" 0.219695 0.222054 NaN"},{"id":124,"pagetitle":"Working with InferenceData","title":"Advanced subsetting","ref":"/ArviZ/stable/working_with_inference_data/#Advanced-subsetting","content":" Advanced subsetting To select the value corresponding to the difference between the Choate and Deerfield schools do: school_idx = [\"Choate\", \"Hotchkiss\", \"Mt. Hermon\"]\nschool_bis_idx = [\"Deerfield\", \"Choate\", \"Lawrenceville\"]\ntheta_school_diff[school=At(school_idx), school_bis=At(school_bis_idx)] 3×500×4×3 DimArray{Float64,4} theta with dimensions: \n Dim{ :school } Categorical{String} String[\"Choate\", \"Hotchkiss\", \"Mt. Hermon\"] Unordered,\n Dim{ :draw } Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{ :chain } Sampled{Int64} Int64[0, 1, 2, 3] ForwardOrdered Irregular Points,\n Dim{ :school_bis } Categorical{String} String[\"Deerfield\", \"Choate\", \"Lawrenceville\"] Unordered\n[:, :, 1, 1]\n 0 1 … 497 498 499 \n \"Choate\" 2.41532 2.1563 -1.56898 3.49509 -0.752459\n \"Hotchkiss\" -4.32577 -1.31781 3.96931 -9.13171 -7.9161\n \"Mt. Hermon\" 5.156 -2.9526 1.70345 -0.526168 2.57385\n [and 11 more slices...]"},{"id":125,"pagetitle":"Working with InferenceData","title":"Add new chains using cat","ref":"/ArviZ/stable/working_with_inference_data/#Add-new-chains-using-cat","content":" Add new chains using cat Suppose after checking the mcse and realizing you need more samples, you rerun the model with two chains and obtain an idata_rerun object. idata_rerun = InferenceData(; posterior=set(post[chain=At([0, 1])]; chain=[4, 5])) InferenceData posterior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[4, 5] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×2)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×2)\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×2)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\" You can combine the two using cat . cat(idata[[:posterior]], idata_rerun; dims=:chain) InferenceData posterior Dataset with dimensions: \n Dim{:draw} Sampled{Int64} Int64[0, 1, …, 498, 499] ForwardOrdered Irregular Points,\n Dim{:chain} Sampled{Int64} Int64[0, 1, …, 4, 5] ForwardOrdered Irregular Points,\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\nand 3 layers:\n :mu Float64 dims: Dim{:draw}, Dim{:chain} (500×6)\n :theta Float64 dims: Dim{:school}, Dim{:draw}, Dim{:chain} (8×500×6)\n :tau Float64 dims: Dim{:draw}, Dim{:chain} (500×6)\n\nwith metadata Dict{String, Any} with 6 entries:\n \"created_at\" => \"2022-10-13T14:37:37.315398\"\n \"inference_library_version\" => \"4.2.2\"\n \"sampling_time\" => 7.48011\n \"tuning_steps\" => 1000\n \"arviz_version\" => \"0.13.0.dev0\"\n \"inference_library\" => \"pymc\""},{"id":128,"pagetitle":"Home","title":"ArviZPythonPlots.jl","ref":"/ArviZPythonPlots/stable/#ArviZPythonPlots.jl","content":" ArviZPythonPlots.jl ArviZPythonPlots.jl provides PyPlot-compatible plotting functions for exploratory analysis of Bayesian models using ArviZ.jl . It uses PythonCall.jl to provide an interface for using the plotting functions in Python ArviZ with Julia types. It also re-exports all methods exported by PythonPlot.jl . For details, see the Example Gallery or the API ."},{"id":129,"pagetitle":"Home","title":"Installation","ref":"/ArviZPythonPlots/stable/#installation","content":" Installation To install ArviZPythonPlots.jl, we first need to install Python ArviZ. From the Julia REPL, type ] to enter the Pkg REPL mode and run pkg> add ArviZPythonPlots"},{"id":132,"pagetitle":"API Overview","title":"API Overview","ref":"/ArviZPythonPlots/stable/api/#api","content":" API Overview Plotting styles rcParams Plotting functions"},{"id":135,"pagetitle":"Plotting functions","title":"Plotting functions","ref":"/ArviZPythonPlots/stable/api/plots/#plots-api","content":" Plotting functions ArviZPythonPlots.plot_autocorr ArviZPythonPlots.plot_bf ArviZPythonPlots.plot_bpv ArviZPythonPlots.plot_compare ArviZPythonPlots.plot_density ArviZPythonPlots.plot_dist ArviZPythonPlots.plot_dist_comparison ArviZPythonPlots.plot_dot ArviZPythonPlots.plot_ecdf ArviZPythonPlots.plot_elpd ArviZPythonPlots.plot_energy ArviZPythonPlots.plot_ess ArviZPythonPlots.plot_forest ArviZPythonPlots.plot_hdi ArviZPythonPlots.plot_kde ArviZPythonPlots.plot_khat ArviZPythonPlots.plot_lm ArviZPythonPlots.plot_loo_pit ArviZPythonPlots.plot_mcse ArviZPythonPlots.plot_pair ArviZPythonPlots.plot_parallel ArviZPythonPlots.plot_posterior ArviZPythonPlots.plot_ppc ArviZPythonPlots.plot_rank ArviZPythonPlots.plot_separation ArviZPythonPlots.plot_trace ArviZPythonPlots.plot_violin"},{"id":136,"pagetitle":"Plotting functions","title":"Reference","ref":"/ArviZPythonPlots/stable/api/plots/#Reference","content":" Reference"},{"id":137,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_autocorr","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_autocorr-Tuple","content":" ArviZPythonPlots.plot_autocorr — Method Bar plot of the autocorrelation function (ACF) for a sequence of data.\n\n The ACF plots are helpful as a convergence diagnostic for posteriors from MCMC\n samples which display autocorrelation.\n\n Parameters\n ----------\n data : InferenceData\n Any object that can be converted to an :class:`arviz.InferenceData` object\n refer to documentation of :func:`arviz.convert_to_dataset` for details\n var_names : list of str, optional\n Variables to be plotted. Prefix the variables by ``~`` when you want to exclude\n them from the plot. See :ref:`this section ` for usage examples.\n filter_vars : {None, \"like\", \"regex\"}, default None\n If `None` (default), interpret `var_names` as the real variables names. If \"like\",\n interpret `var_names` as substrings of the real variables names. If \"regex\",\n interpret `var_names` as regular expressions on the real variables names. See\n :ref:`this section ` for usage examples.\n max_lag : int, optional\n Maximum lag to calculate autocorrelation. By Default, the plot displays the\n first 100 lag or the total number of draws, whichever is smaller.\n combined : bool, default False\n Flag for combining multiple chains into a single chain. If False, chains will be\n plotted separately.\n grid : tuple, optional\n Number of rows and columns. Defaults to None, the rows and columns are\n automatically inferred. See :ref:`this section ` for usage examples.\n figsize : (float, float), optional\n Figure size. If None it will be defined automatically.\n Note this is not used if `ax` is supplied.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If None it will be autoscaled based\n on `figsize`.\n labeller : Labeller, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n ax : 2D array-like of matplotlib_axes or bokeh_figure, optional\n A 2D array of locations into which to plot the densities. If not supplied, ArviZ will create\n its own array of plot areas (and return it).\n backend : {\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_config : dict, optional\n Currently specifies the bounds to use for bokeh axes. Defaults to value set in ``rcParams``.\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : matplotlib_axes or bokeh_figures\n\n See Also\n --------\n autocov : Compute autocovariance estimates for every lag for the input array.\n autocorr : Compute autocorrelation using FFT for every lag for the input array.\n\n Examples\n --------\n Plot default autocorrelation\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data('centered_eight')\n >>> az.plot_autocorr(data)\n\n Plot subset variables by specifying variable name exactly\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_autocorr(data, var_names=['mu', 'tau'] )\n\n\n Combine chains by variable and select variables by excluding some with partial naming\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_autocorr(data, var_names=['~thet'], filter_vars=\"like\", combined=True)\n\n\n Specify maximum lag (x axis bound)\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_autocorr(data, var_names=['mu', 'tau'], max_lag=200, combined=True)\n \n source"},{"id":138,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_bf","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_bf-Tuple","content":" ArviZPythonPlots.plot_bf — Method Approximated Bayes Factor for comparing hypothesis of two nested models.\n\n The Bayes factor is estimated by comparing a model (H1) against a model in which the\n parameter of interest has been restricted to be a point-null (H0). This computation\n assumes the models are nested and thus H0 is a special case of H1.\n\n Notes\n -----\n The bayes Factor is approximated pproximated as the Savage-Dickey density ratio\n algorithm presented in [1]_.\n\n Parameters\n -----------\n idata : InferenceData\n Any object that can be converted to an :class:`arviz.InferenceData` object\n Refer to documentation of :func:`arviz.convert_to_dataset` for details.\n var_name : str, optional\n Name of variable we want to test.\n prior : numpy.array, optional\n In case we want to use different prior, for example for sensitivity analysis.\n ref_val : int, default 0\n Point-null for Bayes factor estimation.\n xlim : tuple, optional\n Set the x limits, which might be used for visualization purposes.\n colors : tuple, default ('C0', 'C1')\n Tuple of valid Matplotlib colors. First element for the prior, second for the posterior.\n figsize : (float, float), optional\n Figure size. If `None` it will be defined automatically.\n textsize: float, optional\n Text size scaling factor for labels, titles and lines. If `None` it will be autoscaled based\n on `figsize`.\n plot_kwargs : dicts, optional\n Additional keywords passed to :func:`matplotlib.pyplot.plot`.\n hist_kwargs : dicts, optional\n Additional keywords passed to :func:`arviz.plot_dist`. Only works for discrete variables.\n ax : axes, optional\n :class:`matplotlib.axes.Axes` or :class:`bokeh.plotting.Figure`.\n backend :{\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n dict : A dictionary with BF10 (Bayes Factor 10 (H1/H0 ratio), and BF01 (H0/H1 ratio).\n axes : matplotlib_axes or bokeh_figure\n\n References\n ----------\n .. [1] Heck, D., 2019. A caveat on the avage-Dickey density ratio:\n The case of computing Bayes factors for regression parameters.\n\n Examples\n --------\n Moderate evidence indicating that the parameter \"a\" is different from zero.\n\n .. plot::\n :context: close-figs\n\n >>> import numpy as np\n >>> import arviz as az\n >>> idata = az.from_dict(posterior={\"a\":np.random.normal(1, 0.5, 5000)},\n ... prior={\"a\":np.random.normal(0, 1, 5000)})\n >>> az.plot_bf(idata, var_name=\"a\", ref_val=0)\n \n source"},{"id":139,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_bpv","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_bpv-Tuple","content":" ArviZPythonPlots.plot_bpv — Method Plot Bayesian p-value for observed data and Posterior/Prior predictive.\n\n Parameters\n ----------\n data : InferenceData\n :class:`arviz.InferenceData` object containing the observed and\n posterior/prior predictive data.\n kind : {\"u_value\", \"p_value\", \"t_stat\"}, default \"u_value\"\n Specify the kind of plot:\n\n * The ``kind=\"p_value\"`` computes :math:`p := p(y* \\leq y | y)`.\n This is the probability of the data y being larger or equal than the predicted data y*.\n The ideal value is 0.5 (half the predictions below and half above the data).\n * The ``kind=\"u_value\"`` argument computes :math:`p_i := p(y_i* \\leq y_i | y)`.\n i.e. like a p_value but per observation :math:`y_i`. This is also known as marginal\n p_value. The ideal distribution is uniform. This is similar to the LOO-PIT\n calculation/plot, the difference is than in LOO-pit plot we compute\n :math:`pi = p(y_i* r \\leq y_i | y_{-i} )`, where :math:`y_{-i}`,\n is all other data except :math:`y_i`.\n * The ``kind=\"t_stat\"`` argument computes :math:`:= p(T(y)* \\leq T(y) | y)`\n where T is any test statistic. See ``t_stat`` argument below for details\n of available options.\n\n t_stat : str, float, or callable, default \"median\"\n Test statistics to compute from the observations and predictive distributions.\n Allowed strings are “mean”, “median” or “std”. Alternative a quantile can be passed\n as a float (or str) in the interval (0, 1). Finally a user defined function is also\n acepted, see examples section for details.\n bpv : bool, default True\n If True add the Bayesian p_value to the legend when ``kind = t_stat``.\n plot_mean : bool, default True\n Whether or not to plot the mean test statistic.\n reference : {\"analytical\", \"samples\", None}, default \"analytical\"\n How to compute the distributions used as reference for ``kind=u_values``\n or ``kind=p_values``. Use `None` to not plot any reference.\n mse : bool, default False\n Show scaled mean square error between uniform distribution and marginal p_value\n distribution.\n n_ref : int, default 100\n Number of reference distributions to sample when ``reference=samples``.\n hdi_prob : float, optional\n Probability for the highest density interval for the analytical reference distribution when\n ``kind=u_values``. Should be in the interval (0, 1]. Defaults to the\n rcParam ``stats.hdi_prob``. See :ref:`this section ` for usage examples.\n color : str, optional\n Matplotlib color\n grid : tuple, optional\n Number of rows and columns. By default, the rows and columns are\n automatically inferred. See :ref:`this section ` for usage examples.\n figsize : (float, float), optional\n Figure size. If None it will be defined automatically.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If None it will be autoscaled based\n on `figsize`.\n data_pairs : dict, optional\n Dictionary containing relations between observed data and posterior/prior predictive data.\n Dictionary structure:\n\n - key = data var_name\n - value = posterior/prior predictive var_name\n\n For example, ``data_pairs = {'y' : 'y_hat'}``\n If None, it will assume that the observed data and the posterior/prior\n predictive data have the same variable name.\n Labeller : Labeller, optional\n Class providing the method ``make_pp_label`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n var_names : list of str, optional\n Variables to be plotted. If `None` all variable are plotted. Prefix the variables by ``~``\n when you want to exclude them from the plot. See the :ref:`this section `\n for usage examples. See :ref:`this section ` for usage examples.\n filter_vars : {None, \"like\", \"regex\"}, default None\n If `None` (default), interpret `var_names` as the real variables names. If \"like\",\n interpret `var_names` as substrings of the real variables names. If \"regex\",\n interpret `var_names` as regular expressions on the real variables names. See\n :ref:`this section ` for usage examples.\n coords : dict, optional\n Dictionary mapping dimensions to selected coordinates to be plotted.\n Dimensions without a mapping specified will include all coordinates for\n that dimension. Defaults to including all coordinates for all\n dimensions if None. See :ref:`this section ` for usage examples.\n flatten : list, optional\n List of dimensions to flatten in observed_data. Only flattens across the coordinates\n specified in the coords argument. Defaults to flattening all of the dimensions.\n flatten_pp : list, optional\n List of dimensions to flatten in posterior_predictive/prior_predictive. Only flattens\n across the coordinates specified in the coords argument. Defaults to flattening all\n of the dimensions. Dimensions should match flatten excluding dimensions for data_pairs\n parameters. If `flatten` is defined and `flatten_pp` is None, then ``flatten_pp=flatten``.\n legend : bool, default True\n Add legend to figure.\n ax : 2D array-like of matplotlib_axes or bokeh_figure, optional\n A 2D array of locations into which to plot the densities. If not supplied, ArviZ will create\n its own array of plot areas (and return it).\n backend : str, optional\n Select plotting backend {\"matplotlib\", \"bokeh\"}. Default \"matplotlib\".\n plot_ref_kwargs : dict, optional\n Extra keyword arguments to control how reference is represented.\n Passed to :meth:`matplotlib.axes.Axes.plot` or\n :meth:`matplotlib.axes.Axes.axhspan` (when ``kind=u_value``\n and ``reference=analytical``).\n backend_kwargs : bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n group : {\"posterior\", \"prior\"}, default \"posterior\"\n Specifies which InferenceData group should be plotted. If \"posterior\", then the values\n in `posterior_predictive` group are compared to the ones in `observed_data`, if \"prior\" then\n the same comparison happens, but with the values in `prior_predictive` group.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : 2D ndarray of matplotlib_axes or bokeh_figure\n\n See Also\n --------\n plot_ppc : Plot for posterior/prior predictive checks.\n plot_loo_pit : Plot Leave-One-Out probability integral transformation (PIT) predictive checks.\n plot_dist_comparison : Plot to compare fitted and unfitted distributions.\n\n References\n ----------\n * Gelman et al. (2013) see http://www.stat.columbia.edu/~gelman/book/ pages 151-153 for details\n\n Examples\n --------\n Plot Bayesian p_values.\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data(\"regression1d\")\n >>> az.plot_bpv(data, kind=\"p_value\")\n\n Plot custom test statistic comparison.\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data(\"regression1d\")\n >>> az.plot_bpv(data, kind=\"t_stat\", t_stat=lambda x:np.percentile(x, q=50, axis=-1))\n \n source"},{"id":140,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_compare","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_compare-Tuple","content":" ArviZPythonPlots.plot_compare — Method Summary plot for model comparison.\n\n Models are compared based on their expected log pointwise predictive density (ELPD).\n This plot is in the style of the one used in [2]_. Chapter 6 in the first edition\n or 7 in the second.\n\n Notes\n -----\n The ELPD is estimated either by Pareto smoothed importance sampling leave-one-out\n cross-validation (LOO) or using the widely applicable information criterion (WAIC).\n We recommend LOO in line with the work presented by [1]_.\n\n Parameters\n ----------\n comp_df : pandas.DataFrame\n Result of the :func:`arviz.compare` method.\n insample_dev : bool, default False\n Plot in-sample ELPD, that is the value of the information criteria without the\n penalization given by the effective number of parameters (p_loo or p_waic).\n plot_standard_error : bool, default True\n Plot the standard error of the ELPD.\n plot_ic_diff : bool, default True\n Plot standard error of the difference in ELPD between each model\n and the top-ranked model.\n order_by_rank : bool, default True\n If True ensure the best model is used as reference.\n legend : bool, default True\n Add legend to figure.\n figsize : (float, float), optional\n If `None`, size is (6, num of models) inches.\n title : bool, default True\n Show a tittle with a description of how to interpret the plot.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If `None` it will be autoscaled based\n on `figsize`.\n labeller : Labeller, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n plot_kwargs : dict, optional\n Optional arguments for plot elements. Currently accepts 'color_ic',\n 'marker_ic', 'color_insample_dev', 'marker_insample_dev', 'color_dse',\n 'marker_dse', 'ls_min_ic' 'color_ls_min_ic', 'fontsize'\n ax : matplotlib_axes or bokeh_figure, optional\n Matplotlib axes or bokeh figure.\n backend : {\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_kwargs : bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : matplotlib_axes or bokeh_figure\n\n See Also\n --------\n plot_elpd : Plot pointwise elpd differences between two or more models.\n compare : Compare models based on PSIS-LOO loo or WAIC waic cross-validation.\n loo : Compute Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO-CV).\n waic : Compute the widely applicable information criterion.\n\n References\n ----------\n .. [1] Vehtari et al. (2016). Practical Bayesian model evaluation using leave-one-out\n cross-validation and WAIC https://arxiv.org/abs/1507.04544\n\n .. [2] McElreath R. (2022). Statistical Rethinking A Bayesian Course with Examples in\n R and Stan, Second edition, CRC Press.\n\n Examples\n --------\n Show default compare plot\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> model_compare = az.compare({'Centered 8 schools': az.load_arviz_data('centered_eight'),\n >>> 'Non-centered 8 schools': az.load_arviz_data('non_centered_eight')})\n >>> az.plot_compare(model_compare)\n\n Include the in-sample ELDP\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_compare(model_compare, insample_dev=True)\n\n \n source"},{"id":141,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_density","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_density-Tuple","content":" ArviZPythonPlots.plot_density — Method Generate KDE plots for continuous variables and histograms for discrete ones.\n\n Plots are truncated at their 100*(1-alpha)% highest density intervals. Plots are grouped per\n variable and colors assigned to models.\n\n Parameters\n ----------\n data : InferenceData or iterable of InferenceData\n Any object that can be converted to an :class:`arviz.InferenceData` object, or an Iterator\n returning a sequence of such objects.\n Refer to documentation of :func:`arviz.convert_to_dataset` for details.\n group : {\"posterior\", \"prior\"}, default \"posterior\"\n Specifies which InferenceData group should be plotted. If \"posterior\", then the values\n in `posterior_predictive` group are compared to the ones in `observed_data`, if \"prior\" then\n the same comparison happens, but with the values in `prior_predictive` group.\n data_labels : list of str, default None\n List with names for the datasets passed as \"data.\" Useful when plotting more than one\n dataset. Must be the same shape as the data parameter.\n var_names : list of str, optional\n List of variables to plot. If multiple datasets are supplied and `var_names` is not None,\n will print the same set of variables for each dataset. Defaults to None, which results in\n all the variables being plotted.\n filter_vars : {None, \"like\", \"regex\"}, default None\n If `None` (default), interpret `var_names` as the real variables names. If \"like\",\n interpret `var_names` as substrings of the real variables names. If \"regex\",\n interpret `var_names` as regular expressions on the real variables names. See\n :ref:`this section ` for usage examples.\n combine_dims : set_like of str, optional\n List of dimensions to reduce. Defaults to reducing only the \"chain\" and \"draw\" dimensions.\n See :ref:`this section ` for usage examples.\n transform : callable\n Function to transform data (defaults to `None` i.e. the identity function).\n hdi_prob : float, default 0.94\n Probability for the highest density interval. Should be in the interval (0, 1].\n See :ref:`this section ` for usage examples.\n point_estimate : str, optional\n Plot point estimate per variable. Values should be 'mean', 'median', 'mode' or None.\n Defaults to 'auto' i.e. it falls back to default set in ``rcParams``.\n colors : str or list of str, optional\n List with valid matplotlib colors, one color per model. Alternative a string can be passed.\n If the string is `cycle`, it will automatically choose a color per model from matplotlib's\n cycle. If a single color is passed, e.g. 'k', 'C2' or 'red' this color will be used for all\n models. Defaults to `cycle`.\n outline : bool, default True\n Use a line to draw KDEs and histograms.\n hdi_markers : str\n A valid `matplotlib.markers` like 'v', used to indicate the limits of the highest density\n interval. Defaults to empty string (no marker).\n shade : float, default 0\n Alpha blending value for the shaded area under the curve, between 0 (no shade) and 1\n (opaque).\n bw : float or str, optional\n If numeric, indicates the bandwidth and must be positive.\n If str, indicates the method to estimate the bandwidth and must be\n one of \"scott\", \"silverman\", \"isj\" or \"experimental\" when `circular` is False\n and \"taylor\" (for now) when `circular` is True.\n Defaults to \"default\" which means \"experimental\" when variable is not circular\n and \"taylor\" when it is.\n circular : bool, default False\n If True, it interprets the values passed are from a circular variable measured in radians\n and a circular KDE is used. Only valid for 1D KDE.\n grid : tuple, optional\n Number of rows and columns. Defaults to ``None``, the rows and columns are\n automatically inferred. See :ref:`this section ` for usage examples.\n figsize : (float, float), optional\n Figure size. If `None` it will be defined automatically.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If `None` it will be autoscaled based\n on `figsize`.\n labeller : Labeller, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n ax : 2D array-like of matplotlib_axes or bokeh_figure, optional\n A 2D array of locations into which to plot the densities. If not supplied, ArviZ will create\n its own array of plot areas (and return it).\n backend : {\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : 2D ndarray of matplotlib_axes or bokeh_figure\n\n See Also\n --------\n plot_dist : Plot distribution as histogram or kernel density estimates.\n plot_posterior : Plot Posterior densities in the style of John K. Kruschke's book.\n\n Examples\n --------\n Plot default density plot\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> centered = az.load_arviz_data('centered_eight')\n >>> non_centered = az.load_arviz_data('non_centered_eight')\n >>> az.plot_density([centered, non_centered])\n\n Plot variables in a 4x5 grid\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_density([centered, non_centered], grid=(4, 5))\n\n Plot subset variables by specifying variable name exactly\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_density([centered, non_centered], var_names=[\"mu\"])\n\n Plot a specific `az.InferenceData` group\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_density([centered, non_centered], var_names=[\"mu\"], group=\"prior\")\n\n Specify highest density interval\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_density([centered, non_centered], var_names=[\"mu\"], hdi_prob=.5)\n\n Shade plots and/or remove outlines\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_density([centered, non_centered], var_names=[\"mu\"], outline=False, shade=.8)\n\n Specify binwidth for kernel density estimation\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_density([centered, non_centered], var_names=[\"mu\"], bw=.9)\n \n source"},{"id":142,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_dist","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_dist-Tuple","content":" ArviZPythonPlots.plot_dist — Method Plot distribution as histogram or kernel density estimates.\n\n By default continuous variables are plotted using KDEs and discrete ones using histograms\n\n Parameters\n ----------\n values : array-like\n Values to plot from an unknown continuous or discrete distribution.\n values2 : array-like, optional\n Values to plot. If present, a 2D KDE or a hexbin will be estimated.\n color : string\n valid matplotlib color.\n kind : string, default \"auto\"\n By default (\"auto\") continuous variables will use the kind defined by rcParam\n ``plot.density_kind`` and discrete ones will use histograms.\n To override this use \"hist\" to plot histograms and \"kde\" for KDEs.\n cumulative : bool, default False\n If true plot the estimated cumulative distribution function. Defaults to False.\n Ignored for 2D KDE.\n label : string\n Text to include as part of the legend.\n rotated : bool, default False\n Whether to rotate the 1D KDE plot 90 degrees.\n rug : bool, default False\n Add a `rug plot `_ for a specific subset\n of values. Ignored for 2D KDE.\n bw : float or str, optional\n If numeric, indicates the bandwidth and must be positive.\n If str, indicates the method to estimate the bandwidth and must be\n one of \"scott\", \"silverman\", \"isj\" or \"experimental\" when ``is_circular`` is False\n and \"taylor\" (for now) when ``is_circular`` is True.\n Defaults to \"experimental\" when variable is not circular and \"taylor\" when it is.\n quantiles : list, optional\n Quantiles in ascending order used to segment the KDE. Use [.25, .5, .75] for quartiles.\n contour : bool, default True\n If True plot the 2D KDE using contours, otherwise plot a smooth 2D KDE.\n fill_last : bool, default True\n If True fill the last contour of the 2D KDE plot.\n figsize : (float, float), optional\n Figure size. If `None` it will be defined automatically.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If `None` it will be autoscaled based\n on `figsize`. Not implemented for bokeh backend.\n plot_kwargs : dict\n Keywords passed to the pdf line of a 1D KDE. Passed to :func:`arviz.plot_kde` as\n ``plot_kwargs``.\n fill_kwargs : dict\n Keywords passed to the fill under the line (use fill_kwargs={'alpha': 0} to disable fill).\n Ignored for 2D KDE. Passed to :func:`arviz.plot_kde` as ``fill_kwargs``.\n rug_kwargs : dict\n Keywords passed to the rug plot. Ignored if ``rug=False`` or for 2D KDE\n Use ``space`` keyword (float) to control the position of the rugplot.\n The larger this number the lower the rugplot. Passed to\n :func:`arviz.plot_kde` as ``rug_kwargs``.\n contour_kwargs : dict\n Keywords passed to the contourplot. Ignored for 1D KDE.\n contourf_kwargs : dict\n Keywords passed to :meth:`matplotlib.axes.Axes.contourf`. Ignored for 1D KDE.\n pcolormesh_kwargs : dict\n Keywords passed to :meth:`matplotlib.axes.Axes.pcolormesh`. Ignored for 1D KDE.\n hist_kwargs : dict\n Keyword arguments used to customize the histogram. Ignored when plotting a KDE.\n They are passed to :meth:`matplotlib.axes.Axes.hist` if using matplotlib,\n or to :meth:`bokeh.plotting.figure.quad` if using bokeh. In bokeh case,\n the following extra keywords are also supported:\n\n * ``color``: replaces the ``fill_color`` and ``line_color`` of the ``quad`` method\n * ``bins``: taken from ``hist_kwargs`` and passed to :func:`numpy.histogram` instead\n * ``density``: normalize histogram to represent a probability density function,\n Defaults to ``True``\n\n * ``cumulative``: plot the cumulative counts. Defaults to ``False``.\n\n is_circular : {False, True, \"radians\", \"degrees\"}, default False\n Select input type {\"radians\", \"degrees\"} for circular histogram or KDE plot. If True,\n default input type is \"radians\". When this argument is present, it interprets the\n values passed are from a circular variable measured in radians and a circular KDE is\n used. Inputs in \"degrees\" will undergo an internal conversion to radians. Only valid\n for 1D KDE.\n ax : matplotlib_axes or bokeh_figure, optional\n Matplotlib or bokeh targets on which to plot. If not supplied, Arviz will create\n its own plot area (and return it).\n backend : {\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_kwargs :dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : matplotlib axes or bokeh figure\n\n See Also\n --------\n plot_posterior : Plot Posterior densities in the style of John K. Kruschke's book.\n plot_density : Generate KDE plots for continuous variables and histograms for discrete ones.\n plot_kde : 1D or 2D KDE plot taking into account boundary conditions.\n\n Examples\n --------\n Plot an integer distribution\n\n .. plot::\n :context: close-figs\n\n >>> import numpy as np\n >>> import arviz as az\n >>> a = np.random.poisson(4, 1000)\n >>> az.plot_dist(a)\n\n Plot a continuous distribution\n\n .. plot::\n :context: close-figs\n\n >>> b = np.random.normal(0, 1, 1000)\n >>> az.plot_dist(b)\n\n Add a rug under the Gaussian distribution\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_dist(b, rug=True)\n\n Segment into quantiles\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_dist(b, rug=True, quantiles=[.25, .5, .75])\n\n Plot as the cumulative distribution\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_dist(b, rug=True, quantiles=[.25, .5, .75], cumulative=True)\n \n source"},{"id":143,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_dist_comparison","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_dist_comparison-Tuple","content":" ArviZPythonPlots.plot_dist_comparison — Method Plot to compare fitted and unfitted distributions.\n\n The resulting plots will show the compared distributions both on\n separate axes (particularly useful when one of them is substantially tighter\n than another), and plotted together, displaying a grid of three plots per\n distribution.\n\n Parameters\n ----------\n data : InferenceData\n Any object that can be converted to an :class:`arviz.InferenceData` object\n containing the posterior/prior data. Refer to documentation of\n :func:`arviz.convert_to_dataset` for details.\n kind : {\"latent\", \"observed\"}, default \"latent\"\n kind of plot to display The \"latent\" option includes {\"prior\", \"posterior\"},\n and the \"observed\" option includes\n {\"observed_data\", \"prior_predictive\", \"posterior_predictive\"}.\n figsize : (float, float), optional\n Figure size. If ``None`` it will be defined automatically.\n textsize : float\n Text size scaling factor for labels, titles and lines. If ``None`` it will be\n autoscaled based on `figsize`.\n var_names : str, list, list of lists, optional\n if str, plot the variable. if list, plot all the variables in list\n of all groups. if list of lists, plot the vars of groups in respective lists.\n See :ref:`this section ` for usage examples.\n coords : dict\n Dictionary mapping dimensions to selected coordinates to be plotted.\n Dimensions without a mapping specified will include all coordinates for\n that dimension. See :ref:`this section ` for usage examples.\n combine_dims : set_like of str, optional\n List of dimensions to reduce. Defaults to reducing only the \"chain\" and \"draw\" dimensions.\n See :ref:`this section ` for usage examples.\n transform : callable\n Function to transform data (defaults to `None` i.e. the identity function).\n legend : bool\n Add legend to figure. By default True.\n labeller : Labeller, optional\n Class providing the method ``make_pp_label`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n ax : (nvars, 3) array-like of matplotlib_axes, optional\n Matplotlib axes: The ax argument should have shape (nvars, 3), where the\n last column is for the combined before/after plots and columns 0 and 1 are\n for the before and after plots, respectively.\n prior_kwargs : dicts, optional\n Additional keywords passed to :func:`arviz.plot_dist` for prior/predictive groups.\n posterior_kwargs : dicts, optional\n Additional keywords passed to :func:`arviz.plot_dist` for posterior/predictive groups.\n observed_kwargs : dicts, optional\n Additional keywords passed to :func:`arviz.plot_dist` for observed_data group.\n backend : {\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : 2D ndarray of matplotlib_axes\n Returned object will have shape (nvars, 3),\n where the last column is the combined plot and the first columns are the single plots.\n\n See Also\n --------\n plot_bpv : Plot Bayesian p-value for observed data and Posterior/Prior predictive.\n\n Examples\n --------\n Plot the prior/posterior plot for specified vars and coords.\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data('rugby')\n >>> az.plot_dist_comparison(data, var_names=[\"defs\"], coords={\"team\" : [\"Italy\"]})\n\n \n source"},{"id":144,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_dot","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_dot-Tuple","content":" ArviZPythonPlots.plot_dot — Method Plot distribution as dot plot or quantile dot plot.\n\n This function uses the Wilkinson's Algorithm [1]_ to allot dots to bins.\n The quantile dot plots was inspired from [2]_.\n\n Parameters\n ----------\n values : array-like\n Values to plot from an unknown continuous or discrete distribution.\n binwidth : float, optional\n Width of the bin for drawing the dot plot.\n dotsize : float, default 1\n The size of the dots relative to the bin width. The default makes dots be\n just about as wide as the bin width.\n stackratio : float, default 1\n The distance between the center of the dots in the same stack relative to the bin height.\n The default makes dots in the same stack just touch each other.\n point_interval : bool, default False\n Plots the point interval. Uses ``hdi_prob`` to plot the HDI interval\n point_estimate : str, optional\n Plot point estimate per variable. Values should be ``mean``, ``median``, ``mode`` or None.\n Defaults to ``auto`` i.e. it falls back to default set in rcParams.\n dotcolor : string, optional\n The color of the dots. Should be a valid matplotlib color.\n intervalcolor : string, optional\n The color of the interval. Should be a valid matplotlib color.\n linewidth : int, default None\n Line width throughout. If None it will be autoscaled based on `figsize`.\n markersize : int, default None\n Markersize throughout. If None it will be autoscaled based on `figsize`.\n markercolor : string, optional\n The color of the marker when plot_interval is True. Should be a valid matplotlib color.\n marker : string, default \"o\"\n The shape of the marker. Valid for matplotlib backend.\n hdi_prob : float, optional\n Valid only when point_interval is True. Plots HDI for chosen percentage of density.\n Defaults to ``stats.hdi_prob`` rcParam. See :ref:`this section `\n for usage examples.\n rotated : bool, default False\n Whether to rotate the dot plot by 90 degrees.\n nquantiles : int, default 50\n Number of quantiles to plot, used for quantile dot plots.\n quartiles : bool, default True\n If True then the quartile interval will be plotted with the HDI.\n figsize : (float,float), optional\n Figure size. If ``None`` it will be defined automatically.\n plot_kwargs : dict, optional\n Keywords passed for customizing the dots. Passed to :class:`mpl:matplotlib.patches.Circle`\n in matplotlib and :meth:`bokeh.plotting.figure.circle` in bokeh.\n backend :{\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n ax : axes, optional\n Matplotlib_axes or bokeh_figure.\n show : bool, optional\n Call backend show function.\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n\n Returns\n -------\n axes : matplotlib_axes or bokeh_figure\n\n See Also\n --------\n plot_dist : Plot distribution as histogram or kernel density estimates.\n\n References\n ----------\n .. [1] Leland Wilkinson (1999) Dot Plots, The American Statistician, 53:3, 276-281,\n DOI: 10.1080/00031305.1999.10474474\n .. [2] Matthew Kay, Tara Kola, Jessica R. Hullman,\n and Sean A. Munson. 2016. When (ish) is My Bus? User-centered Visualizations of Uncertainty\n in Everyday, Mobile Predictive Systems. DOI:https://doi.org/10.1145/2858036.2858558\n\n Examples\n --------\n Plot dot plot for a set of data points\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> import numpy as np\n >>> values = np.random.normal(0, 1, 500)\n >>> az.plot_dot(values)\n\n Manually adjust number of quantiles to plot\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_dot(values, nquantiles=100)\n\n Add a point interval under the dot plot\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_dot(values, point_interval=True)\n\n Rotate the dot plots by 90 degrees i.e swap x and y axis\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_dot(values, point_interval=True, rotated=True)\n\n \n source"},{"id":145,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_ecdf","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_ecdf-Tuple","content":" ArviZPythonPlots.plot_ecdf — Method Plot ECDF or ECDF-Difference Plot with Confidence bands.\n\n Plots of the empirical CDF estimates of an array. When `values2` argument is provided,\n the two empirical CDFs are overlaid with the distribution of `values` on top\n (in a darker shade) and confidence bands in a more transparent shade. Optionally, the difference\n between the two empirical CDFs can be computed, and the PIT for a single dataset or a comparison\n between two samples.\n\n Notes\n -----\n This plot computes the confidence bands with the simulated based algorithm presented in [1]_.\n\n Parameters\n ----------\n values : array-like\n Values to plot from an unknown continuous or discrete distribution.\n values2 : array-like, optional\n Values to compare to the original sample.\n cdf : callable, optional\n Cumulative distribution function of the distribution to compare the original sample.\n difference : bool, default False\n If True then plot ECDF-difference plot otherwise ECDF plot.\n pit : bool, default False\n If True plots the ECDF or ECDF-diff of PIT of sample.\n confidence_bands : bool, default None\n If True plots the simultaneous or pointwise confidence bands with `1 - fpr`\n confidence level.\n pointwise : bool, default False\n If True plots pointwise confidence bands otherwise simultaneous bands.\n npoints : int, default 100\n This denotes the granularity size of our plot i.e the number of evaluation points\n for the ecdf or ecdf-difference plots.\n num_trials : int, default 500\n The number of random ECDFs to generate for constructing simultaneous confidence bands.\n fpr : float, default 0.05\n The type I error rate s.t `1 - fpr` denotes the confidence level of bands.\n figsize : (float,float), optional\n Figure size. If `None` it will be defined automatically.\n fill_band : bool, default True\n If True it fills in between to mark the area inside the confidence interval. Otherwise,\n plot the border lines.\n plot_kwargs : dict, optional\n Additional kwargs passed to :func:`mpl:matplotlib.pyplot.step` or\n :meth:`bokeh.plotting.figure.step`\n fill_kwargs : dict, optional\n Additional kwargs passed to :func:`mpl:matplotlib.pyplot.fill_between` or\n :meth:`bokeh:bokeh.plotting.Figure.varea`\n plot_outline_kwargs : dict, optional\n Additional kwargs passed to :meth:`mpl:matplotlib.axes.Axes.plot` or\n :meth:`bokeh:bokeh.plotting.Figure.line`\n ax :axes, optional\n Matplotlib axes or bokeh figures.\n show : bool, optional\n Call backend show function.\n backend : {\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n\n Returns\n -------\n axes : matplotlib_axes or bokeh_figure\n\n References\n ----------\n .. [1] Säilynoja, T., Bürkner, P.C. and Vehtari, A., 2021. Graphical Test for\n Discrete Uniformity and its Applications in Goodness of Fit Evaluation and\n Multiple Sample Comparison. arXiv preprint arXiv:2103.10522.\n\n Examples\n --------\n Plot ecdf plot for a given sample\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> from scipy.stats import uniform, binom, norm\n\n >>> sample = norm(0,1).rvs(1000)\n >>> az.plot_ecdf(sample)\n\n Plot ecdf plot with confidence bands for comparing a given sample w.r.t a given distribution\n\n .. plot::\n :context: close-figs\n\n >>> distribution = norm(0,1)\n >>> az.plot_ecdf(sample, cdf = distribution.cdf, confidence_bands = True)\n\n Plot ecdf-difference plot with confidence bands for comparing a given sample\n w.r.t a given distribution\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_ecdf(sample, cdf = distribution.cdf,\n >>> confidence_bands = True, difference = True)\n\n Plot ecdf plot with confidence bands for PIT of sample for comparing a given sample\n w.r.t a given distribution\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_ecdf(sample, cdf = distribution.cdf,\n >>> confidence_bands = True, pit = True)\n\n Plot ecdf-difference plot with confidence bands for PIT of sample for comparing a given\n sample w.r.t a given distribution\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_ecdf(sample, cdf = distribution.cdf,\n >>> confidence_bands = True, difference = True, pit = True)\n\n You could also plot the above w.r.t another sample rather than a given distribution.\n For eg: Plot ecdf-difference plot with confidence bands for PIT of sample for\n comparing a given sample w.r.t a given sample\n\n .. plot::\n :context: close-figs\n\n >>> sample2 = norm(0,1).rvs(5000)\n >>> az.plot_ecdf(sample, sample2, confidence_bands = True, difference = True, pit = True)\n\n \n source"},{"id":146,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_elpd","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_elpd-Tuple","content":" ArviZPythonPlots.plot_elpd — Method Plot pointwise elpd differences between two or more models.\n\n Pointwise model comparison based on their expected log pointwise predictive density (ELPD).\n\n Notes\n -----\n The ELPD is estimated either by Pareto smoothed importance sampling leave-one-out\n cross-validation (LOO) or using the widely applicable information criterion (WAIC).\n We recommend LOO in line with the work presented by [1]_.\n\n Parameters\n ----------\n compare_dict : mapping of {str : ELPDData or InferenceData}\n A dictionary mapping the model name to the object containing inference data or the result\n of :func:`arviz.loo` or :func:`arviz.waic` functions.\n Refer to :func:`arviz.convert_to_inference_data` for details on possible dict items.\n color : str or array_like, default \"C0\"\n Colors of the scatter plot. If color is a str all dots will have the same color.\n If it is the size of the observations, each dot will have the specified color.\n Otherwise, it will be interpreted as a list of the dims to be used for the color code.\n xlabels : bool, default False\n Use coords as xticklabels.\n figsize : (float, float), optional\n If `None`, size is (8 + numvars, 8 + numvars).\n textsize : float, optional\n Text size for labels. If `None` it will be autoscaled based on `figsize`.\n coords : mapping, optional\n Coordinates of points to plot. **All** values are used for computation, but only a\n subset can be plotted for convenience. See :ref:`this section `\n for usage examples.\n legend : bool, default False\n Include a legend to the plot. Only taken into account when color argument is a dim name.\n threshold : float, optional\n If some elpd difference is larger than ``threshold * elpd.std()``, show its label. If\n `None`, no observations will be highlighted.\n ic : str, optional\n Information Criterion (\"loo\" for PSIS-LOO, \"waic\" for WAIC) used to compare models.\n Defaults to ``rcParams[\"stats.information_criterion\"]``.\n Only taken into account when input is :class:`arviz.InferenceData`.\n scale : str, optional\n Scale argument passed to :func:`arviz.loo` or :func:`arviz.waic`, see their docs for\n details. Only taken into account when values in ``compare_dict`` are\n :class:`arviz.InferenceData`.\n var_name : str, optional\n Argument passed to to :func:`arviz.loo` or :func:`arviz.waic`, see their docs for\n details. Only taken into account when values in ``compare_dict`` are\n :class:`arviz.InferenceData`.\n plot_kwargs : dicts, optional\n Additional keywords passed to :meth:`matplotlib.axes.Axes.scatter`.\n ax : axes, optional\n :class:`matplotlib.axes.Axes` or :class:`bokeh.plotting.Figure`.\n backend : {\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : matplotlib_axes or bokeh_figure\n\n See Also\n --------\n plot_compare : Summary plot for model comparison.\n loo : Compute Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO-CV).\n waic : Compute the widely applicable information criterion.\n\n References\n ----------\n .. [1] Vehtari et al. (2016). Practical Bayesian model evaluation using leave-one-out\n cross-validation and WAIC https://arxiv.org/abs/1507.04544\n\n Examples\n --------\n Compare pointwise PSIS-LOO for centered and non centered models of the 8-schools problem\n using matplotlib.\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> idata1 = az.load_arviz_data(\"centered_eight\")\n >>> idata2 = az.load_arviz_data(\"non_centered_eight\")\n >>> az.plot_elpd(\n >>> {\"centered model\": idata1, \"non centered model\": idata2},\n >>> xlabels=True\n >>> )\n\n .. bokeh-plot::\n :source-position: above\n\n import arviz as az\n idata1 = az.load_arviz_data(\"centered_eight\")\n idata2 = az.load_arviz_data(\"non_centered_eight\")\n az.plot_elpd(\n {\"centered model\": idata1, \"non centered model\": idata2},\n backend=\"bokeh\"\n )\n\n \n source"},{"id":147,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_energy","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_energy-Tuple","content":" ArviZPythonPlots.plot_energy — Method Plot energy transition distribution and marginal energy distribution in HMC algorithms.\n\n This may help to diagnose poor exploration by gradient-based algorithms like HMC or NUTS.\n The energy function in HMC can identify posteriors with heavy tailed distributions, that\n in practice are challenging for sampling.\n\n This plot is in the style of the one used in [1]_.\n\n Parameters\n ----------\n data : obj\n :class:`xarray.Dataset`, or any object that can be converted (must represent\n ``sample_stats`` and have an ``energy`` variable).\n kind : str, optional\n Type of plot to display (\"kde\", \"hist\").\n bfmi : bool, default True\n If True add to the plot the value of the estimated Bayesian fraction of missing\n information.\n figsize : (float, float), optional\n Figure size. If `None` it will be defined automatically.\n legend : bool, default True\n Flag for plotting legend.\n fill_alpha : tuple, default (1, 0.75)\n Alpha blending value for the shaded area under the curve, between 0\n (no shade) and 1 (opaque).\n fill_color : tuple of valid matplotlib color, default ('C0', 'C5')\n Color for Marginal energy distribution and Energy transition distribution.\n bw : float or str, optional\n If numeric, indicates the bandwidth and must be positive.\n If str, indicates the method to estimate the bandwidth and must be\n one of \"scott\", \"silverman\", \"isj\" or \"experimental\". Defaults to \"experimental\".\n Only works if ``kind='kde'``.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If `None` it will be autoscaled\n based on `figsize`.\n fill_kwargs : dicts, optional\n Additional keywords passed to :func:`arviz.plot_kde` (to control the shade).\n plot_kwargs : dicts, optional\n Additional keywords passed to :func:`arviz.plot_kde` or :func:`matplotlib.pyplot.hist`\n (if ``type='hist'``).\n ax : axes, optional\n :class:`matplotlib.axes.Axes` or :class:`bokeh.plotting.Figure`.\n backend : {\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : matplotlib axes or bokeh figures\n\n See Also\n --------\n bfmi : Calculate the estimated Bayesian fraction of missing information (BFMI).\n\n References\n ----------\n .. [1] Betancourt (2016). Diagnosing Suboptimal Cotangent Disintegrations in\n Hamiltonian Monte Carlo https://arxiv.org/abs/1604.00695\n\n Examples\n --------\n Plot a default energy plot\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data('centered_eight')\n >>> az.plot_energy(data)\n\n Represent energy plot via histograms\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_energy(data, kind='hist')\n\n \n source"},{"id":148,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_ess","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_ess-Tuple","content":" ArviZPythonPlots.plot_ess — Method Generate quantile, local, or evolution ESS plots.\n\n The local and the quantile ESS plots are recommended for checking\n that there are enough samples for all the explored regions of the\n parameter space. Checking local and quantile ESS is particularly\n relevant when working with HDI intervals as opposed to ESS bulk,\n which is suitable for point estimates.\n\n Parameters\n ----------\n idata : InferenceData\n Any object that can be converted to an :class:`arviz.InferenceData` object\n Refer to documentation of :func:`arviz.convert_to_dataset` for details.\n var_names : list of str, optional\n Variables to be plotted. Prefix the variables by ``~`` when you want to exclude\n them from the plot. See :ref:`this section ` for usage examples.\n filter_vars : {None, \"like\", \"regex\"}, default None\n If `None` (default), interpret `var_names` as the real variables names. If \"like\",\n interpret `var_names` as substrings of the real variables names. If \"regex\",\n interpret `var_names` as regular expressions on the real variables names. See\n :ref:`this section ` for usage examples.\n kind : {\"local\", \"quantile\", \"evolution\"}, default \"local\"\n Specify the kind of plot:\n\n * The ``kind=\"local\"`` argument generates the ESS' local efficiency for\n estimating quantiles of a desired posterior.\n * The ``kind=\"quantile\"`` argument generates the ESS' local efficiency\n for estimating small-interval probability of a desired posterior.\n * The ``kind=\"evolution\"`` argument generates the estimated ESS'\n with incrised number of iterations of a desired posterior.\n\n relative : bool, default False\n Show relative ess in plot ``ress = ess / N``.\n coords : dict, optional\n Coordinates of `var_names` to be plotted. Passed to :meth:`xarray.Dataset.sel`.\n See :ref:`this section ` for usage examples.\n grid : tuple, optional\n Number of rows and columns. By default, the rows and columns are\n automatically inferred. See :ref:`this section ` for usage examples.\n figsize : (float, float), optional\n Figure size. If ``None`` it will be defined automatically.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If ``None`` it will be autoscaled\n based on `figsize`.\n rug : bool, default False\n Add a `rug plot `_ for a specific subset of values.\n rug_kind : str, default \"diverging\"\n Variable in sample stats to use as rug mask. Must be a boolean variable.\n n_points : int, default 20\n Number of points for which to plot their quantile/local ess or number of subsets\n in the evolution plot.\n extra_methods : bool, default False\n Plot mean and sd ESS as horizontal lines. Not taken into account if ``kind = 'evolution'``.\n min_ess : int, default 400\n Minimum number of ESS desired. If ``relative=True`` the line is plotted at\n ``min_ess / n_samples`` for local and quantile kinds and as a curve following\n the ``min_ess / n`` dependency in evolution kind.\n labeller : Labeller, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n ax : 2D array-like of matplotlib_axes or bokeh_figure, optional\n A 2D array of locations into which to plot the densities. If not supplied, ArviZ will create\n its own array of plot areas (and return it).\n extra_kwargs : dict, optional\n If evolution plot, `extra_kwargs` is used to plot ess tail and differentiate it\n from ess bulk. Otherwise, passed to extra methods lines.\n text_kwargs : dict, optional\n Only taken into account when ``extra_methods=True``. kwargs passed to ax.annotate\n for extra methods lines labels. It accepts the additional\n key ``x`` to set ``xy=(text_kwargs[\"x\"], mcse)``\n hline_kwargs : dict, optional\n kwargs passed to :func:`~matplotlib.axes.Axes.axhline` or to :class:`~bokeh.models.Span`\n depending on the backend for the horizontal minimum ESS line.\n For relative ess evolution plots the kwargs are passed to\n :func:`~matplotlib.axes.Axes.plot` or to :class:`~bokeh.plotting.figure.line`\n rug_kwargs : dict\n kwargs passed to rug plot.\n backend : {\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n **kwargs\n Passed as-is to :meth:`mpl:matplotlib.axes.Axes.hist` or\n :meth:`mpl:matplotlib.axes.Axes.plot` function depending on the\n value of `kind`.\n\n Returns\n -------\n axes : matplotlib_axes or bokeh_figure\n\n See Also\n --------\n ess : Calculate estimate of the effective sample size.\n\n References\n ----------\n .. [1] Vehtari et al. (2019). Rank-normalization, folding, and\n localization: An improved Rhat for assessing convergence of\n MCMC https://arxiv.org/abs/1903.08008\n\n Examples\n --------\n Plot local ESS.\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> idata = az.load_arviz_data(\"centered_eight\")\n >>> coords = {\"school\": [\"Choate\", \"Lawrenceville\"]}\n >>> az.plot_ess(\n ... idata, kind=\"local\", var_names=[\"mu\", \"theta\"], coords=coords\n ... )\n\n Plot ESS evolution as the number of samples increase. When the model is converging properly,\n both lines in this plot should be roughly linear.\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_ess(\n ... idata, kind=\"evolution\", var_names=[\"mu\", \"theta\"], coords=coords\n ... )\n\n Customize local ESS plot to look like reference paper.\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_ess(\n ... idata, kind=\"local\", var_names=[\"mu\"], drawstyle=\"steps-mid\", color=\"k\",\n ... linestyle=\"-\", marker=None, rug=True, rug_kwargs={\"color\": \"r\"}\n ... )\n\n Customize ESS evolution plot to look like reference paper.\n\n .. plot::\n :context: close-figs\n\n >>> extra_kwargs = {\"color\": \"lightsteelblue\"}\n >>> az.plot_ess(\n ... idata, kind=\"evolution\", var_names=[\"mu\"],\n ... color=\"royalblue\", extra_kwargs=extra_kwargs\n ... )\n\n \n source"},{"id":149,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_forest","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_forest-Tuple","content":" ArviZPythonPlots.plot_forest — Method Forest plot to compare HDI intervals from a number of distributions.\n\n Generate forest or ridge plots to compare distributions from a model or list of models.\n Additionally, the function can display effective sample sizes (ess) and Rhats to visualize\n convergence diagnostics alongside the distributions.\n\n Parameters\n ----------\n data : InferenceData\n Any object that can be converted to an :class:`arviz.InferenceData` object\n Refer to documentation of :func:`arviz.convert_to_dataset` for details.\n kind : {\"foresplot\", \"ridgeplot\"}, default \"forestplot\"\n Specify the kind of plot:\n\n * The ``kind=\"forestplot\"`` generates credible intervals, where the central points are the\n estimated posterior means, the thick lines are the central quartiles, and the thin lines\n represent the :math:`100\\times`(`hdi_prob`)% highest density intervals.\n * The ``kind=\"ridgeplot\"`` option generates density plots (kernel density estimate or\n histograms) in the same graph. Ridge plots can be configured to have different overlap,\n truncation bounds and quantile markers.\n\n model_names : list of str, optional\n List with names for the models in the list of data. Useful when plotting more that one\n dataset.\n var_names : list of str, optional\n Variables to be plotted. Prefix the variables by ``~`` when you want to exclude\n them from the plot. See :ref:`this section ` for usage examples.\n combine_dims : set_like of str, optional\n List of dimensions to reduce. Defaults to reducing only the \"chain\" and \"draw\" dimensions.\n See :ref:`this section ` for usage examples.\n filter_vars : {None, \"like\", \"regex\"}, default None\n If `None` (default), interpret `var_names` as the real variables names. If \"like\",\n interpret `var_names` as substrings of the real variables names. If \"regex\",\n interpret `var_names` as regular expressions on the real variables names. See\n :ref:`this section ` for usage examples.\n transform : callable, optional\n Function to transform data (defaults to None i.e.the identity function).\n coords : dict, optional\n Coordinates of ``var_names`` to be plotted. Passed to :meth:`xarray.Dataset.sel`.\n See :ref:`this section ` for usage examples.\n combined : bool, default False\n Flag for combining multiple chains into a single chain. If False, chains will\n be plotted separately. See :ref:`this section ` for usage examples.\n hdi_prob : float, default 0.94\n Plots highest posterior density interval for chosen percentage of density.\n See :ref:`this section ` for usage examples.\n rope : tuple or dictionary of tuples\n Lower and upper values of the Region of Practical Equivalence. If a list with one interval\n only is provided, the ROPE will be displayed across the y-axis. If more than one\n interval is provided the length of the list should match the number of variables.\n quartiles : bool, default True\n Flag for plotting the interquartile range, in addition to the ``hdi_prob`` intervals.\n r_hat : bool, default False\n Flag for plotting Split R-hat statistics. Requires 2 or more chains.\n ess : bool, default False\n Flag for plotting the effective sample size.\n colors : list or string, optional\n list with valid matplotlib colors, one color per model. Alternative a string can be passed.\n If the string is `cycle`, it will automatically chose a color per model from the matplotlibs\n cycle. If a single color is passed, eg 'k', 'C2', 'red' this color will be used for all\n models. Defaults to 'cycle'.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If `None` it will be autoscaled based\n on ``figsize``.\n linewidth : int, optional\n Line width throughout. If `None` it will be autoscaled based on ``figsize``.\n markersize : int, optional\n Markersize throughout. If `None` it will be autoscaled based on ``figsize``.\n legend : bool, optional\n Show a legend with the color encoded model information.\n Defaults to True, if there are multiple models.\n labeller : Labeller, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n ridgeplot_alpha: float, optional\n Transparency for ridgeplot fill. If ``ridgeplot_alpha=0``, border is colored by model,\n otherwise a `black` outline is used.\n ridgeplot_overlap : float, default 2\n Overlap height for ridgeplots.\n ridgeplot_kind : string, optional\n By default (\"auto\") continuous variables are plotted using KDEs and discrete ones using\n histograms. To override this use \"hist\" to plot histograms and \"density\" for KDEs.\n ridgeplot_truncate : bool, default True\n Whether to truncate densities according to the value of ``hdi_prob``.\n ridgeplot_quantiles : list, optional\n Quantiles in ascending order used to segment the KDE. Use [.25, .5, .75] for quartiles.\n figsize : (float, float), optional\n Figure size. If `None`, it will be defined automatically.\n ax : axes, optional\n :class:`matplotlib.axes.Axes` or :class:`bokeh.plotting.Figure`.\n backend : {\"matplotlib\", \"bokeh\"}, default \"matplotlib\"\n Select plotting backend.\n backend_config : dict, optional\n Currently specifies the bounds to use for bokeh axes. Defaults to value set in ``rcParams``.\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :class:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n 1D ndarray of matplotlib_axes or bokeh_figures\n\n See Also\n --------\n plot_posterior : Plot Posterior densities in the style of John K. Kruschke's book.\n plot_density : Generate KDE plots for continuous variables and histograms for discrete ones.\n summary : Create a data frame with summary statistics.\n\n Examples\n --------\n Forestplot\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> non_centered_data = az.load_arviz_data('non_centered_eight')\n >>> axes = az.plot_forest(non_centered_data,\n >>> kind='forestplot',\n >>> var_names=[\"^the\"],\n >>> filter_vars=\"regex\",\n >>> combined=True,\n >>> figsize=(9, 7))\n >>> axes[0].set_title('Estimated theta for 8 schools model')\n\n Forestplot with multiple datasets\n\n .. plot::\n :context: close-figs\n\n >>> centered_data = az.load_arviz_data('centered_eight')\n >>> axes = az.plot_forest([non_centered_data, centered_data],\n >>> model_names = [\"non centered eight\", \"centered eight\"],\n >>> kind='forestplot',\n >>> var_names=[\"^the\"],\n >>> filter_vars=\"regex\",\n >>> combined=True,\n >>> figsize=(9, 7))\n >>> axes[0].set_title('Estimated theta for 8 schools models')\n\n Forestplot with ropes\n\n .. plot::\n :context: close-figs\n\n >>> rope = {'theta': [{'school': 'Choate', 'rope': (2, 4)}], 'mu': [{'rope': (-2, 2)}]}\n >>> axes = az.plot_forest(non_centered_data,\n >>> rope=rope,\n >>> var_names='~tau',\n >>> combined=True,\n >>> figsize=(9, 7))\n >>> axes[0].set_title('Estimated theta for 8 schools model')\n\n\n Ridgeplot\n\n .. plot::\n :context: close-figs\n\n >>> axes = az.plot_forest(non_centered_data,\n >>> kind='ridgeplot',\n >>> var_names=['theta'],\n >>> combined=True,\n >>> ridgeplot_overlap=3,\n >>> colors='white',\n >>> figsize=(9, 7))\n >>> axes[0].set_title('Estimated theta for 8 schools model')\n\n Ridgeplot non-truncated and with quantiles\n\n .. plot::\n :context: close-figs\n\n >>> axes = az.plot_forest(non_centered_data,\n >>> kind='ridgeplot',\n >>> var_names=['theta'],\n >>> combined=True,\n >>> ridgeplot_truncate=False,\n >>> ridgeplot_quantiles=[.25, .5, .75],\n >>> ridgeplot_overlap=0.7,\n >>> colors='white',\n >>> figsize=(9, 7))\n >>> axes[0].set_title('Estimated theta for 8 schools model')\n \n source"},{"id":150,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_hdi","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_hdi-Tuple","content":" ArviZPythonPlots.plot_hdi — Method \n Plot HDI intervals for regression data.\n\n Parameters\n ----------\n x : array-like\n Values to plot.\n y : array-like, optional\n Values from which to compute the HDI. Assumed shape ``(chain, draw, \\*shape)``.\n Only optional if ``hdi_data`` is present.\n hdi_data : array_like, optional\n Precomputed HDI values to use. Assumed shape is ``(*x.shape, 2)``.\n hdi_prob : float, optional\n Probability for the highest density interval. Defaults to ``stats.hdi_prob`` rcParam.\n color : str, optional\n Color used for the limits of the HDI and fill. Should be a valid matplotlib color.\n circular : bool, optional\n Whether to compute the HDI taking into account ``x`` is a circular variable\n (in the range [-np.pi, np.pi]) or not. Defaults to False (i.e non-circular variables).\n smooth : boolean, optional\n If True the result will be smoothed by first computing a linear interpolation of the data\n over a regular grid and then applying the Savitzky-Golay filter to the interpolated data.\n Defaults to True.\n smooth_kwargs : dict, optional\n Additional keywords modifying the Savitzky-Golay filter. See\n :func:`scipy:scipy.signal.savgol_filter` for details.\n figsize : tuple\n Figure size. If None it will be defined automatically.\n fill_kwargs : dict, optional\n Keywords passed to :meth:`mpl:matplotlib.axes.Axes.fill_between`\n (use ``fill_kwargs={'alpha': 0}`` to disable fill) or to\n :meth:`bokeh.plotting.Figure.patch`.\n plot_kwargs : dict, optional\n HDI limits keyword arguments, passed to :meth:`mpl:matplotlib.axes.Axes.plot` or\n :meth:`bokeh.plotting.Figure.patch`.\n hdi_kwargs : dict, optional\n Keyword arguments passed to :func:`~arviz.hdi`. Ignored if ``hdi_data`` is present.\n ax : axes, optional\n Matplotlib axes or bokeh figures.\n backend : {\"matplotlib\",\"bokeh\"}, optional\n Select plotting backend.\n backend_kwargs : bool, optional\n These are kwargs specific to the backend being used, passed to\n :meth:`mpl:matplotlib.axes.Axes.plot` or\n :meth:`bokeh.plotting.Figure.patch`.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : matplotlib axes or bokeh figures\n\n See Also\n --------\n hdi : Calculate highest density interval (HDI) of array for given probability.\n\n Examples\n --------\n Plot HDI interval of simulated regression data using `y` argument:\n\n .. plot::\n :context: close-figs\n\n >>> import numpy as np\n >>> import arviz as az\n >>> x_data = np.random.normal(0, 1, 100)\n >>> y_data = np.random.normal(2 + x_data * 0.5, 0.5, size=(2, 50, 100))\n >>> az.plot_hdi(x_data, y_data)\n\n ``plot_hdi`` can also be given precalculated values with the argument ``hdi_data``. This example\n shows how to use :func:`~arviz.hdi` to precalculate the values and pass these values to\n ``plot_hdi``. Similarly to an example in ``hdi`` we are using the ``input_core_dims``\n argument of :func:`~arviz.wrap_xarray_ufunc` to manually define the dimensions over which\n to calculate the HDI.\n\n .. plot::\n :context: close-figs\n\n >>> hdi_data = az.hdi(y_data, input_core_dims=[[\"draw\"]])\n >>> ax = az.plot_hdi(x_data, hdi_data=hdi_data[0], color=\"r\", fill_kwargs={\"alpha\": .2})\n >>> az.plot_hdi(x_data, hdi_data=hdi_data[1], color=\"k\", ax=ax, fill_kwargs={\"alpha\": .2})\n\n ``plot_hdi`` can also be used with Inference Data objects. Here we use the posterior predictive\n to plot the HDI interval.\n\n .. plot::\n :context: close-figs\n\n >>> X = np.random.normal(0,1,100)\n >>> Y = np.random.normal(2 + X * 0.5, 0.5, size=(2,10,100))\n >>> idata = az.from_dict(posterior={\"y\": Y}, constant_data={\"x\":X})\n >>> x_data = idata.constant_data.x\n >>> y_data = idata.posterior.y\n >>> az.plot_hdi(x_data, y_data)\n\n \n source"},{"id":151,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_kde","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_kde-Tuple","content":" ArviZPythonPlots.plot_kde — Method 1D or 2D KDE plot taking into account boundary conditions.\n\n Parameters\n ----------\n values : array-like\n Values to plot\n values2 : array-like, optional\n Values to plot. If present, a 2D KDE will be estimated\n cumulative : bool\n If true plot the estimated cumulative distribution function. Defaults to False.\n Ignored for 2D KDE\n rug : bool\n If True adds a rugplot. Defaults to False. Ignored for 2D KDE\n label : string\n Text to include as part of the legend\n bw : float or str, optional\n If numeric, indicates the bandwidth and must be positive.\n If str, indicates the method to estimate the bandwidth and must be\n one of \"scott\", \"silverman\", \"isj\" or \"experimental\" when ``is_circular`` is False\n and \"taylor\" (for now) when ``is_circular`` is True.\n Defaults to \"default\" which means \"experimental\" when variable is not circular\n and \"taylor\" when it is.\n adaptive : bool, optional.\n If True, an adaptative bandwidth is used. Only valid for 1D KDE.\n Defaults to False.\n quantiles : list\n Quantiles in ascending order used to segment the KDE.\n Use [.25, .5, .75] for quartiles. Defaults to None.\n rotated : bool\n Whether to rotate the 1D KDE plot 90 degrees.\n contour : bool\n If True plot the 2D KDE using contours, otherwise plot a smooth 2D KDE.\n Defaults to True.\n hdi_probs : list\n Plots highest density credibility regions for the provided probabilities for a 2D KDE.\n Defaults to matplotlib chosen levels with no fixed probability associated.\n fill_last : bool\n If True fill the last contour of the 2D KDE plot. Defaults to False.\n figsize : (float, float), optional\n Figure size. If None it will be defined automatically.\n textsize : float\n Text size scaling factor for labels, titles and lines. If None it will be autoscaled based\n on ``figsize``. Not implemented for bokeh backend.\n plot_kwargs : dict\n Keywords passed to the pdf line of a 1D KDE. See :meth:`mpl:matplotlib.axes.Axes.plot`\n or :meth:`bokeh:bokeh.plotting.Figure.line` for a description of accepted values.\n fill_kwargs : dict\n Keywords passed to the fill under the line (use ``fill_kwargs={'alpha': 0}``\n to disable fill). Ignored for 2D KDE. Passed to\n :meth:`bokeh.plotting.Figure.patch`.\n rug_kwargs : dict\n Keywords passed to the rug plot. Ignored if ``rug=False`` or for 2D KDE\n Use ``space`` keyword (float) to control the position of the rugplot. The larger this number\n the lower the rugplot. Passed to :class:`bokeh:bokeh.models.glyphs.Scatter`.\n contour_kwargs : dict\n Keywords passed to :meth:`mpl:matplotlib.axes.Axes.contour`\n to draw contour lines or :meth:`bokeh.plotting.Figure.patch`.\n Ignored for 1D KDE.\n contourf_kwargs : dict\n Keywords passed to :meth:`mpl:matplotlib.axes.Axes.contourf`\n to draw filled contours. Ignored for 1D KDE.\n pcolormesh_kwargs : dict\n Keywords passed to :meth:`mpl:matplotlib.axes.Axes.pcolormesh` or\n :meth:`bokeh.plotting.Figure.image`.\n Ignored for 1D KDE.\n is_circular : {False, True, \"radians\", \"degrees\"}. Default False.\n Select input type {\"radians\", \"degrees\"} for circular histogram or KDE plot. If True,\n default input type is \"radians\". When this argument is present, it interprets ``values``\n is a circular variable measured in radians and a circular KDE is used. Inputs in\n \"degrees\" will undergo an internal conversion to radians.\n ax : axes, optional\n Matplotlib axes or bokeh figures.\n legend : bool\n Add legend to the figure. By default True.\n backend: str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default \"matplotlib\".\n backend_kwargs: bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or\n :func:`bokeh.plotting.figure`. For additional documentation\n check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n return_glyph : bool, optional\n Internal argument to return glyphs for bokeh\n\n Returns\n -------\n axes : matplotlib.Axes or bokeh.plotting.Figure\n Object containing the kde plot\n glyphs : list, optional\n Bokeh glyphs present in plot. Only provided if ``return_glyph`` is True.\n\n See Also\n --------\n kde : One dimensional density estimation.\n plot_dist : Plot distribution as histogram or kernel density estimates.\n\n Examples\n --------\n Plot default KDE\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> non_centered = az.load_arviz_data('non_centered_eight')\n >>> mu_posterior = np.concatenate(non_centered.posterior[\"mu\"].values)\n >>> tau_posterior = np.concatenate(non_centered.posterior[\"tau\"].values)\n >>> az.plot_kde(mu_posterior)\n\n\n Plot KDE with rugplot\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(mu_posterior, rug=True)\n\n Plot KDE with adaptive bandwidth\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(mu_posterior, adaptive=True)\n\n Plot KDE with a different bandwidth estimator\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(mu_posterior, bw=\"scott\")\n\n Plot KDE with a bandwidth specified manually\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(mu_posterior, bw=0.4)\n\n Plot KDE for a circular variable\n\n .. plot::\n :context: close-figs\n\n >>> rvs = np.random.vonmises(mu=np.pi, kappa=2, size=500)\n >>> az.plot_kde(rvs, is_circular=True)\n\n\n Plot a cumulative distribution\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(mu_posterior, cumulative=True)\n\n\n\n Rotate plot 90 degrees\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(mu_posterior, rotated=True)\n\n\n Plot 2d contour KDE\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(mu_posterior, values2=tau_posterior)\n\n\n Plot 2d contour KDE, without filling and contour lines using viridis cmap\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(mu_posterior, values2=tau_posterior,\n ... contour_kwargs={\"colors\":None, \"cmap\":plt.cm.viridis},\n ... contourf_kwargs={\"alpha\":0});\n\n Plot 2d contour KDE, set the number of levels to 3.\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(\n ... mu_posterior, values2=tau_posterior,\n ... contour_kwargs={\"levels\":3}, contourf_kwargs={\"levels\":3}\n ... );\n\n Plot 2d contour KDE with 30%, 60% and 90% HDI contours.\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(mu_posterior, values2=tau_posterior, hdi_probs=[0.3, 0.6, 0.9])\n\n Plot 2d smooth KDE\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_kde(mu_posterior, values2=tau_posterior, contour=False)\n\n \n source"},{"id":152,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_khat","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_khat-Tuple","content":" ArviZPythonPlots.plot_khat — Method \n Plot Pareto tail indices for diagnosing convergence.\n\n Parameters\n ----------\n khats : ELPDData containing Pareto shapes information or array of\n Pareto tail indices.\n color : str or array_like, optional\n Colors of the scatter plot, if color is a str all dots will\n have the same color, if it is the size of the observations,\n each dot will have the specified color, otherwise, it will be\n interpreted as a list of the dims to be used for the color\n code. If Matplotlib c argument is passed, it will override\n the color argument\n xlabels : bool, optional\n Use coords as xticklabels\n show_hlines : bool, optional\n Show the horizontal lines, by default at the values [0, 0.5, 0.7, 1].\n show_bins : bool, optional\n Show the percentage of khats falling in each bin, as delimited by hlines.\n bin_format : str, optional\n The string is used as formatting guide calling ``bin_format.format(count, pct)``.\n threshold : float, optional\n Show the labels of k values larger than threshold. Defaults to `None`,\n no observations will be highlighted.\n hover_label : bool, optional\n Show the datapoint label when hovering over it with the mouse. Requires an interactive\n backend.\n hover_format : str, optional\n String used to format the hover label via ``hover_format.format(idx, coord_label)``\n figsize : (float, float), optional\n Figure size. If None it will be defined automatically.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If None it will be autoscaled based\n on figsize.\n coords : mapping, optional\n Coordinates of points to plot. **All** values are used for computation, but only a\n a subset can be plotted for convenience.\n legend : bool, optional\n Include a legend to the plot. Only taken into account when color argument is a dim name.\n markersize : int, optional\n markersize for scatter plot. Defaults to `None` in which case it will\n be chosen based on autoscaling for figsize.\n ax : axes, optional\n Matplotlib axes or bokeh figures.\n hlines_kwargs : dictionary, optional\n Additional keywords passed to\n :meth:`matplotlib.axes.Axes.hlines`.\n backend : str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default \"matplotlib\".\n backend_kwargs : bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or\n :func:`bokeh.plotting.figure`.\n show : bool, optional\n Call backend show function.\n kwargs :\n Additional keywords passed to\n :meth:`matplotlib.axes.Axes.scatter`.\n\n Returns\n -------\n axes : matplotlib_axes or bokeh_figures\n\n See Also\n --------\n psislw : Pareto smoothed importance sampling (PSIS).\n\n Examples\n --------\n Plot estimated pareto shape parameters showing how many fall in each category.\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> radon = az.load_arviz_data(\"radon\")\n >>> loo_radon = az.loo(radon, pointwise=True)\n >>> az.plot_khat(loo_radon, show_bins=True)\n\n Show xlabels\n\n .. plot::\n :context: close-figs\n\n >>> centered_eight = az.load_arviz_data(\"centered_eight\")\n >>> khats = az.loo(centered_eight, pointwise=True).pareto_k\n >>> az.plot_khat(khats, xlabels=True, threshold=1)\n\n Use custom color scheme\n\n .. plot::\n :context: close-figs\n\n >>> counties = radon.posterior.County[radon.constant_data.county_idx].values\n >>> colors = [\n ... \"blue\" if county[-1] in (\"A\", \"N\") else \"green\" for county in counties\n ... ]\n >>> az.plot_khat(loo_radon, color=colors)\n\n Notes\n -----\n The Generalized Pareto distribution (GPD) may be used to diagnose\n convergence rates for importance sampling. GPD has parameters\n offset, scale, and shape. The shape parameter is usually denoted\n with ``k``. ``k`` also tells how many finite moments the\n distribution has. The pre-asymptotic convergence rate of\n importance sampling can be estimated based on the fractional\n number of finite moments of the importance ratio distribution. GPD\n is fitted to the largest importance ratios and the estimated shape\n parameter ``k``, i.e., ``\\hat{k}`` can then be used as a diagnostic\n (most importantly if ``\\hat{k} > 0.7``, then the convergence rate\n is impractically low). See [1]_.\n\n References\n ----------\n .. [1] Vehtari, A., Simpson, D., Gelman, A., Yao, Y., Gabry, J.,\n 2019. Pareto Smoothed Importance Sampling. arXiv:1507.02646 [stat].\n\n \n source"},{"id":153,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_lm","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_lm-Tuple","content":" ArviZPythonPlots.plot_lm — Method Posterior predictive and mean plots for regression-like data.\n\n Parameters\n ----------\n y : str or DataArray or ndarray\n If str, variable name from ``observed_data``.\n idata : InferenceData, Optional\n Optional only if ``y`` is not str.\n x : str, tuple of strings, DataArray or array-like, optional\n If str or tuple, variable name from ``constant_data``.\n If ndarray, could be 1D, or 2D for multiple plots.\n If None, coords name of ``y`` (``y`` should be DataArray).\n y_model : str or Sequence, Optional\n If str, variable name from ``posterior``.\n Its dimensions should be same as ``y`` plus added chains and draws.\n y_hat : str, Optional\n If str, variable name from ``posterior_predictive``.\n Its dimensions should be same as ``y`` plus added chains and draws.\n num_samples : int, Optional, Default 50\n Significant if ``kind_pp`` is \"samples\" or ``kind_model`` is \"lines\".\n Number of samples to be drawn from posterior predictive or\n kind_pp : {\"samples\", \"hdi\"}, Default \"samples\"\n Options to visualize uncertainty in data.\n kind_model : {\"lines\", \"hdi\"}, Default \"lines\"\n Options to visualize uncertainty in mean of the data.\n plot_dim : str, Optional\n Necessary if ``y`` is multidimensional.\n backend : str, Optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default \"matplotlib\".\n y_kwargs : dict, optional\n Passed to :meth:`mpl:matplotlib.axes.Axes.plot` in matplotlib\n and :meth:`bokeh:bokeh.plotting.Figure.circle` in bokeh\n y_hat_plot_kwargs : dict, optional\n Passed to :meth:`mpl:matplotlib.axes.Axes.plot` in matplotlib\n and :meth:`bokeh:bokeh.plotting.Figure.circle` in bokeh\n y_hat_fill_kwargs : dict, optional\n Passed to :func:`arviz.plot_hdi`\n y_model_plot_kwargs : dict, optional\n Passed to :meth:`mpl:matplotlib.axes.Axes.plot` in matplotlib\n and :meth:`bokeh:bokeh.plotting.Figure.line` in bokeh\n y_model_fill_kwargs : dict, optional\n Significant if ``kind_model`` is \"hdi\". Passed to :func:`arviz.plot_hdi`\n y_model_mean_kwargs : dict, optional\n Passed to :meth:`mpl:matplotlib.axes.Axes.plot` in matplotlib\n and :meth:`bokeh:bokeh.plotting.Figure.line` in bokeh\n backend_kwargs : dict, optional\n These are kwargs specific to the backend being used. Passed to\n :func:`matplotlib.pyplot.subplots` or\n :func:`bokeh.plotting.figure`.\n figsize : (float, float), optional\n Figure size. If None it will be defined automatically.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If None it will be\n autoscaled based on ``figsize``.\n axes : 2D numpy array-like of matplotlib_axes or bokeh_figures, optional\n A 2D array of locations into which to plot the densities. If not supplied, Arviz will create\n its own array of plot areas (and return it).\n show : bool, optional\n Call backend show function.\n legend : bool, optional\n Add legend to figure. By default True.\n grid : bool, optional\n Add grid to figure. By default True.\n\n\n Returns\n -------\n axes: matplotlib axes or bokeh figures\n\n See Also\n --------\n plot_ts : Plot timeseries data\n plot_ppc : Plot for posterior/prior predictive checks\n\n Examples\n --------\n Plot regression default plot\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> import numpy as np\n >>> import xarray as xr\n >>> idata = az.load_arviz_data('regression1d')\n >>> x = xr.DataArray(np.linspace(0, 1, 100))\n >>> idata.posterior[\"y_model\"] = idata.posterior[\"intercept\"] + idata.posterior[\"slope\"]*x\n >>> az.plot_lm(idata=idata, y=\"y\", x=x)\n\n Plot regression data and mean uncertainty\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_lm(idata=idata, y=\"y\", x=x, y_model=\"y_model\")\n\n Plot regression data and mean uncertainty in hdi form\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_lm(\n ... idata=idata, y=\"y\", x=x, y_model=\"y_model\", kind_pp=\"hdi\", kind_model=\"hdi\"\n ... )\n\n Plot regression data for multi-dimensional y using plot_dim\n\n .. plot::\n :context: close-figs\n\n >>> data = az.from_dict(\n ... observed_data = { \"y\": np.random.normal(size=(5, 7)) },\n ... posterior_predictive = {\"y\": np.random.randn(4, 1000, 5, 7) / 2},\n ... dims={\"y\": [\"dim1\", \"dim2\"]},\n ... coords={\"dim1\": range(5), \"dim2\": range(7)}\n ... )\n >>> az.plot_lm(idata=data, y=\"y\", plot_dim=\"dim1\")\n \n source"},{"id":154,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_loo_pit","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_loo_pit-Tuple","content":" ArviZPythonPlots.plot_loo_pit — Method Plot Leave-One-Out (LOO) probability integral transformation (PIT) predictive checks.\n\n Parameters\n ----------\n idata : InferenceData\n :class:`arviz.InferenceData` object.\n y : array, DataArray or str\n Observed data. If str, ``idata`` must be present and contain the observed data group\n y_hat : array, DataArray or str\n Posterior predictive samples for ``y``. It must have the same shape as y plus an\n extra dimension at the end of size n_samples (chains and draws stacked). If str or\n None, ``idata`` must contain the posterior predictive group. If None, ``y_hat`` is taken\n equal to y, thus, y must be str too.\n log_weights : array or DataArray\n Smoothed log_weights. It must have the same shape as ``y_hat``\n ecdf : bool, optional\n Plot the difference between the LOO-PIT Empirical Cumulative Distribution Function\n (ECDF) and the uniform CDF instead of LOO-PIT kde.\n In this case, instead of overlaying uniform distributions, the beta ``hdi_prob``\n around the theoretical uniform CDF is shown. This approximation only holds\n for large S and ECDF values not very close to 0 nor 1. For more information, see\n `Vehtari et al. (2019)`, `Appendix G `_.\n ecdf_fill : bool, optional\n Use :meth:`matplotlib.axes.Axes.fill_between` to mark the area\n inside the credible interval. Otherwise, plot the\n border lines.\n n_unif : int, optional\n Number of datasets to simulate and overlay from the uniform distribution.\n use_hdi : bool, optional\n Compute expected hdi values instead of overlaying the sampled uniform distributions.\n hdi_prob : float, optional\n Probability for the highest density interval. Works with ``use_hdi=True`` or ``ecdf=True``.\n figsize : (float, float), optional\n If None, size is (8 + numvars, 8 + numvars)\n textsize : int, optional\n Text size for labels. If None it will be autoscaled based on ``figsize``.\n labeller : Labeller, optional\n Class providing the method ``make_pp_label`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n color : str or array_like, optional\n Color of the LOO-PIT estimated pdf plot. If ``plot_unif_kwargs`` has no \"color\" key,\n a slightly lighter color than this argument will be used for the uniform kde lines.\n This will ensure that LOO-PIT kde and uniform kde have different default colors.\n legend : bool, optional\n Show the legend of the figure.\n ax : axes, optional\n Matplotlib axes or bokeh figures.\n plot_kwargs : dict, optional\n Additional keywords passed to :meth:`matplotlib.axes.Axes.plot`\n for LOO-PIT line (kde or ECDF)\n plot_unif_kwargs : dict, optional\n Additional keywords passed to :meth:`matplotlib.axes.Axes.plot` for\n overlaid uniform distributions or for beta credible interval\n lines if ``ecdf=True``\n hdi_kwargs : dict, optional\n Additional keywords passed to :meth:`matplotlib.axes.Axes.axhspan`\n fill_kwargs : dict, optional\n Additional kwargs passed to :meth:`matplotlib.axes.Axes.fill_between`\n backend : str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default \"matplotlib\".\n backend_kwargs : bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or\n :func:`bokeh.plotting.figure`. For additional documentation\n check the plotting method of the backend.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : matplotlib_axes or bokeh_figures\n\n See Also\n --------\n plot_bpv : Plot Bayesian p-value for observed data and Posterior/Prior predictive.\n loo_pit : Compute leave one out (PSIS-LOO) probability integral transform (PIT) values.\n\n References\n ----------\n * Gabry et al. (2017) see https://arxiv.org/abs/1709.01449\n * https://mc-stan.org/bayesplot/reference/PPC-loo.html\n * Gelman et al. BDA (2014) Section 6.3\n\n Examples\n --------\n Plot LOO-PIT predictive checks overlaying the KDE of the LOO-PIT values to several\n realizations of uniform variable sampling with the same number of observations.\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> idata = az.load_arviz_data(\"radon\")\n >>> az.plot_loo_pit(idata=idata, y=\"y\")\n\n Fill the area containing the 94% highest density interval of the difference between uniform\n variables empirical CDF and the real uniform CDF. A LOO-PIT ECDF clearly outside of these\n theoretical boundaries indicates that the observations and the posterior predictive\n samples do not follow the same distribution.\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_loo_pit(idata=idata, y=\"y\", ecdf=True)\n\n \n source"},{"id":155,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_mcse","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_mcse-Tuple","content":" ArviZPythonPlots.plot_mcse — Method Plot quantile or local Monte Carlo Standard Error.\n\n Parameters\n ----------\n idata : obj\n Any object that can be converted to an :class:`arviz.InferenceData` object\n Refer to documentation of :func:`arviz.convert_to_dataset` for details\n var_names : list of variable names, optional\n Variables to be plotted. Prefix the variables by ``~`` when you want to exclude\n them from the plot.\n filter_vars : {None, \"like\", \"regex\"}, optional, default=None\n If `None` (default), interpret var_names as the real variables names. If \"like\",\n interpret var_names as substrings of the real variables names. If \"regex\",\n interpret var_names as regular expressions on the real variables names. A la\n `pandas.filter`.\n coords : dict, optional\n Coordinates of var_names to be plotted. Passed to :meth:`xarray.Dataset.sel`\n errorbar : bool, optional\n Plot quantile value +/- mcse instead of plotting mcse.\n grid : tuple\n Number of rows and columns. Defaults to None, the rows and columns are\n automatically inferred.\n figsize : (float, float), optional\n Figure size. If None it will be defined automatically.\n textsize : float, optional\n Text size scaling factor for labels, titles and lines. If None it will be autoscaled based\n on figsize.\n extra_methods : bool, optional\n Plot mean and sd MCSE as horizontal lines. Only taken into account when\n ``errorbar=False``.\n rug : bool\n Plot rug plot of values diverging or that reached the max tree depth.\n rug_kind : bool\n Variable in sample stats to use as rug mask. Must be a boolean variable.\n n_points : int\n Number of points for which to plot their quantile/local ess or number of subsets\n in the evolution plot.\n labeller : Labeller, optional\n Class providing the method `make_label_vert` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n ax : 2D array-like of matplotlib_axes or bokeh_figures, optional\n A 2D array of locations into which to plot the densities. If not supplied, Arviz will create\n its own array of plot areas (and return it).\n rug_kwargs : dict\n kwargs passed to rug plot in\n :meth:`mpl:matplotlib.axes.Axes.plot` or :class:`bokeh:bokeh.models.glyphs.Scatter`.\n extra_kwargs : dict, optional\n kwargs passed as extra method lines in\n :meth:`mpl:matplotlib.axes.Axes.axhline` or :class:`bokeh:bokeh.models.Span`\n text_kwargs : dict, optional\n kwargs passed to :meth:`mpl:matplotlib.axes.Axes.annotate` for extra methods lines labels.\n It accepts the additional key ``x`` to set ``xy=(text_kwargs[\"x\"], mcse)``.\n text_kwargs are ignored for the bokeh plotting backend.\n backend : str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default \"matplotlib\".\n backend_kwargs : bool, optional\n These are kwargs specific to the backend being passed to\n :func:`matplotlib.pyplot.subplots` or :func:`bokeh.plotting.figure`.\n show: bool, optional\n Call backend show function.\n **kwargs\n Passed as-is to :meth:`mpl:matplotlib.axes.Axes.hist` or\n :meth:`mpl:matplotlib.axes.Axes.plot` in matplotlib depending on the value of `kind`.\n\n Returns\n -------\n axes : matplotlib axes or bokeh figures\n\n See Also\n --------\n :func:`arviz.mcse`: Calculate Markov Chain Standard Error statistic.\n\n References\n ----------\n * Vehtari et al. (2019) see https://arxiv.org/abs/1903.08008\n\n Examples\n --------\n Plot quantile Monte Carlo Standard Error.\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> idata = az.load_arviz_data(\"centered_eight\")\n >>> coords = {\"school\": [\"Deerfield\", \"Lawrenceville\"]}\n >>> az.plot_mcse(\n ... idata, var_names=[\"mu\", \"theta\"], coords=coords\n ... )\n\n \n source"},{"id":156,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_pair","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_pair-Tuple","content":" ArviZPythonPlots.plot_pair — Method \n Plot a scatter, kde and/or hexbin matrix with (optional) marginals on the diagonal.\n\n Parameters\n ----------\n data: obj\n Any object that can be converted to an :class:`arviz.InferenceData` object.\n Refer to documentation of :func:`arviz.convert_to_dataset` for details\n group: str, optional\n Specifies which InferenceData group should be plotted. Defaults to 'posterior'.\n var_names: list of variable names, optional\n Variables to be plotted, if None all variable are plotted. Prefix the\n variables by ``~`` when you want to exclude them from the plot.\n filter_vars: {None, \"like\", \"regex\"}, optional, default=None\n If `None` (default), interpret var_names as the real variables names. If \"like\",\n interpret var_names as substrings of the real variables names. If \"regex\",\n interpret var_names as regular expressions on the real variables names. A la\n ``pandas.filter``.\n combine_dims : set_like of str, optional\n List of dimensions to reduce. Defaults to reducing only the \"chain\" and \"draw\" dimensions.\n See the :ref:`this section ` for usage examples.\n coords: mapping, optional\n Coordinates of var_names to be plotted. Passed to :meth:`xarray.Dataset.sel`.\n marginals: bool, optional\n If True pairplot will include marginal distributions for every variable\n figsize: figure size tuple\n If None, size is (8 + numvars, 8 + numvars)\n textsize: int\n Text size for labels. If None it will be autoscaled based on ``figsize``.\n kind : str or List[str]\n Type of plot to display (scatter, kde and/or hexbin)\n gridsize: int or (int, int), optional\n Only works for ``kind=hexbin``. The number of hexagons in the x-direction.\n The corresponding number of hexagons in the y-direction is chosen\n such that the hexagons are approximately regular. Alternatively, gridsize\n can be a tuple with two elements specifying the number of hexagons\n in the x-direction and the y-direction.\n divergences: Boolean\n If True divergences will be plotted in a different color, only if group is either 'prior'\n or 'posterior'.\n colorbar: bool\n If True a colorbar will be included as part of the plot (Defaults to False).\n Only works when ``kind=hexbin``\n labeller : labeller instance, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot.\n Read the :ref:`label_guide` for more details and usage examples.\n ax: axes, optional\n Matplotlib axes or bokeh figures.\n divergences_kwargs: dicts, optional\n Additional keywords passed to :meth:`matplotlib.axes.Axes.scatter` for divergences\n scatter_kwargs:\n Additional keywords passed to :meth:`matplotlib.axes.Axes.scatter` when using scatter kind\n kde_kwargs: dict, optional\n Additional keywords passed to :func:`arviz.plot_kde` when using kde kind\n hexbin_kwargs: dict, optional\n Additional keywords passed to :meth:`matplotlib.axes.Axes.hexbin` when\n using hexbin kind\n backend: str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default \"matplotlib\".\n backend_kwargs: bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or\n :func:`bokeh.plotting.figure`.\n marginal_kwargs: dict, optional\n Additional keywords passed to :func:`arviz.plot_dist`, modifying the\n marginal distributions plotted in the diagonal.\n point_estimate: str, optional\n Select point estimate from 'mean', 'mode' or 'median'. The point estimate will be\n plotted using a scatter marker and vertical/horizontal lines.\n point_estimate_kwargs: dict, optional\n Additional keywords passed to :meth:`matplotlib.axes.Axes.axvline`,\n :meth:`matplotlib.axes.Axes.axhline` (matplotlib) or\n :class:`bokeh:bokeh.models.Span` (bokeh)\n point_estimate_marker_kwargs: dict, optional\n Additional keywords passed to :meth:`matplotlib.axes.Axes.scatter`\n or :meth:`bokeh:bokeh.plotting.Figure.square` in point\n estimate plot. Not available in bokeh\n reference_values: dict, optional\n Reference values for the plotted variables. The Reference values will be plotted\n using a scatter marker\n reference_values_kwargs: dict, optional\n Additional keywords passed to :meth:`matplotlib.axes.Axes.plot` or\n :meth:`bokeh:bokeh.plotting.Figure.circle` in reference values plot\n show: bool, optional\n Call backend show function.\n\n Returns\n -------\n axes: matplotlib axes or bokeh figures\n\n Examples\n --------\n KDE Pair Plot\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> centered = az.load_arviz_data('centered_eight')\n >>> coords = {'school': ['Choate', 'Deerfield']}\n >>> az.plot_pair(centered,\n >>> var_names=['theta', 'mu', 'tau'],\n >>> kind='kde',\n >>> coords=coords,\n >>> divergences=True,\n >>> textsize=18)\n\n Hexbin pair plot\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_pair(centered,\n >>> var_names=['theta', 'mu'],\n >>> coords=coords,\n >>> textsize=18,\n >>> kind='hexbin')\n\n Pair plot showing divergences and select variables with regular expressions\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_pair(centered,\n ... var_names=['^t', 'mu'],\n ... filter_vars=\"regex\",\n ... coords=coords,\n ... divergences=True,\n ... textsize=18)\n \n source"},{"id":157,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_parallel","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_parallel-Tuple","content":" ArviZPythonPlots.plot_parallel — Method \n Plot parallel coordinates plot showing posterior points with and without divergences.\n\n Described by https://arxiv.org/abs/1709.01449\n\n Parameters\n ----------\n data: obj\n Any object that can be converted to an :class:`arviz.InferenceData` object\n refer to documentation of :func:`arviz.convert_to_dataset` for details\n var_names: list of variable names\n Variables to be plotted, if `None` all variables are plotted. Can be used to change the\n order of the plotted variables. Prefix the variables by ``~`` when you want to exclude\n them from the plot.\n filter_vars: {None, \"like\", \"regex\"}, optional, default=None\n If `None` (default), interpret var_names as the real variables names. If \"like\",\n interpret var_names as substrings of the real variables names. If \"regex\",\n interpret var_names as regular expressions on the real variables names. A la\n ``pandas.filter``.\n coords: mapping, optional\n Coordinates of ``var_names`` to be plotted.\n Passed to :meth:`xarray.Dataset.sel`.\n figsize: tuple\n Figure size. If None it will be defined automatically.\n textsize: float\n Text size scaling factor for labels, titles and lines. If None it will be autoscaled based\n on ``figsize``.\n legend: bool\n Flag for plotting legend (defaults to True)\n colornd: valid matplotlib color\n color for non-divergent points. Defaults to 'k'\n colord: valid matplotlib color\n color for divergent points. Defaults to 'C1'\n shadend: float\n Alpha blending value for non-divergent points, between 0 (invisible) and 1 (opaque).\n Defaults to .025\n labeller : labeller instance, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot.\n Read the :ref:`label_guide` for more details and usage examples.\n ax: axes, optional\n Matplotlib axes or bokeh figures.\n norm_method: str\n Method for normalizing the data. Methods include normal, minmax and rank.\n Defaults to none.\n backend: str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default \"matplotlib\".\n backend_config: dict, optional\n Currently specifies the bounds to use for bokeh axes.\n Defaults to value set in ``rcParams``.\n backend_kwargs: bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or\n :func:`bokeh.plotting.figure`.\n show: bool, optional\n Call backend show function.\n\n Returns\n -------\n axes: matplotlib axes or bokeh figures\n\n See Also\n --------\n plot_pair : Plot a scatter, kde and/or hexbin matrix with (optional) marginals on the diagonal.\n plot_trace : Plot distribution (histogram or kernel density estimates) and sampled values\n or rank plot\n\n Examples\n --------\n Plot default parallel plot\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data('centered_eight')\n >>> az.plot_parallel(data, var_names=[\"mu\", \"tau\"])\n\n\n Plot parallel plot with normalization\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_parallel(data, var_names=[\"theta\", \"tau\", \"mu\"], norm_method=\"normal\")\n\n Plot parallel plot with minmax\n\n .. plot::\n :context: close-figs\n\n >>> ax = az.plot_parallel(data, var_names=[\"theta\", \"tau\", \"mu\"], norm_method=\"minmax\")\n >>> ax.set_xticklabels(ax.get_xticklabels(), rotation=45)\n\n Plot parallel plot with rank\n\n .. plot::\n :context: close-figs\n\n >>> ax = az.plot_parallel(data, var_names=[\"theta\", \"tau\", \"mu\"], norm_method=\"rank\")\n >>> ax.set_xticklabels(ax.get_xticklabels(), rotation=45)\n \n source"},{"id":158,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_posterior","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_posterior-Tuple","content":" ArviZPythonPlots.plot_posterior — Method Plot Posterior densities in the style of John K. Kruschke's book.\n\n Parameters\n ----------\n data: obj\n Any object that can be converted to an :class:`arviz.InferenceData` object.\n Refer to the documentation of :func:`arviz.convert_to_dataset` for details\n var_names: list of variable names\n Variables to be plotted, two variables are required. Prefix the variables with ``~``\n when you want to exclude them from the plot.\n filter_vars: {None, \"like\", \"regex\"}, optional, default=None\n If `None` (default), interpret var_names as the real variables names. If \"like\",\n interpret var_names as substrings of the real variables names. If \"regex\",\n interpret var_names as regular expressions on the real variables names. A la\n ``pandas.filter``.\n combine_dims : set_like of str, optional\n List of dimensions to reduce. Defaults to reducing only the \"chain\" and \"draw\" dimensions.\n See the :ref:`this section ` for usage examples.\n transform: callable\n Function to transform data (defaults to None i.e.the identity function)\n coords: mapping, optional\n Coordinates of var_names to be plotted. Passed to :meth:`xarray.Dataset.sel`\n grid : tuple\n Number of rows and columns. Defaults to None, the rows and columns are\n automatically inferred.\n figsize: tuple\n Figure size. If None it will be defined automatically.\n textsize: float\n Text size scaling factor for labels, titles and lines. If None it will be autoscaled based\n on ``figsize``.\n hdi_prob: float, optional\n Plots highest density interval for chosen percentage of density.\n Use 'hide' to hide the highest density interval. Defaults to 0.94.\n multimodal: bool\n If true (default) it may compute more than one credible interval if the distribution is\n multimodal and the modes are well separated.\n skipna : bool\n If true ignores nan values when computing the hdi and point estimates. Defaults to false.\n round_to: int, optional\n Controls formatting of floats. Defaults to 2 or the integer part, whichever is bigger.\n point_estimate: Optional[str]\n Plot point estimate per variable. Values should be 'mean', 'median', 'mode' or None.\n Defaults to 'auto' i.e. it falls back to default set in rcParams.\n group: str, optional\n Specifies which InferenceData group should be plotted. Defaults to 'posterior'.\n rope: tuple or dictionary of tuples\n Lower and upper values of the Region Of Practical Equivalence. If a list is provided, its\n length should match the number of variables.\n ref_val: float or dictionary of floats\n display the percentage below and above the values in ref_val. Must be None (default),\n a constant, a list or a dictionary like see an example below. If a list is provided, its\n length should match the number of variables.\n rope_color: str, optional\n Specifies the color of ROPE and displayed percentage within ROPE\n ref_val_color: str, optional\n Specifies the color of the displayed percentage\n kind: str\n Type of plot to display (kde or hist) For discrete variables this argument is ignored and\n a histogram is always used. Defaults to rcParam ``plot.density_kind``\n bw: float or str, optional\n If numeric, indicates the bandwidth and must be positive.\n If str, indicates the method to estimate the bandwidth and must be\n one of \"scott\", \"silverman\", \"isj\" or \"experimental\" when `circular` is False\n and \"taylor\" (for now) when `circular` is True.\n Defaults to \"default\" which means \"experimental\" when variable is not circular\n and \"taylor\" when it is. Only works if `kind == kde`.\n circular: bool, optional\n If True, it interprets the values passed are from a circular variable measured in radians\n and a circular KDE is used. Only valid for 1D KDE. Defaults to False.\n Only works if `kind == kde`.\n bins: integer or sequence or 'auto', optional\n Controls the number of bins,accepts the same keywords :func:`matplotlib.pyplot.hist` does.\n Only works if `kind == hist`. If None (default) it will use `auto` for continuous variables\n and `range(xmin, xmax + 1)` for discrete variables.\n labeller : labeller instance, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n ax: numpy array-like of matplotlib axes or bokeh figures, optional\n A 2D array of locations into which to plot the densities. If not supplied, Arviz will create\n its own array of plot areas (and return it).\n backend: str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default \"matplotlib\".\n backend_kwargs: bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :func:`bokeh.plotting.figure`\n show: bool, optional\n Call backend show function.\n **kwargs\n Passed as-is to :func:`matplotlib.pyplot.hist` or :func:`matplotlib.pyplot.plot` function\n depending on the value of `kind`.\n\n Returns\n -------\n axes: matplotlib axes or bokeh figures\n\n See Also\n --------\n plot_dist : Plot distribution as histogram or kernel density estimates.\n plot_density : Generate KDE plots for continuous variables and histograms for discrete ones.\n plot_forest : Forest plot to compare HDI intervals from a number of distributions.\n\n Examples\n --------\n Show a default kernel density plot following style of John Kruschke\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data('centered_eight')\n >>> az.plot_posterior(data)\n\n Plot subset variables by specifying variable name exactly\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_posterior(data, var_names=['mu'])\n\n Plot Region of Practical Equivalence (rope) and select variables with regular expressions\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_posterior(data, var_names=['mu', '^the'], filter_vars=\"regex\", rope=(-1, 1))\n\n Plot Region of Practical Equivalence for selected distributions\n\n .. plot::\n :context: close-figs\n\n >>> rope = {'mu': [{'rope': (-2, 2)}], 'theta': [{'school': 'Choate', 'rope': (2, 4)}]}\n >>> az.plot_posterior(data, var_names=['mu', 'theta'], rope=rope)\n\n Using `coords` argument to plot only a subset of data\n\n .. plot::\n :context: close-figs\n\n >>> coords = {\"school\": [\"Choate\",\"Phillips Exeter\"]}\n >>> az.plot_posterior(data, var_names=[\"mu\", \"theta\"], coords=coords)\n\n Add reference lines\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_posterior(data, var_names=['mu', 'theta'], ref_val=0)\n\n Show point estimate of distribution\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_posterior(data, var_names=['mu', 'theta'], point_estimate='mode')\n\n Show reference values using variable names and coordinates\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_posterior(data, ref_val= {\"theta\": [{\"school\": \"Deerfield\", \"ref_val\": 4},\n ... {\"school\": \"Choate\", \"ref_val\": 3}]})\n\n Show reference values using a list\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_posterior(data, ref_val=[1] + [5] * 8 + [1])\n\n\n Plot posterior as a histogram\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_posterior(data, var_names=['mu'], kind='hist')\n\n Change size of highest density interval\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_posterior(data, var_names=['mu'], hdi_prob=.75)\n \n source"},{"id":159,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_ppc","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_ppc-Tuple","content":" ArviZPythonPlots.plot_ppc — Method \n Plot for posterior/prior predictive checks.\n\n Parameters\n ----------\n data: az.InferenceData object\n :class:`arviz.InferenceData` object containing the observed and posterior/prior\n predictive data.\n kind: str\n Type of plot to display (\"kde\", \"cumulative\", or \"scatter\"). Defaults to `kde`.\n alpha: float\n Opacity of posterior/prior predictive density curves.\n Defaults to 0.2 for ``kind = kde`` and cumulative, for scatter defaults to 0.7.\n mean: bool\n Whether or not to plot the mean posterior/prior predictive distribution.\n Defaults to ``True``.\n observed: bool, default True\n Whether or not to plot the observed data.\n observed: bool, default False\n Whether or not to plot a rug plot for the observed data. Only valid if `observed` is\n `True` and for kind `kde` or `cumulative`.\n color: str\n Valid matplotlib ``color``. Defaults to ``C0``.\n color: list\n List with valid matplotlib colors corresponding to the posterior/prior predictive\n distribution, observed data and mean of the posterior/prior predictive distribution.\n Defaults to [\"C0\", \"k\", \"C1\"].\n grid : tuple\n Number of rows and columns. Defaults to None, the rows and columns are\n automatically inferred.\n figsize: tuple\n Figure size. If None, it will be defined automatically.\n textsize: float\n Text size scaling factor for labels, titles and lines. If None, it will be\n autoscaled based on ``figsize``.\n data_pairs: dict\n Dictionary containing relations between observed data and posterior/prior predictive data.\n Dictionary structure:\n\n - key = data var_name\n - value = posterior/prior predictive var_name\n\n For example, ``data_pairs = {'y' : 'y_hat'}``\n If None, it will assume that the observed data and the posterior/prior\n predictive data have the same variable name.\n var_names: list of variable names\n Variables to be plotted, if `None` all variable are plotted. Prefix the\n variables by ``~`` when you want to exclude them from the plot.\n filter_vars: {None, \"like\", \"regex\"}, optional, default=None\n If `None` (default), interpret var_names as the real variables names. If \"like\",\n interpret var_names as substrings of the real variables names. If \"regex\",\n interpret var_names as regular expressions on the real variables names. A la\n ``pandas.filter``.\n coords: dict\n Dictionary mapping dimensions to selected coordinates to be plotted.\n Dimensions without a mapping specified will include all coordinates for\n that dimension. Defaults to including all coordinates for all\n dimensions if None.\n flatten: list\n List of dimensions to flatten in ``observed_data``. Only flattens across the coordinates\n specified in the ``coords`` argument. Defaults to flattening all of the dimensions.\n flatten_pp: list\n List of dimensions to flatten in posterior_predictive/prior_predictive. Only flattens\n across the coordinates specified in the ``coords`` argument. Defaults to flattening all\n of the dimensions. Dimensions should match flatten excluding dimensions for ``data_pairs``\n parameters. If ``flatten`` is defined and ``flatten_pp`` is None, then\n ``flatten_pp = flatten``.\n num_pp_samples: int\n The number of posterior/prior predictive samples to plot. For ``kind`` = 'scatter' and\n ``animation = False`` if defaults to a maximum of 5 samples and will set jitter to 0.7.\n unless defined. Otherwise it defaults to all provided samples.\n random_seed: int\n Random number generator seed passed to ``numpy.random.seed`` to allow\n reproducibility of the plot. By default, no seed will be provided\n and the plot will change each call if a random sample is specified\n by ``num_pp_samples``.\n jitter: float\n If ``kind`` is \"scatter\", jitter will add random uniform noise to the height\n of the ppc samples and observed data. By default 0.\n animated: bool\n Create an animation of one posterior/prior predictive sample per frame.\n Defaults to ``False``. Only works with matploblib backend.\n To run animations inside a notebook you have to use the `nbAgg` matplotlib's backend.\n Try with `%matplotlib notebook` or `%matplotlib nbAgg`. You can switch back to the\n default matplotlib's backend with `%matplotlib inline` or `%matplotlib auto`.\n If switching back and forth between matplotlib's backend, you may need to run twice the cell\n with the animation.\n If you experience problems rendering the animation try setting\n `animation_kwargs({'blit':False}`) or changing the matplotlib's backend (e.g. to TkAgg)\n If you run the animation from a script write `ax, ani = az.plot_ppc(.)`\n animation_kwargs : dict\n Keywords passed to :class:`matplotlib.animation.FuncAnimation`. Ignored with\n matplotlib backend.\n legend : bool\n Add legend to figure. By default ``True``.\n labeller : labeller instance, optional\n Class providing the method ``make_pp_label`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n ax: numpy array-like of matplotlib axes or bokeh figures, optional\n A 2D array of locations into which to plot the densities. If not supplied, Arviz will create\n its own array of plot areas (and return it).\n backend: str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default to \"matplotlib\".\n backend_kwargs: bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :func:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n group: {\"prior\", \"posterior\"}, optional\n Specifies which InferenceData group should be plotted. Defaults to 'posterior'.\n Other value can be 'prior'.\n show: bool, optional\n Call backend show function.\n\n Returns\n -------\n axes: matplotlib axes or bokeh figures\n\n See Also\n --------\n plot_bpv: Plot Bayesian p-value for observed data and Posterior/Prior predictive.\n plot_lm: Posterior predictive and mean plots for regression-like data.\n plot_ppc: plot for posterior/prior predictive checks.\n plot_ts: Plot timeseries data.\n\n Examples\n --------\n Plot the observed data KDE overlaid on posterior predictive KDEs.\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data('radon')\n >>> az.plot_ppc(data, data_pairs={\"y\":\"y\"})\n\n Plot the overlay with empirical CDFs.\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_ppc(data, kind='cumulative')\n\n Use the ``coords`` and ``flatten`` parameters to plot selected variable dimensions\n across multiple plots. We will now modify the dimension ``obs_id`` to contain\n indicate the name of the county where the measure was taken. The change has to\n be done on both ``posterior_predictive`` and ``observed_data`` groups, which is\n why we will use :meth:`~arviz.InferenceData.map` to apply the same function to\n both groups. Afterwards, we will select the counties to be plotted with the\n ``coords`` arg.\n\n .. plot::\n :context: close-figs\n\n >>> obs_county = data.posterior[\"County\"][data.constant_data[\"county_idx\"]]\n >>> data = data.assign_coords(obs_id=obs_county, groups=\"observed_vars\")\n >>> az.plot_ppc(data, coords={'obs_id': ['ANOKA', 'BELTRAMI']}, flatten=[])\n\n Plot the overlay using a stacked scatter plot that is particularly useful\n when the sample sizes are small.\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_ppc(data, kind='scatter', flatten=[],\n >>> coords={'obs_id': ['AITKIN', 'BELTRAMI']})\n\n Plot random posterior predictive sub-samples.\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_ppc(data, num_pp_samples=30, random_seed=7)\n \n source"},{"id":160,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_rank","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_rank-Tuple","content":" ArviZPythonPlots.plot_rank — Method Plot rank order statistics of chains.\n\n From the paper: Rank plots are histograms of the ranked posterior draws (ranked over all\n chains) plotted separately for each chain.\n If all of the chains are targeting the same posterior, we expect the ranks in each chain to be\n uniform, whereas if one chain has a different location or scale parameter, this will be\n reflected in the deviation from uniformity. If rank plots of all chains look similar, this\n indicates good mixing of the chains.\n\n This plot was introduced by Aki Vehtari, Andrew Gelman, Daniel Simpson, Bob Carpenter,\n Paul-Christian Burkner (2019): Rank-normalization, folding, and localization: An improved R-hat\n for assessing convergence of MCMC. arXiv preprint https://arxiv.org/abs/1903.08008\n\n\n Parameters\n ----------\n data: obj\n Any object that can be converted to an :class:`arviz.InferenceData` object.\n Refer to documentation of :func:`arviz.convert_to_dataset` for details\n var_names: string or list of variable names\n Variables to be plotted. Prefix the variables by ``~`` when you want to exclude\n them from the plot.\n filter_vars: {None, \"like\", \"regex\"}, optional, default=None\n If `None` (default), interpret var_names as the real variables names. If \"like\",\n interpret var_names as substrings of the real variables names. If \"regex\",\n interpret var_names as regular expressions on the real variables names. A la\n ``pandas.filter``.\n transform: callable\n Function to transform data (defaults to None i.e.the identity function)\n coords: mapping, optional\n Coordinates of var_names to be plotted. Passed to :meth:`xarray.Dataset.sel`\n bins: None or passed to np.histogram\n Binning strategy used for histogram. By default uses twice the result of Sturges' formula.\n See :func:`numpy.histogram` documentation for, other available arguments.\n kind: string\n If bars (defaults), ranks are represented as stacked histograms (one per chain). If vlines\n ranks are represented as vertical lines above or below ``ref_line``.\n colors: string or list of strings\n List with valid matplotlib colors, one color per model. Alternative a string can be passed.\n If the string is `cycle`, it will automatically choose a color per model from matplotlib's\n cycle. If a single color is passed, e.g. 'k', 'C2' or 'red' this color will be used for all\n models. Defaults to `cycle`.\n ref_line: boolean\n Whether to include a dashed line showing where a uniform distribution would lie\n labels: bool\n whether to plot or not the x and y labels, defaults to True\n labeller : labeller instance, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n grid : tuple\n Number of rows and columns. Defaults to None, the rows and columns are\n automatically inferred.\n figsize: tuple\n Figure size. If None it will be defined automatically.\n ax: numpy array-like of matplotlib axes or bokeh figures, optional\n A 2D array of locations into which to plot the densities. If not supplied, ArviZ will create\n its own array of plot areas (and return it).\n backend: str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default \"matplotlib\".\n ref_line_kwargs : dict, optional\n Reference line keyword arguments, passed to :meth:`mpl:matplotlib.axes.Axes.axhline` or\n :class:`bokeh:bokeh.models.Span`.\n bar_kwargs : dict, optional\n Bars keyword arguments, passed to :meth:`mpl:matplotlib.axes.Axes.bar` or\n :meth:`bokeh:bokeh.plotting.Figure.vbar`.\n vlines_kwargs : dict, optional\n Vlines keyword arguments, passed to :meth:`mpl:matplotlib.axes.Axes.vlines` or\n :meth:`bokeh:bokeh.plotting.Figure.multi_line`.\n marker_vlines_kwargs : dict, optional\n Marker for the vlines keyword arguments, passed to :meth:`mpl:matplotlib.axes.Axes.plot` or\n :meth:`bokeh:bokeh.plotting.Figure.circle`.\n backend_kwargs: bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or\n :func:`bokeh.plotting.figure`. For additional documentation\n check the plotting method of the backend.\n show: bool, optional\n Call backend show function.\n\n Returns\n -------\n axes: matplotlib axes or bokeh figures\n\n See Also\n --------\n plot_trace : Plot distribution (histogram or kernel density estimates) and\n sampled values or rank plot.\n\n Examples\n --------\n Show a default rank plot\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data('centered_eight')\n >>> az.plot_rank(data)\n\n Recreate Figure 13 from the arxiv preprint\n\n .. plot::\n :context: close-figs\n\n >>> data = az.load_arviz_data('centered_eight')\n >>> az.plot_rank(data, var_names='tau')\n\n Use vlines to compare results for centered vs noncentered models\n\n .. plot::\n :context: close-figs\n\n >>> import matplotlib.pyplot as plt\n >>> centered_data = az.load_arviz_data('centered_eight')\n >>> noncentered_data = az.load_arviz_data('non_centered_eight')\n >>> _, ax = plt.subplots(1, 2, figsize=(12, 3))\n >>> az.plot_rank(centered_data, var_names=\"mu\", kind='vlines', ax=ax[0])\n >>> az.plot_rank(noncentered_data, var_names=\"mu\", kind='vlines', ax=ax[1])\n\n Change the aesthetics using kwargs\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_rank(noncentered_data, var_names=\"mu\", kind=\"vlines\",\n >>> vlines_kwargs={'lw':0}, marker_vlines_kwargs={'lw':3});\n \n source"},{"id":161,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_separation","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_separation-Tuple","content":" ArviZPythonPlots.plot_separation — Method Separation plot for binary outcome models.\n\n Model predictions are sorted and plotted using a color code according to\n the observed data.\n\n Parameters\n ----------\n idata : InferenceData\n :class:`arviz.InferenceData` object.\n y : array, DataArray or str\n Observed data. If str, ``idata`` must be present and contain the observed data group\n y_hat : array, DataArray or str\n Posterior predictive samples for ``y``. It must have the same shape as ``y``. If str or\n None, ``idata`` must contain the posterior predictive group.\n y_hat_line : bool, optional\n Plot the sorted ``y_hat`` predictions.\n expected_events : bool, optional\n Plot the total number of expected events.\n figsize : figure size tuple, optional\n If None, size is (8 + numvars, 8 + numvars)\n textsize: int, optional\n Text size for labels. If None it will be autoscaled based on ``figsize``.\n color : str, optional\n Color to assign to the positive class. The negative class will be plotted using the\n same color and an `alpha=0.3` transparency.\n legend : bool, optional\n Show the legend of the figure.\n ax: axes, optional\n Matplotlib axes or bokeh figures.\n plot_kwargs : dict, optional\n Additional keywords passed to :meth:`mpl:matplotlib.axes.Axes.bar` or\n :meth:`bokeh:bokeh.plotting.Figure.vbar` for separation plot.\n y_hat_line_kwargs : dict, optional\n Additional keywords passed to ax.plot for ``y_hat`` line.\n exp_events_kwargs : dict, optional\n Additional keywords passed to ax.scatter for ``expected_events`` marker.\n backend: str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default \"matplotlib\".\n backend_kwargs: bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or\n :func:`bokeh.plotting.figure`.\n show : bool, optional\n Call backend show function.\n\n Returns\n -------\n axes : matplotlib axes or bokeh figures\n\n See Also\n --------\n plot_ppc : Plot for posterior/prior predictive checks.\n\n References\n ----------\n .. [1] Greenhill, B. *et al.*, The Separation Plot: A New Visual Method\n for Evaluating the Fit of Binary Models, *American Journal of\n Political Science*, (2011) see https://doi.org/10.1111/j.1540-5907.2011.00525.x\n\n Examples\n --------\n Separation plot for a logistic regression model.\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> idata = az.load_arviz_data('classification10d')\n >>> az.plot_separation(idata=idata, y='outcome', y_hat='outcome', figsize=(8, 1))\n\n \n source"},{"id":162,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_trace","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_trace-Tuple","content":" ArviZPythonPlots.plot_trace — Method Plot distribution (histogram or kernel density estimates) and sampled values or rank plot.\n\n If `divergences` data is available in `sample_stats`, will plot the location of divergences as\n dashed vertical lines.\n\n Parameters\n ----------\n data: obj\n Any object that can be converted to an :class:`arviz.InferenceData` object\n Refer to documentation of :func:`arviz.convert_to_dataset` for details\n var_names: str or list of str, optional\n One or more variables to be plotted. Prefix the variables by ``~`` when you want\n to exclude them from the plot.\n filter_vars: {None, \"like\", \"regex\"}, optional, default=None\n If `None` (default), interpret var_names as the real variables names. If \"like\",\n interpret var_names as substrings of the real variables names. If \"regex\",\n interpret var_names as regular expressions on the real variables names. A la\n ``pandas.filter``.\n coords: dict of {str: slice or array_like}, optional\n Coordinates of var_names to be plotted. Passed to :meth:`xarray.Dataset.sel`\n divergences: {\"bottom\", \"top\", None}, optional\n Plot location of divergences on the traceplots.\n kind: {\"trace\", \"rank_bars\", \"rank_vlines\"}, optional\n Choose between plotting sampled values per iteration and rank plots.\n transform: callable, optional\n Function to transform data (defaults to None i.e.the identity function)\n figsize: tuple of (float, float), optional\n If None, size is (12, variables * 2)\n rug: bool, optional\n If True adds a rugplot of samples. Defaults to False. Ignored for 2D KDE.\n Only affects continuous variables.\n lines: list of tuple of (str, dict, array_like), optional\n List of (var_name, {'coord': selection}, [line, positions]) to be overplotted as\n vertical lines on the density and horizontal lines on the trace.\n circ_var_names : str or list of str, optional\n List of circular variables to account for when plotting KDE.\n circ_var_units : str\n Whether the variables in ``circ_var_names`` are in \"degrees\" or \"radians\".\n compact: bool, optional\n Plot multidimensional variables in a single plot.\n compact_prop: str or dict {str: array_like}, optional\n Defines the property name and the property values to distinguish different\n dimensions with compact=True.\n When compact=True it defaults to color, it is\n ignored otherwise.\n combined: bool, optional\n Flag for combining multiple chains into a single line. If False (default), chains will be\n plotted separately.\n chain_prop: str or dict {str: array_like}, optional\n Defines the property name and the property values to distinguish different chains.\n If compact=True it defaults to linestyle,\n otherwise it uses the color to distinguish\n different chains.\n legend: bool, optional\n Add a legend to the figure with the chain color code.\n plot_kwargs, fill_kwargs, rug_kwargs, hist_kwargs: dict, optional\n Extra keyword arguments passed to :func:`arviz.plot_dist`. Only affects continuous\n variables.\n trace_kwargs: dict, optional\n Extra keyword arguments passed to :meth:`matplotlib.axes.Axes.plot`\n labeller : labeller instance, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n rank_kwargs : dict, optional\n Extra keyword arguments passed to :func:`arviz.plot_rank`\n axes: axes, optional\n Matplotlib axes or bokeh figures.\n backend: {\"matplotlib\", \"bokeh\"}, optional\n Select plotting backend.\n backend_config: dict, optional\n Currently specifies the bounds to use for bokeh axes. Defaults to value set in rcParams.\n backend_kwargs: dict, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or\n :func:`bokeh.plotting.figure`.\n show: bool, optional\n Call backend show function.\n\n Returns\n -------\n axes: matplotlib axes or bokeh figures\n\n See Also\n --------\n plot_rank : Plot rank order statistics of chains.\n\n Examples\n --------\n Plot a subset variables and select them with partial naming\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data('non_centered_eight')\n >>> coords = {'school': ['Choate', 'Lawrenceville']}\n >>> az.plot_trace(data, var_names=('theta'), filter_vars=\"like\", coords=coords)\n\n Show all dimensions of multidimensional variables in the same plot\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_trace(data, compact=True)\n\n Display a rank plot instead of trace\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_trace(data, var_names=[\"mu\", \"tau\"], kind=\"rank_bars\")\n\n Combine all chains into one distribution and select variables with regular expressions\n\n .. plot::\n :context: close-figs\n\n >>> az.plot_trace(\n >>> data, var_names=('^theta'), filter_vars=\"regex\", coords=coords, combined=True\n >>> )\n\n\n Plot reference lines against distribution and trace\n\n .. plot::\n :context: close-figs\n\n >>> lines = (('theta_t',{'school': \"Choate\"}, [-1]),)\n >>> az.plot_trace(data, var_names=('theta_t', 'theta'), coords=coords, lines=lines)\n\n \n source"},{"id":163,"pagetitle":"Plotting functions","title":"ArviZPythonPlots.plot_violin","ref":"/ArviZPythonPlots/stable/api/plots/#ArviZPythonPlots.plot_violin-Tuple","content":" ArviZPythonPlots.plot_violin — Method Plot posterior of traces as violin plot.\n\n Notes\n -----\n If multiple chains are provided for a variable they will be combined\n\n Parameters\n ----------\n data: obj\n Any object that can be converted to an :class:`arviz.InferenceData` object\n Refer to documentation of :func:`arviz.convert_to_dataset` for details\n var_names: list of variable names, optional\n Variables to be plotted, if None all variable are plotted. Prefix the\n variables by ``~`` when you want to exclude them from the plot.\n combine_dims : set_like of str, optional\n List of dimensions to reduce. Defaults to reducing only the \"chain\" and \"draw\" dimensions.\n See the :ref:`this section ` for usage examples.\n filter_vars: {None, \"like\", \"regex\"}, optional, default=None\n If `None` (default), interpret var_names as the real variables names. If \"like\",\n interpret var_names as substrings of the real variables names. If \"regex\",\n interpret var_names as regular expressions on the real variables names. A la\n ``pandas.filter``.\n transform: callable\n Function to transform data (defaults to None i.e. the identity function).\n quartiles: bool, optional\n Flag for plotting the interquartile range, in addition to the ``hdi_prob`` * 100%\n intervals. Defaults to ``True``.\n rug: bool\n If ``True`` adds a jittered rugplot. Defaults to ``False``.\n side : {\"both\", \"left\", \"right\"}, default \"both\"\n If ``both``, both sides of the violin plot are rendered. If ``left`` or ``right``, only\n the respective side is rendered. By separately plotting left and right halfs with\n different data, split violin plots can be achieved.\n hdi_prob: float, optional\n Plots highest posterior density interval for chosen percentage of density.\n Defaults to 0.94.\n shade: float\n Alpha blending value for the shaded area under the curve, between 0\n (no shade) and 1 (opaque). Defaults to 0.\n bw: float or str, optional\n If numeric, indicates the bandwidth and must be positive.\n If str, indicates the method to estimate the bandwidth and must be\n one of \"scott\", \"silverman\", \"isj\" or \"experimental\" when ``circular`` is ``False``\n and \"taylor\" (for now) when ``circular`` is ``True``.\n Defaults to \"default\" which means \"experimental\" when variable is not circular\n and \"taylor\" when it is.\n circular: bool, optional.\n If ``True``, it interprets `values` is a circular variable measured in radians\n and a circular KDE is used. Defaults to ``False``.\n grid : tuple\n Number of rows and columns. Defaults to None, the rows and columns are\n automatically inferred.\n figsize: tuple\n Figure size. If None it will be defined automatically.\n textsize: int\n Text size of the point_estimates, axis ticks, and highest density interval. If None it will\n be autoscaled based on ``figsize``.\n labeller : labeller instance, optional\n Class providing the method ``make_label_vert`` to generate the labels in the plot titles.\n Read the :ref:`label_guide` for more details and usage examples.\n sharex: bool\n Defaults to ``True``, violinplots share a common x-axis scale.\n sharey: bool\n Defaults to ``True``, violinplots share a common y-axis scale.\n ax: numpy array-like of matplotlib axes or bokeh figures, optional\n A 2D array of locations into which to plot the densities. If not supplied, Arviz will create\n its own array of plot areas (and return it).\n shade_kwargs: dicts, optional\n Additional keywords passed to :meth:`matplotlib.axes.Axes.fill_between`, or\n :meth:`matplotlib.axes.Axes.barh` to control the shade.\n rug_kwargs: dict\n Keywords passed to the rug plot. If true only the right half side of the violin will be\n plotted.\n backend: str, optional\n Select plotting backend {\"matplotlib\",\"bokeh\"}. Default to \"matplotlib\".\n backend_kwargs: bool, optional\n These are kwargs specific to the backend being used, passed to\n :func:`matplotlib.pyplot.subplots` or :func:`bokeh.plotting.figure`.\n For additional documentation check the plotting method of the backend.\n show: bool, optional\n Call backend show function.\n\n Returns\n -------\n axes: matplotlib axes or bokeh figures\n\n See Also\n --------\n plot_forest: Forest plot to compare HDI intervals from a number of distributions.\n\n Examples\n --------\n Show a default violin plot\n\n .. plot::\n :context: close-figs\n\n >>> import arviz as az\n >>> data = az.load_arviz_data('centered_eight')\n >>> az.plot_violin(data)\n\n \n source"},{"id":166,"pagetitle":"rcParams","title":"rcParams","ref":"/ArviZPythonPlots/stable/api/rcparams/#rcparams-api","content":" rcParams ArviZPythonPlots.rcParams ArviZPythonPlots.rc_context"},{"id":167,"pagetitle":"rcParams","title":"Reference","ref":"/ArviZPythonPlots/stable/api/rcparams/#Reference","content":" Reference"},{"id":168,"pagetitle":"rcParams","title":"ArviZPythonPlots.rcParams","ref":"/ArviZPythonPlots/stable/api/rcparams/#ArviZPythonPlots.rcParams","content":" ArviZPythonPlots.rcParams — Constant Class to contain ArviZ default parameters.\n\n It is implemented as a dict with validation when setting items.\n \n source"},{"id":169,"pagetitle":"rcParams","title":"ArviZPythonPlots.rc_context","ref":"/ArviZPythonPlots/stable/api/rcparams/#ArviZPythonPlots.rc_context-Tuple","content":" ArviZPythonPlots.rc_context — Method \n Return a context manager for managing rc settings.\n\n Parameters\n ----------\n rc : dict, optional\n Mapping containing the rcParams to modify temporally.\n fname : str, optional\n Filename of the file containing the rcParams to use inside the rc_context.\n\n Examples\n --------\n This allows one to do::\n\n with az.rc_context(fname='pystan.rc'):\n idata = az.load_arviz_data(\"radon\")\n az.plot_posterior(idata, var_names=[\"gamma\"])\n\n The plot would have settings from 'screen.rc'\n\n A dictionary can also be passed to the context manager::\n\n with az.rc_context(rc={'plot.max_subplots': None}, fname='pystan.rc'):\n idata = az.load_arviz_data(\"radon\")\n az.plot_posterior(idata, var_names=[\"gamma\"])\n\n The 'rc' dictionary takes precedence over the settings loaded from\n 'fname'. Passing a dictionary only is also valid.\n \n source"},{"id":172,"pagetitle":"Plotting styles","title":"Plotting styles","ref":"/ArviZPythonPlots/stable/api/style/#style-api","content":" Plotting styles ArviZPythonPlots.styles ArviZPythonPlots.use_style"},{"id":173,"pagetitle":"Plotting styles","title":"Reference","ref":"/ArviZPythonPlots/stable/api/style/#Reference","content":" Reference"},{"id":174,"pagetitle":"Plotting styles","title":"ArviZPythonPlots.styles","ref":"/ArviZPythonPlots/stable/api/style/#ArviZPythonPlots.styles-Tuple{}","content":" ArviZPythonPlots.styles — Method styles() -> Vector{String} Get all available matplotlib styles for use with use_style source"},{"id":175,"pagetitle":"Plotting styles","title":"ArviZPythonPlots.use_style","ref":"/ArviZPythonPlots/stable/api/style/#ArviZPythonPlots.use_style-Tuple{Any}","content":" ArviZPythonPlots.use_style — Method use_style(style::String)\nuse_style(style::Vector{String}) Use matplotlib style settings from a style specification style . The style name of \"default\" is reserved for reverting back to the default style settings. ArviZ-specific styles include [\"arviz-whitegrid\", \"arviz-darkgrid\", \"arviz-colors\", \"arviz-white\", \"arviz-doc\"] . To see all available style specifications, use styles() . If a Vector of styles is provided, they are applied from first to last. source"},{"id":178,"pagetitle":"Examples gallery","title":"Example Gallery","ref":"/ArviZPythonPlots/stable/examples/#Example-Gallery","content":" Example Gallery"},{"id":179,"pagetitle":"Examples gallery","title":"Autocorrelation Plot","ref":"/ArviZPythonPlots/stable/examples/#Autocorrelation-Plot","content":" Autocorrelation Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"centered_eight\")\nplot_autocorr(data; var_names=[\"tau\", \"mu\"])\ngcf() See plot_autocorr"},{"id":180,"pagetitle":"Examples gallery","title":"Bayes Factor Plot","ref":"/ArviZPythonPlots/stable/examples/#Bayes-Factor-Plot","content":" Bayes Factor Plot using ArviZ, ArviZPythonPlots\n\nuse_style(\"arviz-darkgrid\")\n\nidata = from_namedtuple((a = 1 .+ randn(5_000) ./ 2,), prior=(a = randn(5_000),))\nplot_bf(idata; var_name=\"a\", ref_val=0)\ngcf() See plot_bf"},{"id":181,"pagetitle":"Examples gallery","title":"Bayesian P-Value Posterior Plot","ref":"/ArviZPythonPlots/stable/examples/#Bayesian-P-Value-Posterior-Plot","content":" Bayesian P-Value Posterior Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"regression1d\")\nplot_bpv(data)\ngcf() See plot_bpv"},{"id":182,"pagetitle":"Examples gallery","title":"Bayesian P-Value with Median T Statistic Posterior Plot","ref":"/ArviZPythonPlots/stable/examples/#Bayesian-P-Value-with-Median-T-Statistic-Posterior-Plot","content":" Bayesian P-Value with Median T Statistic Posterior Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"regression1d\")\nplot_bpv(data; kind=\"t_stat\", t_stat=\"0.5\")\ngcf() See plot_bpv"},{"id":183,"pagetitle":"Examples gallery","title":"Compare Plot","ref":"/ArviZPythonPlots/stable/examples/#Compare-Plot","content":" Compare Plot using ArviZ, ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\nmodel_compare = compare(\n (\n var\"Centered 8 schools\" = load_example_data(\"centered_eight\"),\n var\"Non-centered 8 schools\" = load_example_data(\"non_centered_eight\"),\n ),\n)\nplot_compare(model_compare; figsize=(12, 4))\ngcf() See compare , plot_compare"},{"id":184,"pagetitle":"Examples gallery","title":"Density Plot","ref":"/ArviZPythonPlots/stable/examples/#Density-Plot","content":" Density Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ncentered_data = load_example_data(\"centered_eight\")\nnon_centered_data = load_example_data(\"non_centered_eight\")\nplot_density(\n [centered_data, non_centered_data];\n data_labels=[\"Centered\", \"Non Centered\"],\n var_names=[\"theta\"],\n shade=0.1,\n)\ngcf() See plot_density"},{"id":185,"pagetitle":"Examples gallery","title":"Dist Plot","ref":"/ArviZPythonPlots/stable/examples/#Dist-Plot","content":" Dist Plot using ArviZPythonPlots, Distributions, Random\n\nRandom.seed!(308)\n\nuse_style(\"arviz-darkgrid\")\n\na = rand(Poisson(4), 1000)\nb = rand(Normal(0, 1), 1000)\n_, ax = subplots(1, 2; figsize=(10, 4))\nplot_dist(a; color=\"C1\", label=\"Poisson\", ax=ax[0])\nplot_dist(b; color=\"C2\", label=\"Gaussian\", ax=ax[1])\ngcf() See plot_dist"},{"id":186,"pagetitle":"Examples gallery","title":"Dot Plot","ref":"/ArviZPythonPlots/stable/examples/#Dot-Plot","content":" Dot Plot using ArviZPythonPlots\n\nuse_style(\"arviz-darkgrid\")\n\ndata = randn(1000)\nplot_dot(data; dotcolor=\"C1\", point_interval=true)\ntitle(\"Gaussian Distribution\")\ngcf() See plot_dot"},{"id":187,"pagetitle":"Examples gallery","title":"ECDF Plot","ref":"/ArviZPythonPlots/stable/examples/#ECDF-Plot","content":" ECDF Plot using ArviZPythonPlots, Distributions\n\nuse_style(\"arviz-darkgrid\")\n\nsample = randn(1_000)\ndist = Normal()\nplot_ecdf(sample; cdf=x -> cdf(dist, x), confidence_bands=true)\ngcf() See plot_ecdf"},{"id":188,"pagetitle":"Examples gallery","title":"ELPD Plot","ref":"/ArviZPythonPlots/stable/examples/#ELPD-Plot","content":" ELPD Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\nd1 = load_example_data(\"centered_eight\")\nd2 = load_example_data(\"non_centered_eight\")\nplot_elpd(Dict(\"Centered eight\" => d1, \"Non centered eight\" => d2); xlabels=true)\ngcf() See plot_elpd"},{"id":189,"pagetitle":"Examples gallery","title":"Energy Plot","ref":"/ArviZPythonPlots/stable/examples/#Energy-Plot","content":" Energy Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"centered_eight\")\nplot_energy(data; figsize=(12, 8))\ngcf() See plot_energy"},{"id":190,"pagetitle":"Examples gallery","title":"ESS Evolution Plot","ref":"/ArviZPythonPlots/stable/examples/#ESS-Evolution-Plot","content":" ESS Evolution Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\nidata = load_example_data(\"radon\")\nplot_ess(idata; var_names=[\"b\"], kind=\"evolution\")\ngcf() See plot_ess"},{"id":191,"pagetitle":"Examples gallery","title":"ESS Local Plot","ref":"/ArviZPythonPlots/stable/examples/#ESS-Local-Plot","content":" ESS Local Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\nidata = load_example_data(\"non_centered_eight\")\nplot_ess(idata; var_names=[\"mu\"], kind=\"local\", marker=\"_\", ms=20, mew=2, rug=true)\ngcf() See plot_ess"},{"id":192,"pagetitle":"Examples gallery","title":"ESS Quantile Plot","ref":"/ArviZPythonPlots/stable/examples/#ESS-Quantile-Plot","content":" ESS Quantile Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\nidata = load_example_data(\"radon\")\nplot_ess(idata; var_names=[\"sigma\"], kind=\"quantile\", color=\"C4\")\ngcf() See plot_ess"},{"id":193,"pagetitle":"Examples gallery","title":"Forest Plot","ref":"/ArviZPythonPlots/stable/examples/#Forest-Plot","content":" Forest Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ncentered_data = load_example_data(\"centered_eight\")\nnon_centered_data = load_example_data(\"non_centered_eight\")\nplot_forest(\n [centered_data, non_centered_data];\n model_names=[\"Centered\", \"Non Centered\"],\n var_names=[\"mu\"],\n)\ntitle(\"Estimated theta for eight schools model\")\ngcf() See plot_forest"},{"id":194,"pagetitle":"Examples gallery","title":"Ridge Plot","ref":"/ArviZPythonPlots/stable/examples/#Ridge-Plot","content":" Ridge Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\nrugby_data = load_example_data(\"rugby\")\nplot_forest(\n rugby_data;\n kind=\"ridgeplot\",\n var_names=[\"defs\"],\n linewidth=4,\n combined=true,\n ridgeplot_overlap=1.5,\n colors=\"blue\",\n figsize=(9, 4),\n)\ntitle(\"Relative defensive strength\\nof Six Nation rugby teams\")\ngcf() See plot_forest"},{"id":195,"pagetitle":"Examples gallery","title":"Plot HDI","ref":"/ArviZPythonPlots/stable/examples/#Plot-HDI","content":" Plot HDI using Random\nusing ArviZPythonPlots\n\nRandom.seed!(308)\n\nuse_style(\"arviz-darkgrid\")\n\nx_data = randn(100)\ny_data = 2 .+ x_data .* 0.5\ny_data_rep = 0.5 .* randn(200, 100) .+ transpose(y_data)\n\nplot(x_data, y_data; color=\"C6\")\nplot_hdi(x_data, y_data_rep; color=\"k\", plot_kwargs=Dict(\"ls\" => \"--\"))\ngcf() See plot_hdi"},{"id":196,"pagetitle":"Examples gallery","title":"Joint Plot","ref":"/ArviZPythonPlots/stable/examples/#Joint-Plot","content":" Joint Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"non_centered_eight\")\nplot_pair(\n data;\n var_names=[\"theta\"],\n coords=Dict(\"school\" => [\"Choate\", \"Phillips Andover\"]),\n kind=\"hexbin\",\n marginals=true,\n figsize=(10, 10),\n)\ngcf() See plot_pair"},{"id":197,"pagetitle":"Examples gallery","title":"KDE Plot","ref":"/ArviZPythonPlots/stable/examples/#KDE-Plot","content":" KDE Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"centered_eight\")\n\n## Combine different posterior draws from different chains\nobs = data.posterior_predictive.obs\nsize_obs = size(obs)\ny_hat = reshape(obs, prod(size_obs[1:2]), size_obs[3:end]...)\n\nplot_kde(\n y_hat;\n label=\"Estimated Effect\\n of SAT Prep\",\n rug=true,\n plot_kwargs=Dict(\"linewidth\" => 2, \"color\" => \"black\"),\n rug_kwargs=Dict(\"color\" => \"black\"),\n)\ngcf() See plot_kde"},{"id":198,"pagetitle":"Examples gallery","title":"2d KDE","ref":"/ArviZPythonPlots/stable/examples/#d-KDE","content":" 2d KDE using Random\nusing ArviZPythonPlots\n\nRandom.seed!(308)\n\nuse_style(\"arviz-darkgrid\")\n\nplot_kde(rand(100), rand(100))\ngcf() See plot_kde"},{"id":199,"pagetitle":"Examples gallery","title":"KDE Quantiles Plot","ref":"/ArviZPythonPlots/stable/examples/#KDE-Quantiles-Plot","content":" KDE Quantiles Plot using Random\nusing Distributions\nusing ArviZPythonPlots\n\nRandom.seed!(308)\n\nuse_style(\"arviz-darkgrid\")\n\ndist = rand(Beta(rand(Uniform(0.5, 10)), 5), 1000)\nplot_kde(dist; quantiles=[0.25, 0.5, 0.75])\ngcf() See plot_kde"},{"id":200,"pagetitle":"Examples gallery","title":"Pareto Shape Plot","ref":"/ArviZPythonPlots/stable/examples/#Pareto-Shape-Plot","content":" Pareto Shape Plot using ArviZ, ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\nidata = load_example_data(\"radon\")\nloo_data = loo(idata)\nplot_khat(loo_data; show_bins=true)\ngcf() See loo , plot_khat"},{"id":201,"pagetitle":"Examples gallery","title":"LOO-PIT ECDF Plot","ref":"/ArviZPythonPlots/stable/examples/#LOO-PIT-ECDF-Plot","content":" LOO-PIT ECDF Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\nidata = load_example_data(\"radon\")\n\nplot_loo_pit(idata; y=\"y\", ecdf=true, color=\"maroon\")\ngcf() See loo_pit , plot_loo_pit"},{"id":202,"pagetitle":"Examples gallery","title":"LOO-PIT Overlay Plot","ref":"/ArviZPythonPlots/stable/examples/#LOO-PIT-Overlay-Plot","content":" LOO-PIT Overlay Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\nidata = load_example_data(\"non_centered_eight\")\nplot_loo_pit(; idata, y=\"obs\", color=\"indigo\")\ngcf() See loo_pit , plot_loo_pit"},{"id":203,"pagetitle":"Examples gallery","title":"Quantile Monte Carlo Standard Error Plot","ref":"/ArviZPythonPlots/stable/examples/#Quantile-Monte-Carlo-Standard-Error-Plot","content":" Quantile Monte Carlo Standard Error Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"centered_eight\")\nplot_mcse(data; var_names=[\"tau\", \"mu\"], rug=true, extra_methods=true)\ngcf() See plot_mcse"},{"id":204,"pagetitle":"Examples gallery","title":"Quantile MCSE Errobar Plot","ref":"/ArviZPythonPlots/stable/examples/#Quantile-MCSE-Errobar-Plot","content":" Quantile MCSE Errobar Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"radon\")\nplot_mcse(data; var_names=[\"sigma_a\"], color=\"C4\", errorbar=true)\ngcf() See plot_mcse"},{"id":205,"pagetitle":"Examples gallery","title":"Pair Plot","ref":"/ArviZPythonPlots/stable/examples/#Pair-Plot","content":" Pair Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ncentered = load_example_data(\"centered_eight\")\ncoords = Dict(\"school\" => [\"Choate\", \"Deerfield\"])\nplot_pair(\n centered; var_names=[\"theta\", \"mu\", \"tau\"], coords, divergences=true, textsize=22\n)\ngcf() See plot_pair"},{"id":206,"pagetitle":"Examples gallery","title":"Hexbin Pair Plot","ref":"/ArviZPythonPlots/stable/examples/#Hexbin-Pair-Plot","content":" Hexbin Pair Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ncentered = load_example_data(\"centered_eight\")\ncoords = Dict(\"school\" => [\"Choate\", \"Deerfield\"])\nplot_pair(\n centered;\n var_names=[\"theta\", \"mu\", \"tau\"],\n kind=\"hexbin\",\n coords,\n colorbar=true,\n divergences=true,\n)\ngcf() See plot_pair"},{"id":207,"pagetitle":"Examples gallery","title":"KDE Pair Plot","ref":"/ArviZPythonPlots/stable/examples/#KDE-Pair-Plot","content":" KDE Pair Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ncentered = load_example_data(\"centered_eight\")\ncoords = Dict(\"school\" => [\"Choate\", \"Deerfield\"])\nplot_pair(\n centered;\n var_names=[\"theta\", \"mu\", \"tau\"],\n kind=\"kde\",\n coords,\n divergences=true,\n textsize=22,\n)\ngcf() See plot_pair"},{"id":208,"pagetitle":"Examples gallery","title":"Point Estimate Pair Plot","ref":"/ArviZPythonPlots/stable/examples/#Point-Estimate-Pair-Plot","content":" Point Estimate Pair Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ncentered = load_example_data(\"centered_eight\")\ncoords = Dict(\"school\" => [\"Choate\", \"Deerfield\"])\nplot_pair(\n centered;\n var_names=[\"mu\", \"theta\"],\n kind=[\"scatter\", \"kde\"],\n kde_kwargs=Dict(\"fill_last\" => false),\n marginals=true,\n coords,\n point_estimate=\"median\",\n figsize=(10, 8),\n)\ngcf() See plot_pair"},{"id":209,"pagetitle":"Examples gallery","title":"Parallel Plot","ref":"/ArviZPythonPlots/stable/examples/#Parallel-Plot","content":" Parallel Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"centered_eight\")\nax = plot_parallel(data; var_names=[\"theta\", \"tau\", \"mu\"])\nax.set_xticklabels(ax.get_xticklabels(); rotation=70)\ndraw()\ngcf() See plot_parallel"},{"id":210,"pagetitle":"Examples gallery","title":"Posterior Plot","ref":"/ArviZPythonPlots/stable/examples/#Posterior-Plot","content":" Posterior Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"centered_eight\")\ncoords = Dict(\"school\" => [\"Choate\"])\nplot_posterior(data; var_names=[\"mu\", \"theta\"], coords, rope=(-1, 1))\ngcf() See plot_posterior"},{"id":211,"pagetitle":"Examples gallery","title":"Posterior Predictive Check Plot","ref":"/ArviZPythonPlots/stable/examples/#Posterior-Predictive-Check-Plot","content":" Posterior Predictive Check Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"non_centered_eight\")\nplot_ppc(data; data_pairs=Dict(\"obs\" => \"obs\"), alpha=0.03, figsize=(12, 6), textsize=14)\ngcf() See plot_ppc"},{"id":212,"pagetitle":"Examples gallery","title":"Posterior Predictive Check Cumulative Plot","ref":"/ArviZPythonPlots/stable/examples/#Posterior-Predictive-Check-Cumulative-Plot","content":" Posterior Predictive Check Cumulative Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"non_centered_eight\")\nplot_ppc(data; alpha=0.3, kind=\"cumulative\", figsize=(12, 6), textsize=14)\ngcf() See plot_ppc"},{"id":213,"pagetitle":"Examples gallery","title":"Rank Plot","ref":"/ArviZPythonPlots/stable/examples/#Rank-Plot","content":" Rank Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"centered_eight\")\nplot_rank(data; var_names=[\"tau\", \"mu\"])\ngcf() See plot_rank"},{"id":214,"pagetitle":"Examples gallery","title":"Regression Plot","ref":"/ArviZPythonPlots/stable/examples/#Regression-Plot","content":" Regression Plot using ArviZ, ArviZPythonPlots, ArviZExampleData, DimensionalData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"regression1d\")\nx = range(0, 1; length=100)\nposterior = data.posterior\nconstant_data = convert_to_dataset((; x); default_dims=())\ny_model = broadcast_dims(muladd, posterior.intercept, posterior.slope, constant_data.x)\nposterior = merge(posterior, (; y_model))\ndata = merge(data, InferenceData(; posterior, constant_data))\nplot_lm(\"y\"; idata=data, x=\"x\", y_model=\"y_model\")\ngcf() See plot_lm"},{"id":215,"pagetitle":"Examples gallery","title":"Separation Plot","ref":"/ArviZPythonPlots/stable/examples/#Separation-Plot","content":" Separation Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"classification10d\")\nplot_separation(data; y=\"outcome\", y_hat=\"outcome\", figsize=(8, 1))\ngcf() See plot_separation"},{"id":216,"pagetitle":"Examples gallery","title":"Trace Plot","ref":"/ArviZPythonPlots/stable/examples/#Trace-Plot","content":" Trace Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"non_centered_eight\")\nplot_trace(data; var_names=[\"tau\", \"mu\"])\ngcf() See plot_trace"},{"id":217,"pagetitle":"Examples gallery","title":"Violin Plot","ref":"/ArviZPythonPlots/stable/examples/#Violin-Plot","content":" Violin Plot using ArviZPythonPlots, ArviZExampleData\n\nuse_style(\"arviz-darkgrid\")\n\ndata = load_example_data(\"non_centered_eight\")\nplot_violin(data; var_names=[\"mu\", \"tau\"])\ngcf() See plot_violin"},{"id":218,"pagetitle":"Examples gallery","title":"Styles","ref":"/ArviZPythonPlots/stable/examples/#Styles","content":" Styles using ArviZPythonPlots, Distributions, PythonCall\n\nx = range(0, 1; length=100)\ndist = pdf.(Beta(2, 5), x)\n\nstyle_list = [\n \"default\",\n [\"default\", \"arviz-colors\"],\n \"arviz-darkgrid\",\n \"arviz-whitegrid\",\n \"arviz-white\",\n \"arviz-grayscale\",\n [\"arviz-white\", \"arviz-redish\"],\n [\"arviz-white\", \"arviz-bluish\"],\n [\"arviz-white\", \"arviz-orangish\"],\n [\"arviz-white\", \"arviz-brownish\"],\n [\"arviz-white\", \"arviz-purplish\"],\n [\"arviz-white\", \"arviz-cyanish\"],\n [\"arviz-white\", \"arviz-greenish\"],\n [\"arviz-white\", \"arviz-royish\"],\n [\"arviz-white\", \"arviz-viridish\"],\n [\"arviz-white\", \"arviz-plasmish\"],\n \"arviz-doc\",\n \"arviz-docgrid\",\n]\n\nfig = figure(; figsize=(20, 10))\nfor (idx, style) in enumerate(style_list)\n pywith(pyplot.style.context(style; after_reset=true)) do _\n ax = fig.add_subplot(5, 4, idx; label=idx)\n colors = pyplot.rcParams[\"axes.prop_cycle\"].by_key()[\"color\"]\n for i in 0:(length(colors) - 1)\n ax.plot(x, dist .- i, \"C$i\"; label=\"C$i\")\n end\n ax.set_title(style)\n ax.set_xlabel(\"x\")\n ax.set_ylabel(\"f(x)\"; rotation=0, labelpad=15)\n ax.set_xticklabels([])\n end\nend\ntight_layout()\ngcf()"},{"id":221,"pagetitle":"Home","title":"PosteriorStats","ref":"/PosteriorStats/stable/#PosteriorStats","content":" PosteriorStats PosteriorStats implements widely-used and well-characterized statistical analyses for the Bayesian workflow. These functions generally estimate properties of posterior and/or posterior predictive distributions. The default implementations defined here operate on Monte Carlo samples. See the API for details."},{"id":222,"pagetitle":"Home","title":"Extending this package","ref":"/PosteriorStats/stable/#Extending-this-package","content":" Extending this package The methods defined here are intended to be extended by two types of packages. packages that implement data types for storing Monte Carlo samples packages that implement other representations for posterior distributions than Monte Carlo draws"},{"id":225,"pagetitle":"API","title":"API","ref":"/PosteriorStats/stable/api/#API","content":" API"},{"id":226,"pagetitle":"API","title":"Summary statistics","ref":"/PosteriorStats/stable/api/#Summary-statistics","content":" Summary statistics"},{"id":227,"pagetitle":"API","title":"PosteriorStats.SummaryStats","ref":"/PosteriorStats/stable/api/#PosteriorStats.SummaryStats","content":" PosteriorStats.SummaryStats — Type struct SummaryStats{D, V<:(AbstractVector)} A container for a column table of values computed by summarize . This object implements the Tables and TableTraits column table interfaces. It has a custom show method. SummaryStats behaves like an OrderedDict of columns, where the columns can be accessed using either Symbol s or a 1-based integer index. name::String : The name of the collection of summary statistics, used as the table title in display. data::Any : The summary statistics for each parameter. It must implement the Tables interface. parameter_names::AbstractVector : Names of the parameters SummaryStats([name::String,] data[, parameter_names])\nSummaryStats(data[, parameter_names]; name::String=\"SummaryStats\") Construct a SummaryStats from tabular data with optional stats name and param_names . data must not contain a column :parameter , as this is reserved for the parameter names, which are always in the first column. source"},{"id":228,"pagetitle":"API","title":"PosteriorStats.default_diagnostics","ref":"/PosteriorStats/stable/api/#PosteriorStats.default_diagnostics","content":" PosteriorStats.default_diagnostics — Function default_diagnostics(focus=Statistics.mean; kwargs...) Default diagnostics to be computed with summarize . The value of focus determines the diagnostics to be returned: Statistics.mean : mcse_mean , mcse_std , ess_tail , ess_bulk , rhat Statistics.median : mcse_median , ess_tail , ess_bulk , rhat source"},{"id":229,"pagetitle":"API","title":"PosteriorStats.default_stats","ref":"/PosteriorStats/stable/api/#PosteriorStats.default_stats","content":" PosteriorStats.default_stats — Function default_stats(focus=Statistics.mean; prob_interval=0.94, kwargs...) Default statistics to be computed with summarize . The value of focus determines the statistics to be returned: Statistics.mean : mean , std , hdi_3% , hdi_97% Statistics.median : median , mad , eti_3% , eti_97% If prob_interval is set to a different value than the default, then different HDI and ETI statistics are computed accordingly. hdi refers to the highest-density interval, while eti refers to the equal-tailed interval (i.e. the credible interval computed from symmetric quantiles). See also: hdi source"},{"id":230,"pagetitle":"API","title":"PosteriorStats.default_summary_stats","ref":"/PosteriorStats/stable/api/#PosteriorStats.default_summary_stats","content":" PosteriorStats.default_summary_stats — Function default_summary_stats(focus=Statistics.mean; kwargs...) Combinatiton of default_stats and default_diagnostics to be used with summarize . source"},{"id":231,"pagetitle":"API","title":"PosteriorStats.summarize","ref":"/PosteriorStats/stable/api/#PosteriorStats.summarize","content":" PosteriorStats.summarize — Function summarize(data, stats_funs...; name=\"SummaryStats\", [var_names]) -> SummaryStats Compute the summary statistics in stats_funs on each param in data . stats_funs is a collection of functions that reduces a matrix with shape (draws, chains) to a scalar or a collection of scalars. Alternatively, an item in stats_funs may be a Pair of the form name => fun specifying the name to be used for the statistic or of the form (name1, ...) => fun when the function returns a collection. When the function returns a collection, the names in this latter format must be provided. If no stats functions are provided, then those specified in default_summary_stats are computed. var_names specifies the names of the parameters in data . If not provided, the names are inferred from data . To support computing summary statistics from a custom object, overload this method specifying the type of data . See also SummaryStats , default_summary_stats , default_stats , default_diagnostics . Examples Compute mean , std and the Monte Carlo standard error (MCSE) of the mean estimate: julia> using Statistics, StatsBase\n\njulia> x = randn(1000, 4, 3) .+ reshape(0:10:20, 1, 1, :);\n\njulia> summarize(x, mean, std, :mcse_mean => sem; name=\"Mean/Std\")\nMean/Std\n mean std mcse_mean\n 1 0.0003 0.990 0.016\n 2 10.02 0.988 0.016\n 3 19.98 0.988 0.016 Avoid recomputing the mean by using mean_and_std , and provide parameter names: julia> summarize(x, (:mean, :std) => mean_and_std, mad; var_names=[:a, :b, :c])\nSummaryStats\n mean std mad\n a 0.000305 0.990 0.978\n b 10.0 0.988 0.995\n c 20.0 0.988 0.979 Note that when an estimator and its MCSE are both computed, the MCSE is used to determine the number of significant digits that will be displayed. julia> summarize(x; var_names=[:a, :b, :c])\nSummaryStats\n mean std hdi_3% hdi_97% mcse_mean mcse_std ess_tail ess_bulk r ⋯\n a 0.0003 0.99 -1.92 1.78 0.016 0.012 3567 3663 1 ⋯\n b 10.02 0.99 8.17 11.9 0.016 0.011 3841 3906 1 ⋯\n c 19.98 0.99 18.1 21.9 0.016 0.012 3892 3749 1 ⋯\n 1 column omitted Compute just the statistics with an 89% HDI on all parameters, and provide the parameter names: julia> summarize(x, default_stats(; prob_interval=0.89)...; var_names=[:a, :b, :c])\nSummaryStats\n mean std hdi_5.5% hdi_94.5%\n a 0.000305 0.990 -1.63 1.52\n b 10.0 0.988 8.53 11.6\n c 20.0 0.988 18.5 21.6 Compute the summary stats focusing on Statistics.median : julia> summarize(x, default_summary_stats(median)...; var_names=[:a, :b, :c])\nSummaryStats\n median mad eti_3% eti_97% mcse_median ess_tail ess_median rhat\n a 0.004 0.978 -1.83 1.89 0.020 3567 3336 1.00\n b 10.02 0.995 8.17 11.9 0.023 3841 3787 1.00\n c 19.99 0.979 18.1 21.9 0.020 3892 3829 1.00 source"},{"id":232,"pagetitle":"API","title":"General statistics","ref":"/PosteriorStats/stable/api/#General-statistics","content":" General statistics"},{"id":233,"pagetitle":"API","title":"PosteriorStats.hdi","ref":"/PosteriorStats/stable/api/#PosteriorStats.hdi","content":" PosteriorStats.hdi — Function hdi(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper) Estimate the unimodal highest density interval (HDI) of samples for the probability prob . The HDI is the minimum width Bayesian credible interval (BCI). That is, it is the smallest possible interval containing (100*prob) % of the probability mass. [Hyndman1996] samples is an array of shape (draws[, chains[, params...]]) . If multiple parameters are present, then lower and upper are arrays with the shape (params...,) , computed separately for each marginal. This implementation uses the algorithm of [ChenShao1999] . Note Any default value of prob is arbitrary. The default value of prob=0.94 instead of a more common default like prob=0.95 is chosen to reminder the user of this arbitrariness. Examples Here we calculate the 83% HDI for a normal random variable: julia> x = randn(2_000);\n\njulia> hdi(x; prob=0.83) |> pairs\npairs(::NamedTuple) with 2 entries:\n :lower => -1.38266\n :upper => 1.25982 We can also calculate the HDI for a 3-dimensional array of samples: julia> x = randn(1_000, 1, 1) .+ reshape(0:5:10, 1, 1, :);\n\njulia> hdi(x) |> pairs\npairs(::NamedTuple) with 2 entries:\n :lower => [-1.9674, 3.0326, 8.0326]\n :upper => [1.90028, 6.90028, 11.9003] source"},{"id":234,"pagetitle":"API","title":"PosteriorStats.hdi!","ref":"/PosteriorStats/stable/api/#PosteriorStats.hdi!","content":" PosteriorStats.hdi! — Function hdi!(samples::AbstractArray{<:Real}; prob=0.94) -> (; lower, upper) A version of hdi that sorts samples in-place while computing the HDI. source"},{"id":235,"pagetitle":"API","title":"LOO and WAIC","ref":"/PosteriorStats/stable/api/#LOO-and-WAIC","content":" LOO and WAIC"},{"id":236,"pagetitle":"API","title":"PosteriorStats.AbstractELPDResult","ref":"/PosteriorStats/stable/api/#PosteriorStats.AbstractELPDResult","content":" PosteriorStats.AbstractELPDResult — Type abstract type AbstractELPDResult An abstract type representing the result of an ELPD computation. Every subtype stores estimates of both the expected log predictive density ( elpd ) and the effective number of parameters p , as well as standard errors and pointwise estimates of each, from which other relevant estimates can be computed. Subtypes implement the following functions: elpd_estimates information_criterion source"},{"id":237,"pagetitle":"API","title":"PosteriorStats.PSISLOOResult","ref":"/PosteriorStats/stable/api/#PosteriorStats.PSISLOOResult","content":" PosteriorStats.PSISLOOResult — Type Results of Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO). See also: loo , AbstractELPDResult estimates : Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p) pointwise : Pointwise estimates psis_result : Pareto-smoothed importance sampling (PSIS) results source"},{"id":238,"pagetitle":"API","title":"PosteriorStats.WAICResult","ref":"/PosteriorStats/stable/api/#PosteriorStats.WAICResult","content":" PosteriorStats.WAICResult — Type Results of computing the widely applicable information criterion (WAIC). See also: waic , AbstractELPDResult estimates : Estimates of the expected log pointwise predictive density (ELPD) and effective number of parameters (p) pointwise : Pointwise estimates source"},{"id":239,"pagetitle":"API","title":"PosteriorStats.elpd_estimates","ref":"/PosteriorStats/stable/api/#PosteriorStats.elpd_estimates","content":" PosteriorStats.elpd_estimates — Function elpd_estimates(result::AbstractELPDResult; pointwise=false) -> (; elpd, elpd_mcse, lpd) Return the (E)LPD estimates from the result . source"},{"id":240,"pagetitle":"API","title":"PosteriorStats.information_criterion","ref":"/PosteriorStats/stable/api/#PosteriorStats.information_criterion","content":" PosteriorStats.information_criterion — Function information_criterion(elpd, scale::Symbol) Compute the information criterion for the given scale from the elpd estimate. scale must be one of (:deviance, :log, :negative_log) . See also: loo , waic source information_criterion(result::AbstractELPDResult, scale::Symbol; pointwise=false) Compute information criterion for the given scale from the existing ELPD result . scale must be one of (:deviance, :log, :negative_log) . If pointwise=true , then pointwise estimates are returned. source"},{"id":241,"pagetitle":"API","title":"PosteriorStats.loo","ref":"/PosteriorStats/stable/api/#PosteriorStats.loo","content":" PosteriorStats.loo — Function loo(log_likelihood; reff=nothing, kwargs...) -> PSISLOOResult{<:NamedTuple,<:NamedTuple} Compute the Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO). [Vehtari2017] [LOOFAQ] log_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]) . Keywords reff::Union{Real,AbstractArray{<:Real}} : The relative effective sample size(s) of the likelihood values. If an array, it must have the same data dimensions as the corresponding log-likelihood variable. If not provided, then this is estimated using MCMCDiagnosticTools.ess . kwargs : Remaining keywords are forwarded to [ PSIS.psis ]. See also: PSISLOOResult , waic Examples Manually compute $R_\\mathrm{eff}$ and calculate PSIS-LOO of a model: julia> using ArviZExampleData, MCMCDiagnosticTools\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> reff = ess(log_like; kind=:basic, split_chains=1, relative=true);\n\njulia> loo(log_like; reff)\nPSISLOOResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.34\n\nand PSISResult with 500 draws, 4 chains, and 8 parameters\nPareto shape (k) diagnostic values:\n Count Min. ESS\n (-Inf, 0.5] good 7 (87.5%) 151\n (0.5, 0.7] okay 1 (12.5%) 446 source"},{"id":242,"pagetitle":"API","title":"PosteriorStats.waic","ref":"/PosteriorStats/stable/api/#PosteriorStats.waic","content":" PosteriorStats.waic — Function waic(log_likelihood::AbstractArray) -> WAICResult{<:NamedTuple,<:NamedTuple} Compute the widely applicable information criterion (WAIC). [Watanabe2010] [Vehtari2017] [LOOFAQ] log_likelihood must be an array of log-likelihood values with shape (chains, draws[, params...]) . See also: WAICResult , loo Examples Calculate WAIC of a model: julia> using ArviZExampleData\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> waic(log_like)\nWAICResult with estimates\n elpd elpd_mcse p p_mcse\n -31 1.4 0.9 0.33 source"},{"id":243,"pagetitle":"API","title":"Model comparison","ref":"/PosteriorStats/stable/api/#Model-comparison","content":" Model comparison"},{"id":244,"pagetitle":"API","title":"PosteriorStats.ModelComparisonResult","ref":"/PosteriorStats/stable/api/#PosteriorStats.ModelComparisonResult","content":" PosteriorStats.ModelComparisonResult — Type ModelComparisonResult Result of model comparison using ELPD. This struct implements the Tables and TableTraits interfaces. Each field returns a collection of the corresponding entry for each model: name : Names of the models, if provided. rank : Ranks of the models (ordered by decreasing ELPD) elpd_diff : ELPD of a model subtracted from the largest ELPD of any model elpd_diff_mcse : Monte Carlo standard error of the ELPD difference weight : Model weights computed with weights_method elpd_result : AbstactELPDResult s for each model, which can be used to access useful stats like ELPD estimates, pointwise estimates, and Pareto shape values for PSIS-LOO weights_method : Method used to compute model weights with model_weights source"},{"id":245,"pagetitle":"API","title":"PosteriorStats.compare","ref":"/PosteriorStats/stable/api/#PosteriorStats.compare","content":" PosteriorStats.compare — Function compare(models; kwargs...) -> ModelComparisonResult Compare models based on their expected log pointwise predictive density (ELPD). The ELPD is estimated either by Pareto smoothed importance sampling leave-one-out cross-validation (LOO) or using the widely applicable information criterion (WAIC). We recommend loo. Read more theory here - in a paper by some of the leading authorities on model comparison dx.doi.org/10.1111/1467-9868.00353 Arguments models : a Tuple , NamedTuple , or AbstractVector whose values are either AbstractELPDResult entries or any argument to elpd_method . Keywords weights_method::AbstractModelWeightsMethod=Stacking() : the method to be used to weight the models. See model_weights for details elpd_method=loo : a method that computes an AbstractELPDResult from an argument in models . sort::Bool=true : Whether to sort models by decreasing ELPD. Returns ModelComparisonResult : A container for the model comparison results. The fields contain a similar collection to models . Examples Compare the centered and non centered models of the eight school problem using the defaults: loo and Stacking weights. A custom myloo method formates the inputs as expected by loo . julia> using ArviZExampleData\n\njulia> models = (\n centered=load_example_data(\"centered_eight\"),\n non_centered=load_example_data(\"non_centered_eight\"),\n );\n\njulia> function myloo(idata)\n log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1))\n return loo(log_like)\n end;\n\njulia> mc = compare(models; elpd_method=myloo)\n┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.\n└ @ PSIS ~/.julia/packages/PSIS/...\nModelComparisonResult with Stacking weights\n rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯\n non_centered 1 -31 1.4 0 0.0 1.0 0.9 ⋯\n centered 2 -31 1.4 0.06 0.067 0.0 0.9 ⋯\n 1 column omitted\njulia> mc.weight |> pairs\npairs(::NamedTuple) with 2 entries:\n :non_centered => 1.0\n :centered => 5.34175e-19 Compare the same models from pre-computed PSIS-LOO results and computing BootstrappedPseudoBMA weights: julia> elpd_results = mc.elpd_result;\n\njulia> compare(elpd_results; weights_method=BootstrappedPseudoBMA())\nModelComparisonResult with BootstrappedPseudoBMA weights\n rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯\n non_centered 1 -31 1.4 0 0.0 0.52 0.9 ⋯\n centered 2 -31 1.4 0.06 0.067 0.48 0.9 ⋯\n 1 column omitted source"},{"id":246,"pagetitle":"API","title":"PosteriorStats.model_weights","ref":"/PosteriorStats/stable/api/#PosteriorStats.model_weights","content":" PosteriorStats.model_weights — Function model_weights(elpd_results; method=Stacking())\nmodel_weights(method::AbstractModelWeightsMethod, elpd_results) Compute weights for each model in elpd_results using method . elpd_results is a Tuple , NamedTuple , or AbstractVector with AbstractELPDResult entries. The weights are returned in the same type of collection. Stacking is the recommended approach, as it performs well even when the true data generating process is not included among the candidate models. See [YaoVehtari2018] for details. See also: AbstractModelWeightsMethod , compare Examples Compute Stacking weights for two models: julia> using ArviZExampleData\n\njulia> models = (\n centered=load_example_data(\"centered_eight\"),\n non_centered=load_example_data(\"non_centered_eight\"),\n );\n\njulia> elpd_results = map(models) do idata\n log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1))\n return loo(log_like)\n end;\n┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.\n└ @ PSIS ~/.julia/packages/PSIS/...\n\njulia> model_weights(elpd_results; method=Stacking()) |> pairs\npairs(::NamedTuple) with 2 entries:\n :centered => 5.34175e-19\n :non_centered => 1.0 Now we compute BootstrappedPseudoBMA weights for the same models: julia> model_weights(elpd_results; method=BootstrappedPseudoBMA()) |> pairs\npairs(::NamedTuple) with 2 entries:\n :centered => 0.483723\n :non_centered => 0.516277 source The following model weighting methods are available"},{"id":247,"pagetitle":"API","title":"PosteriorStats.AbstractModelWeightsMethod","ref":"/PosteriorStats/stable/api/#PosteriorStats.AbstractModelWeightsMethod","content":" PosteriorStats.AbstractModelWeightsMethod — Type abstract type AbstractModelWeightsMethod An abstract type representing methods for computing model weights. Subtypes implement model_weights (method, elpd_results) . source"},{"id":248,"pagetitle":"API","title":"PosteriorStats.BootstrappedPseudoBMA","ref":"/PosteriorStats/stable/api/#PosteriorStats.BootstrappedPseudoBMA","content":" PosteriorStats.BootstrappedPseudoBMA — Type struct BootstrappedPseudoBMA{R<:Random.AbstractRNG, T<:Real} <: AbstractModelWeightsMethod Model weighting method using pseudo Bayesian Model Averaging using Akaike-type weighting with the Bayesian bootstrap (pseudo-BMA+) [YaoVehtari2018] . The Bayesian bootstrap stabilizes the model weights. BootstrappedPseudoBMA(; rng=Random.default_rng(), samples=1_000, alpha=1)\nBootstrappedPseudoBMA(rng, samples, alpha) Construct the method. rng::Random.AbstractRNG : The random number generator to use for the Bayesian bootstrap samples::Int64 : The number of samples to draw for bootstrapping alpha::Real : The shape parameter in the Dirichlet distribution used for the Bayesian bootstrap. The default (1) corresponds to a uniform distribution on the simplex. See also: Stacking source"},{"id":249,"pagetitle":"API","title":"PosteriorStats.PseudoBMA","ref":"/PosteriorStats/stable/api/#PosteriorStats.PseudoBMA","content":" PosteriorStats.PseudoBMA — Type struct PseudoBMA <: AbstractModelWeightsMethod Model weighting method using pseudo Bayesian Model Averaging (pseudo-BMA) and Akaike-type weighting. PseudoBMA(; regularize=false)\nPseudoBMA(regularize) Construct the method with optional regularization of the weights using the standard error of the ELPD estimate. Note This approach is not recommended, as it produces unstable weight estimates. It is recommended to instead use BootstrappedPseudoBMA to stabilize the weights or Stacking . For details, see [YaoVehtari2018] . See also: Stacking source"},{"id":250,"pagetitle":"API","title":"PosteriorStats.Stacking","ref":"/PosteriorStats/stable/api/#PosteriorStats.Stacking","content":" PosteriorStats.Stacking — Type struct Stacking{O<:Optim.AbstractOptimizer} <: AbstractModelWeightsMethod Model weighting using stacking of predictive distributions [YaoVehtari2018] . Stacking(; optimizer=Optim.LBFGS(), options=Optim.Options()\nStacking(optimizer[, options]) Construct the method, optionally customizing the optimization. optimizer::Optim.AbstractOptimizer : The optimizer to use for the optimization of the weights. The optimizer must support projected gradient optimization via a manifold field. options::Optim.Options : The Optim options to use for the optimization of the weights. See also: BootstrappedPseudoBMA source"},{"id":251,"pagetitle":"API","title":"Predictive checks","ref":"/PosteriorStats/stable/api/#Predictive-checks","content":" Predictive checks"},{"id":252,"pagetitle":"API","title":"PosteriorStats.loo_pit","ref":"/PosteriorStats/stable/api/#PosteriorStats.loo_pit","content":" PosteriorStats.loo_pit — Function loo_pit(y, y_pred, log_weights; kwargs...) -> Union{Real,AbstractArray} Compute leave-one-out probability integral transform (LOO-PIT) checks. Arguments y : array of observations with shape (params...,) y_pred : array of posterior predictive samples with shape (draws, chains, params...) . log_weights : array of normalized log LOO importance weights with shape (draws, chains, params...) . Keywords is_discrete : If not provided, then it is set to true iff elements of y and y_pred are all integer-valued. If true , then data are smoothed using smooth_data to make them non-discrete before estimating LOO-PIT values. kwargs : Remaining keywords are forwarded to smooth_data if data is discrete. Returns pitvals : LOO-PIT values with same size as y . If y is a scalar, then pitvals is a scalar. LOO-PIT is a marginal posterior predictive check. If $y_{-i}$ is the array $y$ of observations with the $i$ th observation left out, and $y_i^*$ is a posterior prediction of the $i$ th observation, then the LOO-PIT value for the $i$ th observation is defined as \\[P(y_i^* \\le y_i \\mid y_{-i}) = \\int_{-\\infty}^{y_i} p(y_i^* \\mid y_{-i}) \\mathrm{d} y_i^*\\] The LOO posterior predictions and the corresponding observations should have similar distributions, so if conditional predictive distributions are well-calibrated, then all LOO-PIT values should be approximately uniformly distributed on $[0, 1]$ . [Gabry2019] Examples Calculate LOO-PIT values using as test quantity the observed values themselves. julia> using ArviZExampleData\n\njulia> idata = load_example_data(\"centered_eight\");\n\njulia> y = idata.observed_data.obs;\n\njulia> y_pred = PermutedDimsArray(idata.posterior_predictive.obs, (:draw, :chain, :school));\n\njulia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school));\n\njulia> log_weights = loo(log_like).psis_result.log_weights;\n\njulia> loo_pit(y, y_pred, log_weights)\n8-element DimArray{Float64,1} with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.943511\n \"Deerfield\" 0.63797\n \"Phillips Andover\" 0.316697\n \"Phillips Exeter\" 0.582252\n \"Hotchkiss\" 0.295321\n \"Lawrenceville\" 0.403318\n \"St. Paul's\" 0.902508\n \"Mt. Hermon\" 0.655275 Calculate LOO-PIT values using as test quantity the square of the difference between each observation and mu . julia> using Statistics\n\njulia> mu = idata.posterior.mu;\n\njulia> T = y .- median(mu);\n\njulia> T_pred = y_pred .- mu;\n\njulia> loo_pit(T .^ 2, T_pred .^ 2, log_weights)\n8-element DimArray{Float64,1} with dimensions:\n Dim{:school} Categorical{String} String[Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered\n \"Choate\" 0.873577\n \"Deerfield\" 0.243686\n \"Phillips Andover\" 0.357563\n \"Phillips Exeter\" 0.149908\n \"Hotchkiss\" 0.435094\n \"Lawrenceville\" 0.220627\n \"St. Paul's\" 0.775086\n \"Mt. Hermon\" 0.296706 source"},{"id":253,"pagetitle":"API","title":"PosteriorStats.r2_score","ref":"/PosteriorStats/stable/api/#PosteriorStats.r2_score","content":" PosteriorStats.r2_score — Function r2_score(y_true::AbstractVector, y_pred::AbstractArray) -> (; r2, r2_std) $R²$ for linear Bayesian regression models. [GelmanGoodrich2019] Arguments y_true : Observed data of length noutputs y_pred : Predicted data with size (ndraws[, nchains], noutputs) Examples julia> using ArviZExampleData\n\njulia> idata = load_example_data(\"regression1d\");\n\njulia> y_true = idata.observed_data.y;\n\njulia> y_pred = PermutedDimsArray(idata.posterior_predictive.y, (:draw, :chain, :y_dim_0));\n\njulia> r2_score(y_true, y_pred) |> pairs\npairs(::NamedTuple) with 2 entries:\n :r2 => 0.683197\n :r2_std => 0.0368838 source"},{"id":254,"pagetitle":"API","title":"Utilities","ref":"/PosteriorStats/stable/api/#Utilities","content":" Utilities"},{"id":255,"pagetitle":"API","title":"PosteriorStats.smooth_data","ref":"/PosteriorStats/stable/api/#PosteriorStats.smooth_data","content":" PosteriorStats.smooth_data — Function smooth_data(y; dims=:, interp_method=CubicSpline, offset_frac=0.01) Smooth y along dims using interp_method . interp_method is a 2-argument callabale that takes the arguments y and x and returns a DataInterpolations.jl interpolation method, defaulting to a cubic spline interpolator. offset_frac is the fraction of the length of y to use as an offset when interpolating. source Hyndman1996 Rob J. Hyndman (1996) Computing and Graphing Highest Density Regions, Amer. Stat., 50(2): 120-6. DOI: 10.1080/00031305.1996.10474359 jstor . ChenShao1999 Ming-Hui Chen & Qi-Man Shao (1999) Monte Carlo Estimation of Bayesian Credible and HPD Intervals, J Comput. Graph. Stat., 8:1, 69-92. DOI: 10.1080/10618600.1999.10474802 jstor . Vehtari2017 Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544 LOOFAQ Aki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html Watanabe2010 Watanabe, S. Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory. 11(116):3571−3594, 2010. https://jmlr.csail.mit.edu/papers/v11/watanabe10a.html Vehtari2017 Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017). doi: 10.1007/s11222-016-9696-4 arXiv: 1507.04544 LOOFAQ Aki Vehtari. Cross-validation FAQ. https://mc-stan.org/loo/articles/online-only/faq.html YaoVehtari2018 Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030 YaoVehtari2018 Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030 YaoVehtari2018 Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030 YaoVehtari2018 Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman. Using Stacking to Average Bayesian Predictive Distributions. 2018. Bayesian Analysis. 13, 3, 917–1007. doi: 10.1214/17-BA1091 arXiv: 1704.02030 Gabry2019 Gabry, J., Simpson, D., Vehtari, A., Betancourt, M. & Gelman, A. Visualization in Bayesian Workflow. J. R. Stat. Soc. Ser. A Stat. Soc. 182, 389–402 (2019). doi: 10.1111/rssa.12378 arXiv: 1709.01449 GelmanGoodrich2019 Andrew Gelman, Ben Goodrich, Jonah Gabry & Aki Vehtari (2019) R-squared for Bayesian Regression Models, The American Statistician, 73:3, 307-9, DOI: 10.1080/00031305.2018.1549100 ."},{"id":258,"pagetitle":"Home","title":"PSIS","ref":"/PSIS/stable/#PSIS","content":" PSIS PSIS.jl implements the Pareto smoothed importance sampling (PSIS) algorithm from [VehtariSimpson2021] . Given a set of importance weights used in some estimator, PSIS both improves the reliability of the estimates by smoothing the importance weights and acts as a diagnostic of the reliability of the estimates. See psis for details."},{"id":259,"pagetitle":"Home","title":"Example","ref":"/PSIS/stable/#Example","content":" Example In this example, we use PSIS to smooth log importance ratios for importance sampling 30 isotropic Student $t$ -distributed parameters using standard normal distributions as proposals. using PSIS, Distributions\nproposal = Normal()\ntarget = TDist(7)\nndraws, nchains, nparams = (1_000, 1, 30)\nx = rand(proposal, ndraws, nchains, nparams)\nlog_ratios = logpdf.(target, x) .- logpdf.(proposal, x)\nresult = psis(log_ratios) ┌ Warning: 8 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable.\n└ @ PSIS ~/work/PSIS.jl/PSIS.jl/src/core.jl:323\n┌ Warning: 1 parameters had Pareto shape values k > 1. Corresponding importance sampling estimates are likely to be unstable and are unlikely to converge with additional samples.\n└ @ PSIS ~/work/PSIS.jl/PSIS.jl/src/core.jl:326 PSISResult with 1000 draws, 1 chains, and 30 parameters\nPareto shape (k) diagnostic values:\n Count Min. ESS \n (-Inf, 0.5] good 7 (23.3%) 959\n (0.5, 0.7] okay 14 (46.7%) 927\n (0.7, 1] bad 8 (26.7%) ——\n (1, Inf) very bad 1 (3.3%) —— As indicated by the warnings, this is a poor choice of a proposal distribution, and estimates are unlikely to converge (see PSISResult for an explanation of the shape thresholds). When running PSIS with many parameters, it is useful to plot the Pareto shape values to diagnose convergence. See Plotting PSIS results for examples. VehtariSimpson2021 Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO]"},{"id":262,"pagetitle":"API","title":"API","ref":"/PSIS/stable/api/#API","content":" API"},{"id":263,"pagetitle":"API","title":"Core functionality","ref":"/PSIS/stable/api/#Core-functionality","content":" Core functionality"},{"id":264,"pagetitle":"API","title":"PSIS.PSISResult","ref":"/PSIS/stable/api/#PSIS.PSISResult","content":" PSIS.PSISResult — Type PSISResult Result of Pareto-smoothed importance sampling (PSIS) using psis . Properties log_weights : un-normalized Pareto-smoothed log weights weights : normalized Pareto-smoothed weights (allocates a copy) pareto_shape : Pareto $k=ξ$ shape parameter nparams : number of parameters in log_weights ndraws : number of draws in log_weights nchains : number of chains in log_weights reff : the ratio of the effective sample size of the unsmoothed importance ratios and the actual sample size. ess : estimated effective sample size of estimate of mean using smoothed importance samples (see ess_is ) tail_length : length of the upper tail of log_weights that was smoothed tail_dist : the generalized Pareto distribution that was fit to the tail of log_weights . Note that the tail weights are scaled to have a maximum of 1, so tail_dist * exp(maximum(log_ratios)) is the corresponding fit directly to the tail of log_ratios . normalized::Bool :indicates whether log_weights are log-normalized along the sample dimensions. Diagnostic The pareto_shape parameter $k=ξ$ of the generalized Pareto distribution tail_dist can be used to diagnose reliability and convergence of estimates using the importance weights [VehtariSimpson2021] . if $k < \\frac{1}{3}$ , importance sampling is stable, and importance sampling (IS) and PSIS both are reliable. if $k ≤ \\frac{1}{2}$ , then the importance ratio distributon has finite variance, and the central limit theorem holds. As $k$ approaches the upper bound, IS becomes less reliable, while PSIS still works well but with a higher RMSE. if $\\frac{1}{2} < k ≤ 0.7$ , then the variance is infinite, and IS can behave quite poorly. However, PSIS works well in this regime. if $0.7 < k ≤ 1$ , then it quickly becomes impractical to collect enough importance weights to reliably compute estimates, and importance sampling is not recommended. if $k > 1$ , then neither the variance nor the mean of the raw importance ratios exists. The convergence rate is close to zero, and bias can be large with practical sample sizes. See PSISPlots.paretoshapeplot for a diagnostic plot. source"},{"id":265,"pagetitle":"API","title":"PSIS.psis","ref":"/PSIS/stable/api/#PSIS.psis","content":" PSIS.psis — Function psis(log_ratios, reff = 1.0; kwargs...) -> PSISResult\npsis!(log_ratios, reff = 1.0; kwargs...) -> PSISResult Compute Pareto smoothed importance sampling (PSIS) log weights [VehtariSimpson2021] . While psis computes smoothed log weights out-of-place, psis! smooths them in-place. Arguments log_ratios : an array of logarithms of importance ratios, with size (draws, [chains, [parameters...]]) , where chains>1 would be used when chains are generated using Markov chain Monte Carlo. reff::Union{Real,AbstractArray} : the ratio(s) of effective sample size of log_ratios and the actual sample size reff = ess/(draws * chains) , used to account for autocorrelation, e.g. due to Markov chain Monte Carlo. If an array, it must have the size (parameters...,) to match log_ratios . Keywords warn=true : If true , warning messages are delivered normalize=true : If true , the log-weights will be log-normalized so that exp.(log_weights) sums to 1 along the sample dimensions. Returns result : a PSISResult object containing the results of the Pareto-smoothing. A warning is raised if the Pareto shape parameter $k ≥ 0.7$ . See PSISResult for details and PSISPlots.paretoshapeplot for a diagnostic plot. source"},{"id":266,"pagetitle":"API","title":"PSIS.ess_is","ref":"/PSIS/stable/api/#PSIS.ess_is","content":" PSIS.ess_is — Function ess_is(weights; reff=1) Estimate effective sample size (ESS) for importance sampling over the sample dimensions. Given normalized weights $w_{1:n}$ , the ESS is estimated using the L2-norm of the weights: \\[\\mathrm{ESS}(w_{1:n}) = \\frac{r_{\\mathrm{eff}}}{\\sum_{i=1}^n w_i^2}\\] where $r_{\\mathrm{eff}}$ is the relative efficiency of the log_weights . ess_is(result::PSISResult; bad_shape_nan=true) Estimate ESS for Pareto-smoothed importance sampling. Note ESS estimates for Pareto shape values $k > 0.7$ , which are unreliable and misleadingly high, are set to NaN . To avoid this, set bad_shape_nan=false . source"},{"id":267,"pagetitle":"API","title":"Plotting","ref":"/PSIS/stable/api/#Plotting","content":" Plotting"},{"id":268,"pagetitle":"API","title":"PSIS.PSISPlots","ref":"/PSIS/stable/api/#PSIS.PSISPlots","content":" PSIS.PSISPlots — Module A module defining paretoshapeplot for plotting Pareto shape values with Plots.jl source"},{"id":269,"pagetitle":"API","title":"PSIS.PSISPlots.paretoshapeplot","ref":"/PSIS/stable/api/#PSIS.PSISPlots.paretoshapeplot","content":" PSIS.PSISPlots.paretoshapeplot — Function paretoshapeplot(values; showlines=false, ...)\nparetoshapeplot!(values; showlines=false, kwargs...) Plot shape parameters of fitted Pareto tail distributions for diagnosing convergence. values may be either a vector of Pareto shape parameters or a PSIS.PSISResult . If showlines==true , horizontal lines indicating relevant Pareto shape thresholds are drawn. See PSIS.PSISResult for an explanation of the thresholds. All remaining kwargs are forwarded to the plotting function. See psis , PSISResult . Examples using PSIS, Distributions, Plots\nproposal = Normal()\ntarget = TDist(7)\nx = rand(proposal, 1_000, 100)\nlog_ratios = logpdf.(target, x) .- logpdf.(proposal, x)\nresult = psis(log_ratios)\nparetoshapeplot(result) We can also plot the Pareto shape parameters directly: paretoshapeplot(result.pareto_shape) We can also use plot directly: plot(result.pareto_shape; showlines=true) source VehtariSimpson2021 Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO] VehtariSimpson2021 Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J. (2021). Pareto smoothed importance sampling. arXiv:1507.02646v7 [stat.CO]"},{"id":272,"pagetitle":"Internal","title":"Internal","ref":"/PSIS/stable/internal/#Internal","content":" Internal"},{"id":273,"pagetitle":"Internal","title":"PSIS.GeneralizedPareto","ref":"/PSIS/stable/internal/#PSIS.GeneralizedPareto","content":" PSIS.GeneralizedPareto — Type GeneralizedPareto{T<:Real} The generalized Pareto distribution. This is equivalent to Distributions.GeneralizedPareto and can be converted to one with convert(Distributions.GeneralizedPareto, d) . Constructor GeneralizedPareto(μ, σ, k) Construct the generalized Pareto distribution (GPD) with location parameter $μ$ , scale parameter $σ$ and shape parameter $k$ . Note The shape parameter $k$ is equivalent to the commonly used shape parameter $ξ$ . This is the same parameterization used by [VehtariSimpson2021] and is related to that used by [ZhangStephens2009] as $k \\mapsto -k$ . source"},{"id":274,"pagetitle":"Internal","title":"PSIS.fit_gpd","ref":"/PSIS/stable/internal/#PSIS.fit_gpd-Tuple{AbstractArray}","content":" PSIS.fit_gpd — Method fit_gpd(x; μ=0, kwargs...) Fit a GeneralizedPareto with location μ to the data x . The fit is performed using the Empirical Bayes method of [ZhangStephens2009] . Keywords prior_adjusted::Bool=true , If true , a weakly informative Normal prior centered on $\\frac{1}{2}$ is used for the shape $k$ . sorted::Bool=issorted(x) : If true , x is assumed to be sorted. If false , a sorted copy of x is made. min_points::Int=30 : The minimum number of quadrature points to use when estimating the posterior mean of $\\theta = \\frac{\\xi}{\\sigma}$ . source ZhangStephens2009 Jin Zhang & Michael A. Stephens (2009) A New and Efficient Estimation Method for the Generalized Pareto Distribution, Technometrics, 51:3, 316-325, DOI: 10.1198/tech.2009.08017"},{"id":277,"pagetitle":"Plotting","title":"Plotting PSIS results","ref":"/PSIS/stable/plotting/#Plotting-PSIS-results","content":" Plotting PSIS results PSIS.jl includes plotting recipes for PSISResult using any Plots.jl backend, as well as the utility plotting function PSISPlots.paretoshapeplot . We demonstrate this with a simple example. using PSIS, Distributions\nproposal = Normal()\ntarget = TDist(7)\nndraws, nchains, nparams = (1_000, 1, 20)\nx = rand(proposal, ndraws, nchains, nparams)\nlog_ratios = logpdf.(target, x) .- logpdf.(proposal, x)\nresult = psis(log_ratios) PSISResult with 1000 draws, 1 chains, and 20 parameters\nPareto shape (k) diagnostic values:\n Count Min. ESS \n (-Inf, 0.5] good 4 (20.0%) 959\n (0.5, 0.7] okay 10 (50.0%) 927\n (0.7, 1] bad 6 (30.0%) ——"},{"id":278,"pagetitle":"Plotting","title":"Plots.jl","ref":"/PSIS/stable/plotting/#Plots.jl","content":" Plots.jl PSISResult objects can be plotted directly: using Plots\nplot(result; showlines=true, marker=:+, legend=false, linewidth=2) This is equivalent to calling PSISPlots.paretoshapeplot(result; kwargs...) ."},{"id":281,"pagetitle":"Home","title":"MCMCDiagnosticTools","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools","content":" MCMCDiagnosticTools MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo."},{"id":282,"pagetitle":"Home","title":"Background","ref":"/MCMCDiagnosticTools/stable/#Background","content":" Background Some methods were originally part of Mamba.jl and then MCMCChains.jl . This package is a joint collaboration between the Turing and ArviZ projects."},{"id":283,"pagetitle":"Home","title":"Effective sample size and $\\widehat{R}$","ref":"/MCMCDiagnosticTools/stable/#Effective-sample-size-and-\\\\widehat{R}","content":" Effective sample size and $\\widehat{R}$"},{"id":284,"pagetitle":"Home","title":"MCMCDiagnosticTools.ess","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.ess","content":" MCMCDiagnosticTools.ess — Function ess(\n samples::AbstractArray{<:Union{Missing,Real}};\n kind=:bulk,\n relative::Bool=false,\n autocov_method=AutocovMethod(),\n split_chains::Int=2,\n maxlag::Int=250,\n kwargs...\n) Estimate the effective sample size (ESS) of the samples of shape (draws, [chains[, parameters...]]) with the autocov_method . Optionally, the kind of ESS estimate to be computed can be specified (see below). Some kind s accept additional kwargs . If relative is true , the relative ESS is returned, i.e. ess / (draws * chains) . split_chains indicates the number of chains each chain is split into. When split_chains > 1 , then the diagnostics check for within-chain convergence. When d = mod(draws, split_chains) > 0 , i.e. the chains cannot be evenly split, then 1 draw is discarded after each of the first d splits within each chain. There must be at least 3 draws in each chain after splitting. maxlag indicates the maximum lag for which autocovariance is computed and must be greater than 0. For a given estimand, it is recommended that the ESS is at least 100 * chains and that $\\widehat{R} < 1.01$ . [VehtariGelman2021] See also: AutocovMethod , FFTAutocovMethod , BDAAutocovMethod , rhat , ess_rhat , mcse Kinds of ESS estimates If kind isa a Symbol , it may take one of the following values: :bulk : basic ESS computed on rank-normalized draws. This kind diagnoses poor convergence in the bulk of the distribution due to trends or different locations of the chains. :tail : minimum of the quantile-ESS for the symmetric quantiles where tail_prob=0.1 is the probability in the tails. This kind diagnoses poor convergence in the tails of the distribution. If this kind is chosen, kwargs may contain a tail_prob keyword. :basic : basic ESS, equivalent to specifying kind=Statistics.mean . Note While Bulk-ESS is conceptually related to basic ESS, it is well-defined even if the chains do not have finite variance. [VehtariGelman2021] For each parameter, rank-normalization proceeds by first ranking the inputs using \"tied ranking\" and then transforming the ranks to normal quantiles so that the result is standard normally distributed. This transform is monotonic. Otherwise, kind specifies one of the following estimators, whose ESS is to be estimated: Statistics.mean Statistics.median Statistics.std StatsBase.mad Base.Fix2(Statistics.quantile, p::Real) source"},{"id":285,"pagetitle":"Home","title":"MCMCDiagnosticTools.rhat","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.rhat","content":" MCMCDiagnosticTools.rhat — Function rhat(samples::AbstractArray{Union{Real,Missing}}; kind::Symbol=:rank, split_chains=2) Compute the $\\widehat{R}$ diagnostics for each parameter in samples of shape (draws, [chains[, parameters...]]) . [VehtariGelman2021] kind indicates the kind of $\\widehat{R}$ to compute (see below). split_chains indicates the number of chains each chain is split into. When split_chains > 1 , then the diagnostics check for within-chain convergence. When d = mod(draws, split_chains) > 0 , i.e. the chains cannot be evenly split, then 1 draw is discarded after each of the first d splits within each chain. See also ess , ess_rhat , rstar Kinds of $\\widehat{R}$ The following kind s are supported: :rank : maximum of $\\widehat{R}$ with kind=:bulk and kind=:tail . :bulk : basic $\\widehat{R}$ computed on rank-normalized draws. This kind diagnoses poor convergence in the bulk of the distribution due to trends or different locations of the chains. :tail : $\\widehat{R}$ computed on draws folded around the median and then rank-normalized. This kind diagnoses poor convergence in the tails of the distribution due to different scales of the chains. :basic : Classic $\\widehat{R}$ . source"},{"id":286,"pagetitle":"Home","title":"MCMCDiagnosticTools.ess_rhat","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.ess_rhat","content":" MCMCDiagnosticTools.ess_rhat — Function ess_rhat(\n samples::AbstractArray{<:Union{Missing,Real}};\n kind::Symbol=:rank,\n kwargs...,\n) -> NamedTuple{(:ess, :rhat)} Estimate the effective sample size and $\\widehat{R}$ of the samples of shape (draws, [chains[, parameters...]]) . When both ESS and $\\widehat{R}$ are needed, this method is often more efficient than calling ess and rhat separately. See rhat for a description of supported kind s and ess for a description of kwargs . source The following autocov_method s are supported:"},{"id":287,"pagetitle":"Home","title":"MCMCDiagnosticTools.AutocovMethod","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.AutocovMethod","content":" MCMCDiagnosticTools.AutocovMethod — Type AutocovMethod <: AbstractAutocovMethod The AutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains. It is is based on the discussion by [VehtariGelman2021] and uses the biased estimator of the autocovariance, as discussed by [Geyer1992] . source"},{"id":288,"pagetitle":"Home","title":"MCMCDiagnosticTools.FFTAutocovMethod","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.FFTAutocovMethod","content":" MCMCDiagnosticTools.FFTAutocovMethod — Type FFTAutocovMethod <: AbstractAutocovMethod The FFTAutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains. The algorithm is the same as the one of AutocovMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation. Info To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl . source"},{"id":289,"pagetitle":"Home","title":"MCMCDiagnosticTools.BDAAutocovMethod","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.BDAAutocovMethod","content":" MCMCDiagnosticTools.BDAAutocovMethod — Type BDAAutocovMethod <: AbstractAutocovMethod The BDAAutocovMethod uses a standard algorithm for estimating the mean autocovariance of MCMC chains. It is is based on the discussion by [VehtariGelman2021] . and uses the variogram estimator of the autocorrelation function discussed by [BDA3] . source"},{"id":290,"pagetitle":"Home","title":"Monte Carlo standard error","ref":"/MCMCDiagnosticTools/stable/#Monte-Carlo-standard-error","content":" Monte Carlo standard error"},{"id":291,"pagetitle":"Home","title":"MCMCDiagnosticTools.mcse","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.mcse","content":" MCMCDiagnosticTools.mcse — Function mcse(samples::AbstractArray{<:Union{Missing,Real}}; kind=Statistics.mean, kwargs...) Estimate the Monte Carlo standard errors (MCSE) of the estimator kind applied to samples of shape (draws, [chains[, parameters...]]) . See also: ess Kinds of MCSE estimates The estimator whose MCSE should be estimated is specified with kind . kind must accept a vector of the same eltype as samples and return a real estimate. For the following estimators, the effective sample size ess and an estimate of the asymptotic variance are used to compute the MCSE, and kwargs are forwarded to ess : Statistics.mean Statistics.median Statistics.std Base.Fix2(Statistics.quantile, p::Real) For other estimators, the subsampling bootstrap method (SBM) [FlegalJones2011] [Flegal2012] is used as a fallback, and the only accepted kwargs are batch_size , which indicates the size of the overlapping batches used to estimate the MCSE, defaulting to floor(Int, sqrt(draws * chains)) . Note that SBM tends to underestimate the MCSE, especially for highly autocorrelated chains. One should verify that autocorrelation is low by checking the bulk- and tail-ESS values. source"},{"id":292,"pagetitle":"Home","title":"R⋆ diagnostic","ref":"/MCMCDiagnosticTools/stable/#R-diagnostic","content":" R⋆ diagnostic"},{"id":293,"pagetitle":"Home","title":"MCMCDiagnosticTools.rstar","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.rstar","content":" MCMCDiagnosticTools.rstar — Function rstar(\n rng::Random.AbstractRNG=Random.default_rng(),\n classifier,\n samples,\n chain_indices::AbstractVector{Int};\n subset::Real=0.7,\n split_chains::Int=2,\n verbosity::Int=0,\n) Compute the $R^*$ convergence statistic of the table samples with the classifier . samples must be either an AbstractMatrix , an AbstractVector , or a table (i.e. implements the Tables.jl interface) whose rows are draws and whose columns are parameters. chain_indices indicates the chain ids of each row of samples . This method supports ragged chains, i.e. chains of nonequal lengths. source rstar(\n rng::Random.AbstractRNG=Random.default_rng(),\n classifier,\n samples::AbstractArray{<:Real};\n subset::Real=0.7,\n split_chains::Int=2,\n verbosity::Int=0,\n) Compute the $R^*$ convergence statistic of the samples with the classifier . samples is an array of draws with the shape (draws, [chains[, parameters...]]) .` This implementation is an adaption of algorithms 1 and 2 described by Lambert and Vehtari. The classifier has to be a supervised classifier of the MLJ framework (see the MLJ documentation for a list of supported models). It is trained with a subset of the samples from each chain. Each chain is split into split_chains separate chains to additionally check for within-chain convergence. The training of the classifier can be inspected by adjusting the verbosity level. If the classifier is deterministic, i.e., if it predicts a class, the value of the $R^*$ statistic is returned (algorithm 1). If the classifier is probabilistic, i.e., if it outputs probabilities of classes, the scaled Poisson-binomial distribution of the $R^*$ statistic is returned (algorithm 2). Note The correctness of the statistic depends on the convergence of the classifier used internally in the statistic. Examples julia> using MLJBase, MLJIteration, EvoTrees, Statistics, StatisticalMeasures\n\njulia> samples = fill(4.0, 100, 3, 2); One can compute the distribution of the $R^*$ statistic (algorithm 2) with a probabilistic classifier. For instance, we can use a gradient-boosted trees model with nrounds = 100 sequentially stacked trees and learning rate eta = 0.05 : julia> model = EvoTreeClassifier(; nrounds=100, eta=0.05);\n\njulia> distribution = rstar(model, samples);\n\njulia> round(mean(distribution); digits=2)\n1.0f0 Note, however, that it is recommended to determine nrounds based on early-stopping. With the MLJ framework, this can be achieved in the following way (see the MLJ documentation for additional explanations): julia> model = IteratedModel(;\n model=EvoTreeClassifier(; eta=0.05),\n iteration_parameter=:nrounds,\n resampling=Holdout(),\n measures=log_loss,\n controls=[Step(5), Patience(2), NumberLimit(100)],\n retrain=true,\n );\n\njulia> distribution = rstar(model, samples);\n\njulia> round(mean(distribution); digits=2)\n1.0f0 For deterministic classifiers, a single $R^*$ statistic (algorithm 1) is returned. Deterministic classifiers can also be derived from probabilistic classifiers by e.g. predicting the mode. In MLJ this corresponds to a pipeline of models. julia> evotree_deterministic = Pipeline(model; operation=predict_mode);\n\njulia> value = rstar(evotree_deterministic, samples);\n\njulia> round(value; digits=2)\n1.0 References Lambert, B., & Vehtari, A. (2020). $R^*$ : A robust MCMC convergence diagnostic with uncertainty using decision tree classifiers. source"},{"id":294,"pagetitle":"Home","title":"Bayesian fraction of missing information","ref":"/MCMCDiagnosticTools/stable/#Bayesian-fraction-of-missing-information","content":" Bayesian fraction of missing information"},{"id":295,"pagetitle":"Home","title":"MCMCDiagnosticTools.bfmi","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.bfmi","content":" MCMCDiagnosticTools.bfmi — Function bfmi(energy::AbstractVector{<:Real}) -> Real\nbfmi(energy::AbstractMatrix{<:Real}; dims::Int=1) -> AbstractVector{<:Real} Calculate the estimated Bayesian fraction of missing information (BFMI). When sampling with Hamiltonian Monte Carlo (HMC), BFMI quantifies how well momentum resampling matches the marginal energy distribution. The current advice is that values smaller than 0.3 indicate poor sampling. However, this threshold is provisional and may change. A BFMI value below the threshold often indicates poor adaptation of sampling parameters or that the target distribution has heavy tails that were not well explored by the Markov chain. For more information, see Section 6.1 of [Betancourt2018] or [Betancourt2016] for a complete account. energy is either a vector of Hamiltonian energies of draws or a matrix of energies of draws for multiple chains. dims indicates the dimension in energy that contains the draws. The default dims=1 assumes energy has the shape draws or (draws, chains) . If a different shape is provided, dims must be set accordingly. If energy is a vector, a single BFMI value is returned. Otherwise, a vector of BFMI values for each chain is returned. source"},{"id":296,"pagetitle":"Home","title":"Other diagnostics","ref":"/MCMCDiagnosticTools/stable/#Other-diagnostics","content":" Other diagnostics Note These diagnostics are older and less widely used."},{"id":297,"pagetitle":"Home","title":"MCMCDiagnosticTools.discretediag","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.discretediag","content":" MCMCDiagnosticTools.discretediag — Function discretediag(samples::AbstractArray{<:Real,3}; frac=0.3, method=:weiss, nsim=1_000) Compute discrete diagnostic on samples with shape (draws, chains, parameters) . method can be one of :weiss , :hangartner , :DARBOOT , :MCBOOT , :billinsgley , and :billingsleyBOOT . References Benjamin E. Deonovic, & Brian J. Smith. (2017). Convergence diagnostics for MCMC draws of a categorical variable. source"},{"id":298,"pagetitle":"Home","title":"MCMCDiagnosticTools.gelmandiag","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.gelmandiag","content":" MCMCDiagnosticTools.gelmandiag — Function gelmandiag(samples::AbstractArray{<:Real,3}; alpha::Real=0.95) Compute the Gelman, Rubin and Brooks diagnostics [Gelman1992] [Brooks1998] on samples with shape (draws, chains, parameters) . Values of the diagnostic’s potential scale reduction factor (PSRF) that are close to one suggest convergence. As a rule-of-thumb, convergence is rejected if the 97.5 percentile of a PSRF is greater than 1.2. source"},{"id":299,"pagetitle":"Home","title":"MCMCDiagnosticTools.gelmandiag_multivariate","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.gelmandiag_multivariate","content":" MCMCDiagnosticTools.gelmandiag_multivariate — Function gelmandiag_multivariate(samples::AbstractArray{<:Real,3}; alpha::Real=0.05) Compute the multivariate Gelman, Rubin and Brooks diagnostics on samples with shape (draws, chains, parameters) . source"},{"id":300,"pagetitle":"Home","title":"MCMCDiagnosticTools.gewekediag","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.gewekediag","content":" MCMCDiagnosticTools.gewekediag — Function gewekediag(x::AbstractVector{<:Real}; first::Real=0.1, last::Real=0.5, kwargs...) Compute the Geweke diagnostic [Geweke1991] from the first and last proportion of samples x . The diagnostic is designed to asses convergence of posterior means estimated with autocorrelated samples. It computes a normal-based test statistic comparing the sample means in two windows containing proportions of the first and last iterations. Users should ensure that there is sufficient separation between the two windows to assume that their samples are independent. A non-significant test p-value indicates convergence. Significant p-values indicate non-convergence and the possible need to discard initial samples as a burn-in sequence or to simulate additional samples. kwargs are forwarded to mcse . source"},{"id":301,"pagetitle":"Home","title":"MCMCDiagnosticTools.heideldiag","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.heideldiag","content":" MCMCDiagnosticTools.heideldiag — Function heideldiag(\n x::AbstractVector{<:Real}; alpha::Real=0.05, eps::Real=0.1, start::Int=1, kwargs...\n) Compute the Heidelberger and Welch diagnostic [Heidelberger1983] . This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1] . kwargs are forwarded to mcse . source"},{"id":302,"pagetitle":"Home","title":"MCMCDiagnosticTools.rafterydiag","ref":"/MCMCDiagnosticTools/stable/#MCMCDiagnosticTools.rafterydiag","content":" MCMCDiagnosticTools.rafterydiag — Function rafterydiag(\n x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)\n) Compute the Raftery and Lewis diagnostic [Raftery1992] . This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\\theta_q$ , such that $\\Pr(\\theta \\le \\theta_q) = q$ , within a desired degree of accuracy. In particular, if $\\hat{\\theta}_q$ is the estimand and $\\Pr(\\theta \\le \\hat{\\theta}_q) = \\hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s , where $\\Pr(q - r < \\hat{P}_q < q + r) = s$ . Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large). Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value. source VehtariGelman2021 Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008 VehtariGelman2021 Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008 VehtariGelman2021 Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008 Geyer1992 Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483. VehtariGelman2021 Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008 BDA3 Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press. FlegalJones2011 Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf Flegal2012 Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18 Betancourt2018 Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME] Betancourt2016 Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME] Gelman1992 Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472. Brooks1998 Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455. Geweke1991 Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis. Heidelberger1983 Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144. Raftery1992 A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992."},{"id":305,"pagetitle":"Home","title":"InferenceObjects","ref":"/InferenceObjects/stable/#InferenceObjects","content":" InferenceObjects InferenceObjects.jl is a Julia implementation of the InferenceData schema for storing results of Bayesian inference. Its purpose is to serve the following three goals: Usefulness in the analysis of Bayesian inference results. Reproducibility of Bayesian inference analysis. Interoperability between different inference backends and programming languages. The implementation consists primarily of the InferenceData and Dataset structures. InferenceObjects also provides the function convert_to_inference_data , which may be overloaded by inference packages to define how various inference outputs can be converted to an InferenceData . For examples of how InferenceData can be used, see the ArviZ.jl documentation ."},{"id":308,"pagetitle":"Dataset","title":"Dataset","ref":"/InferenceObjects/stable/dataset/#Dataset","content":" Dataset InferenceObjects.Dataset InferenceObjects.convert_to_dataset InferenceObjects.namedtuple_to_dataset"},{"id":309,"pagetitle":"Dataset","title":"Type definition","ref":"/InferenceObjects/stable/dataset/#Type-definition","content":" Type definition"},{"id":310,"pagetitle":"Dataset","title":"InferenceObjects.Dataset","ref":"/InferenceObjects/stable/dataset/#InferenceObjects.Dataset","content":" InferenceObjects.Dataset — Type Dataset{L} <: DimensionalData.AbstractDimStack{L} Container of dimensional arrays sharing some dimensions. This type is an DimensionalData.AbstractDimStack that implements the same interface as DimensionalData.DimStack and has identical usage. When a Dataset is passed to Python, it is converted to an xarray.Dataset without copying the data. That is, the Python object shares the same memory as the Julia object. However, if an xarray.Dataset is passed to Julia, its data must be copied. Constructors Dataset(data::DimensionalData.AbstractDimArray...)\nDataset(data::Tuple{Vararg{<:DimensionalData.AbstractDimArray}})\nDataset(data::NamedTuple{Keys,Vararg{<:DimensionalData.AbstractDimArray}})\nDataset(\n data::NamedTuple,\n dims::Tuple{Vararg{DimensionalData.Dimension}};\n metadata=DimensionalData.NoMetadata(),\n) In most cases, use convert_to_dataset to create a Dataset instead of directly using a constructor. source"},{"id":311,"pagetitle":"Dataset","title":"General conversion","ref":"/InferenceObjects/stable/dataset/#General-conversion","content":" General conversion"},{"id":312,"pagetitle":"Dataset","title":"InferenceObjects.convert_to_dataset","ref":"/InferenceObjects/stable/dataset/#InferenceObjects.convert_to_dataset","content":" InferenceObjects.convert_to_dataset — Function convert_to_dataset(obj; group = :posterior, kwargs...) -> Dataset Convert a supported object to a Dataset . In most cases, this function calls convert_to_inference_data and returns the corresponding group . source"},{"id":313,"pagetitle":"Dataset","title":"InferenceObjects.namedtuple_to_dataset","ref":"/InferenceObjects/stable/dataset/#InferenceObjects.namedtuple_to_dataset","content":" InferenceObjects.namedtuple_to_dataset — Function namedtuple_to_dataset(data; kwargs...) -> Dataset Convert NamedTuple mapping variable names to arrays to a Dataset . Any non-array values will be converted to a 0-dimensional array. Keywords attrs::AbstractDict{<:AbstractString} : a collection of metadata to attach to the dataset, in addition to defaults. Values should be JSON serializable. library::Union{String,Module} : library used for performing inference. Will be attached to the attrs metadata. dims : a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are: Symbol : dimension name Type{<:DimensionsionalData.Dimension} : dimension type DimensionsionalData.Dimension : dimension, potentially with indices Nothing : no dimension name provided, dimension name is automatically generated coords : a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated. source"},{"id":314,"pagetitle":"Dataset","title":"DimensionalData","ref":"/InferenceObjects/stable/dataset/#DimensionalData","content":" DimensionalData As a DimensionalData.AbstractDimStack , Dataset also implements the AbstractDimStack API and can be used like a DimStack . See DimensionalData's documentation for example usage."},{"id":315,"pagetitle":"Dataset","title":"Tables inteface","ref":"/InferenceObjects/stable/dataset/#Tables-inteface","content":" Tables inteface Dataset implements the Tables interface. This allows Dataset s to be used as sources for any function that can accept a table. For example, it's straightforward to: write to CSV with CSV.jl flatten to a DataFrame with DataFrames.jl plot with StatsPlots.jl plot with AlgebraOfGraphics.jl"},{"id":318,"pagetitle":"InferenceData","title":"InferenceData","ref":"/InferenceObjects/stable/inference_data/#InferenceData","content":" InferenceData InferenceObjects.InferenceData Base.cat Base.getindex Base.getproperty Base.merge Base.propertynames Base.setindex InferenceObjects.convert_to_inference_data InferenceObjects.from_dict InferenceObjects.from_namedtuple InferenceObjects.from_netcdf InferenceObjects.to_netcdf"},{"id":319,"pagetitle":"InferenceData","title":"Type definition","ref":"/InferenceObjects/stable/inference_data/#Type-definition","content":" Type definition"},{"id":320,"pagetitle":"InferenceData","title":"InferenceObjects.InferenceData","ref":"/InferenceObjects/stable/inference_data/#InferenceObjects.InferenceData","content":" InferenceObjects.InferenceData — Type InferenceData{group_names,group_types} Container for inference data storage using DimensionalData. This object implements the InferenceData schema . Internally, groups are stored in a NamedTuple , which can be accessed using parent(::InferenceData) . Constructors InferenceData(groups::NamedTuple)\nInferenceData(; groups...) Construct an inference data from either a NamedTuple or keyword arguments of groups. Groups must be Dataset objects. Instead of directly creating an InferenceData , use the exported from_xyz functions or convert_to_inference_data . source"},{"id":321,"pagetitle":"InferenceData","title":"Property interface","ref":"/InferenceObjects/stable/inference_data/#Property-interface","content":" Property interface"},{"id":322,"pagetitle":"InferenceData","title":"Base.getproperty","ref":"/InferenceObjects/stable/inference_data/#Base.getproperty","content":" Base.getproperty — Function getproperty(data::InferenceData, name::Symbol) -> Dataset Get group with the specified name . source"},{"id":323,"pagetitle":"InferenceData","title":"Base.propertynames","ref":"/InferenceObjects/stable/inference_data/#Base.propertynames","content":" Base.propertynames — Function propertynames(data::InferenceData) -> Tuple{Symbol} Get names of groups source"},{"id":324,"pagetitle":"InferenceData","title":"Indexing interface","ref":"/InferenceObjects/stable/inference_data/#Indexing-interface","content":" Indexing interface"},{"id":325,"pagetitle":"InferenceData","title":"Base.getindex","ref":"/InferenceObjects/stable/inference_data/#Base.getindex","content":" Base.getindex — Function Base.getindex(data::InferenceData, groups::Symbol; coords...) -> Dataset\nBase.getindex(data::InferenceData, groups; coords...) -> InferenceData Return a new InferenceData containing the specified groups sliced to the specified coords. coords specifies a dimension name mapping to an index, a DimensionalData.Selector , or an IntervalSets.AbstractInterval . If one or more groups lack the specified dimension, a warning is raised but can be ignored. All groups that contain the dimension must also contain the specified indices, or an exception will be raised. Examples Select data from all groups for just the specified id values. julia> using InferenceObjects, DimensionalData\n\njulia> idata = from_namedtuple(\n (θ=randn(4, 100, 4), τ=randn(4, 100));\n prior=(θ=randn(4, 100, 4), τ=randn(4, 100)),\n observed_data=(y=randn(4),),\n dims=(θ=[:id], y=[:id]),\n coords=(id=[\"a\", \"b\", \"c\", \"d\"],),\n )\nInferenceData with groups:\n > posterior\n > prior\n > observed_data\n\njulia> idata.posterior\nDataset with dimensions:\n Dim{:chain} Sampled 1:4 ForwardOrdered Regular Points,\n Dim{:draw} Sampled 1:100 ForwardOrdered Regular Points,\n Dim{:id} Categorical String[a, b, c, d] ForwardOrdered\nand 2 layers:\n :θ Float64 dims: Dim{:chain}, Dim{:draw}, Dim{:id} (4×100×4)\n :τ Float64 dims: Dim{:chain}, Dim{:draw} (4×100)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2022-08-11T11:15:21.4\"\n\njulia> idata_sel = idata[id=At([\"a\", \"b\"])]\nInferenceData with groups:\n > posterior\n > prior\n > observed_data\n\njulia> idata_sel.posterior\nDataset with dimensions:\n Dim{:chain} Sampled 1:4 ForwardOrdered Regular Points,\n Dim{:draw} Sampled 1:100 ForwardOrdered Regular Points,\n Dim{:id} Categorical String[a, b] ForwardOrdered\nand 2 layers:\n :θ Float64 dims: Dim{:chain}, Dim{:draw}, Dim{:id} (4×100×2)\n :τ Float64 dims: Dim{:chain}, Dim{:draw} (4×100)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2022-08-11T11:15:21.4\" Select data from just the posterior, returning a Dataset if the indices index more than one element from any of the variables: julia> idata[:observed_data, id=At([\"a\"])]\nDataset with dimensions:\n Dim{:id} Categorical String[a] ForwardOrdered\nand 1 layer:\n :y Float64 dims: Dim{:id} (1)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2022-08-11T11:19:25.982\" Note that if a single index is provided, the behavior is still to slice so that the dimension is preserved. source"},{"id":326,"pagetitle":"InferenceData","title":"Base.setindex","ref":"/InferenceObjects/stable/inference_data/#Base.setindex","content":" Base.setindex — Function Base.setindex(data::InferenceData, group::Dataset, name::Symbol) -> InferenceData Create a new InferenceData containing the group with the specified name . If a group with name is already in data , it is replaced. source"},{"id":327,"pagetitle":"InferenceData","title":"Iteration interface","ref":"/InferenceObjects/stable/inference_data/#Iteration-interface","content":" Iteration interface InferenceData also implements the same iteration interface as its underlying NamedTuple . That is, iterating over an InferenceData iterates over its groups."},{"id":328,"pagetitle":"InferenceData","title":"General conversion","ref":"/InferenceObjects/stable/inference_data/#General-conversion","content":" General conversion"},{"id":329,"pagetitle":"InferenceData","title":"InferenceObjects.convert_to_inference_data","ref":"/InferenceObjects/stable/inference_data/#InferenceObjects.convert_to_inference_data","content":" InferenceObjects.convert_to_inference_data — Function convert_to_inference_data(obj; group, kwargs...) -> InferenceData Convert a supported object to an InferenceData object. If obj converts to a single dataset, group specifies which dataset in the resulting InferenceData that is. See convert_to_dataset Arguments obj can be many objects. Basic supported types are: InferenceData : return unchanged Dataset / DimensionalData.AbstractDimStack : add to InferenceData as the only group NamedTuple / AbstractDict : create a Dataset as the only group AbstractArray{<:Real} : create a Dataset as the only group, given an arbitrary name, if the name is not set More specific types may be documented separately. Keywords group::Symbol = :posterior : If obj converts to a single dataset, assign the resulting dataset to this group. dims : a collection mapping variable names to collections of objects containing dimension names. Acceptable such objects are: Symbol : dimension name Type{<:DimensionsionalData.Dimension} : dimension type DimensionsionalData.Dimension : dimension, potentially with indices Nothing : no dimension name provided, dimension name is automatically generated coords : a collection indexable by dimension name specifying the indices of the given dimension. If indices for a dimension in dims are provided, they are used even if the dimension contains its own indices. If a dimension is missing, its indices are automatically generated. kwargs : remaining keywords forwarded to converter functions source"},{"id":330,"pagetitle":"InferenceData","title":"InferenceObjects.from_dict","ref":"/InferenceObjects/stable/inference_data/#InferenceObjects.from_dict","content":" InferenceObjects.from_dict — Function from_dict(posterior::AbstractDict; kwargs...) -> InferenceData Convert a Dict to an InferenceData . Arguments posterior : The data to be converted. Its strings must be Symbol or AbstractString , and its values must be arrays. Keywords posterior_predictive::Any=nothing : Draws from the posterior predictive distribution sample_stats::Any=nothing : Statistics of the posterior sampling process predictions::Any=nothing : Out-of-sample predictions for the posterior. prior::Dict=nothing : Draws from the prior prior_predictive::Any=nothing : Draws from the prior predictive distribution sample_stats_prior::Any=nothing : Statistics of the prior sampling process observed_data::NamedTuple : Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values. constant_data::NamedTuple : Model constants, data included in the model which is not modeled as a random variable. Keys are parameter names and values. predictions_constant_data::NamedTuple : Constants relevant to the model predictions (i.e. new x values in a linear regression). log_likelihood : Pointwise log-likelihood for the data. It is recommended to use this argument as a NamedTuple whose keys are observed variable names and whose values are log likelihood arrays. library : Name of library that generated the draws coords : Map from named dimension to named indices dims : Map from variable name to names of its dimensions Returns InferenceData : The data with groups corresponding to the provided data Examples using InferenceObjects\nnchains = 2\nndraws = 100\n\ndata = Dict(\n :x => rand(ndraws, nchains),\n :y => randn(2, ndraws, nchains),\n :z => randn(3, 2, ndraws, nchains),\n)\nidata = from_dict(data) source"},{"id":331,"pagetitle":"InferenceData","title":"InferenceObjects.from_namedtuple","ref":"/InferenceObjects/stable/inference_data/#InferenceObjects.from_namedtuple","content":" InferenceObjects.from_namedtuple — Function from_namedtuple(posterior::NamedTuple; kwargs...) -> InferenceData\nfrom_namedtuple(posterior::Vector{Vector{<:NamedTuple}}; kwargs...) -> InferenceData\nfrom_namedtuple(\n posterior::NamedTuple,\n sample_stats::Any,\n posterior_predictive::Any,\n predictions::Any,\n log_likelihood::Any;\n kwargs...\n) -> InferenceData Convert a NamedTuple or container of NamedTuple s to an InferenceData . If containers are passed, they are flattened into a single NamedTuple with array elements whose first dimensions correspond to the dimensions of the containers. Arguments posterior : The data to be converted. It may be of the following types: ::NamedTuple : The keys are the variable names and the values are arrays with dimensions (ndraws, nchains[, sizes...]) . ::Vector{Vector{<:NamedTuple}} : A vector of length nchains whose elements have length ndraws . Keywords posterior_predictive::Any=nothing : Draws from the posterior predictive distribution sample_stats::Any=nothing : Statistics of the posterior sampling process predictions::Any=nothing : Out-of-sample predictions for the posterior. prior=nothing : Draws from the prior. Accepts the same types as posterior . prior_predictive::Any=nothing : Draws from the prior predictive distribution sample_stats_prior::Any=nothing : Statistics of the prior sampling process observed_data::NamedTuple : Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Keys are parameter names and values. constant_data::NamedTuple : Model constants, data included in the model which is not modeled as a random variable. Keys are parameter names and values. predictions_constant_data::NamedTuple : Constants relevant to the model predictions (i.e. new x values in a linear regression). log_likelihood : Pointwise log-likelihood for the data. It is recommended to use this argument as a NamedTuple whose keys are observed variable names and whose values are log likelihood arrays. library : Name of library that generated the draws coords : Map from named dimension to named indices dims : Map from variable name to names of its dimensions Returns InferenceData : The data with groups corresponding to the provided data Note If a NamedTuple is provided for observed_data , constant_data , or predictions constant data`, any non-array values (e.g. integers) are converted to 0-dimensional arrays. Examples using InferenceObjects\nnchains = 2\nndraws = 100\n\ndata1 = (\n x=rand(ndraws, nchains), y=randn(ndraws, nchains, 2), z=randn(ndraws, nchains, 3, 2)\n)\nidata1 = from_namedtuple(data1)\n\ndata2 = [[(x=rand(), y=randn(2), z=randn(3, 2)) for _ in 1:ndraws] for _ in 1:nchains];\nidata2 = from_namedtuple(data2) source"},{"id":332,"pagetitle":"InferenceData","title":"General functions","ref":"/InferenceObjects/stable/inference_data/#General-functions","content":" General functions"},{"id":333,"pagetitle":"InferenceData","title":"Base.cat","ref":"/InferenceObjects/stable/inference_data/#Base.cat","content":" Base.cat — Function cat(data::InferenceData...; [groups=keys(data[1]),] dims) -> InferenceData Concatenate InferenceData objects along the specified dimension dims . Only the groups in groups are concatenated. Remaining groups are merge d into the new InferenceData object. Examples Here is how we can concatenate all groups of two InferenceData objects along the existing chain dimension: julia> coords = (; a_dim=[\"x\", \"y\", \"z\"]);\n\njulia> dims = dims=(; a=[:a_dim]);\n\njulia> data = Dict(:a => randn(100, 4, 3), :b => randn(100, 4));\n\njulia> idata = from_dict(data; coords=coords, dims=dims)\nInferenceData with groups:\n > posterior\n\njulia> idata_cat1 = cat(idata, idata; dims=:chain)\nInferenceData with groups:\n > posterior\n\njulia> idata_cat1.posterior\nDataset with dimensions:\n Dim{:draw},\n Dim{:chain},\n Dim{:a_dim} Categorical{String} String[\"x\", \"y\", \"z\"] ForwardOrdered\nand 2 layers:\n :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim} (100×8×3)\n :b Float64 dims: Dim{:draw}, Dim{:chain} (100×8)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-04-03T18:41:35.779\" Alternatively, we can concatenate along a new run dimension, which will be created. julia> idata_cat2 = cat(idata, idata; dims=:run)\nInferenceData with groups:\n > posterior\n\njulia> idata_cat2.posterior\nDataset with dimensions:\n Dim{:draw},\n Dim{:chain},\n Dim{:a_dim} Categorical{String} String[\"x\", \"y\", \"z\"] ForwardOrdered,\n Dim{:run}\nand 2 layers:\n :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim}, Dim{:run} (100×4×3×2)\n :b Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:run} (100×4×2)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-04-03T18:41:35.779\" We can also concatenate only a subset of groups and merge the rest, which is useful when some groups are present only in some of the InferenceData objects or will be identical in all of them: julia> observed_data = Dict(:y => randn(10));\n\njulia> idata2 = from_dict(data; observed_data=observed_data, coords=coords, dims=dims)\nInferenceData with groups:\n > posterior\n > observed_data\n\njulia> idata_cat3 = cat(idata, idata2; groups=(:posterior,), dims=:run)\nInferenceData with groups:\n > posterior\n > observed_data\n\njulia> idata_cat3.posterior\nDataset with dimensions:\n Dim{:draw},\n Dim{:chain},\n Dim{:a_dim} Categorical{String} String[\"x\", \"y\", \"z\"] ForwardOrdered,\n Dim{:run}\nand 2 layers:\n :a Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:a_dim}, Dim{:run} (100×4×3×2)\n :b Float64 dims: Dim{:draw}, Dim{:chain}, Dim{:run} (100×4×2)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-04-03T18:41:35.779\"\n\njulia> idata_cat3.observed_data\nDataset with dimensions: Dim{:y_dim_1}\nand 1 layer:\n :y Float64 dims: Dim{:y_dim_1} (10)\n\nwith metadata Dict{String, Any} with 1 entry:\n \"created_at\" => \"2023-02-17T15:11:00.59\" source"},{"id":334,"pagetitle":"InferenceData","title":"Base.merge","ref":"/InferenceObjects/stable/inference_data/#Base.merge","content":" Base.merge — Function merge(data::InferenceData...) -> InferenceData Merge InferenceData objects. The result contains all groups in data and others . If a group appears more than once, the one that occurs last is kept. See also: cat Examples Here we merge an InferenceData containing only a posterior group with one containing only a prior group to create a new one containing both groups. julia> idata1 = from_dict(Dict(:a => randn(100, 4, 3), :b => randn(100, 4)))\nInferenceData with groups:\n > posterior\n\njulia> idata2 = from_dict(; prior=Dict(:a => randn(100, 1, 3), :c => randn(100, 1)))\nInferenceData with groups:\n > prior\n\njulia> idata_merged = merge(idata1, idata2)\nInferenceData with groups:\n > posterior\n > prior source"},{"id":335,"pagetitle":"InferenceData","title":"I/O extensions","ref":"/InferenceObjects/stable/inference_data/#I/O-extensions","content":" I/O extensions The following types of storage are provided via extensions."},{"id":336,"pagetitle":"InferenceData","title":"NetCDF I/O using NCDatasets.jl","ref":"/InferenceObjects/stable/inference_data/#NetCDF-I/O-using-NCDatasets.jl","content":" NetCDF I/O using NCDatasets.jl"},{"id":337,"pagetitle":"InferenceData","title":"InferenceObjects.from_netcdf","ref":"/InferenceObjects/stable/inference_data/#InferenceObjects.from_netcdf","content":" InferenceObjects.from_netcdf — Function from_netcdf(path::AbstractString; kwargs...) -> InferenceData Load an InferenceData from an unopened NetCDF file. Remaining kwargs are passed to NCDatasets.NCDataset . This method loads data eagerly. To instead load data lazily, pass an opened NCDataset to from_netcdf . Note This method requires that NCDatasets is loaded before it can be used. Examples julia> using InferenceObjects, NCDatasets\n\njulia> idata = from_netcdf(\"centered_eight.nc\")\nInferenceData with groups:\n > posterior\n > posterior_predictive\n > sample_stats\n > prior\n > observed_data from_netcdf(ds::NCDatasets.NCDataset; load_mode) -> InferenceData Load an InferenceData from an opened NetCDF file. load_mode defaults to :lazy , which avoids reading variables into memory. Operations on these arrays will be slow. load_mode can also be :eager , which copies all variables into memory. It is then safe to close ds . If load_mode is :lazy and ds is closed after constructing InferenceData , using the variable arrays will have undefined behavior. Examples Here is how we might load an InferenceData from an InferenceData lazily from a web-hosted NetCDF file. julia> using HTTP, InferenceObjects, NCDatasets\n\njulia> resp = HTTP.get(\"https://github.com/arviz-devs/arviz_example_data/blob/main/data/centered_eight.nc?raw=true\");\n\njulia> ds = NCDataset(\"centered_eight\", \"r\"; memory = resp.body);\n\njulia> idata = from_netcdf(ds)\nInferenceData with groups:\n > posterior\n > posterior_predictive\n > sample_stats\n > prior\n > observed_data\n\njulia> idata_copy = copy(idata); # disconnect from the loaded dataset\n\njulia> close(ds); source"},{"id":338,"pagetitle":"InferenceData","title":"InferenceObjects.to_netcdf","ref":"/InferenceObjects/stable/inference_data/#InferenceObjects.to_netcdf","content":" InferenceObjects.to_netcdf — Function to_netcdf(data, dest::AbstractString; group::Symbol=:posterior, kwargs...)\nto_netcdf(data, dest::NCDatasets.NCDataset; group::Symbol=:posterior) Write data to a NetCDF file. data is any type that can be converted to an InferenceData using convert_to_inference_data . If not an InferenceData , then group specifies which group the data represents. dest specifies either the path to the NetCDF file or an opened NetCDF file. If dest is a path, remaining kwargs are passed to NCDatasets.NCDataset . Note This method requires that NCDatasets is loaded before it can be used. Examples julia> using InferenceObjects, NCDatasets\n\njulia> idata = from_namedtuple((; x = randn(4, 100, 3), z = randn(4, 100)))\nInferenceData with groups:\n > posterior\n\njulia> to_netcdf(idata, \"data.nc\")\n\"data.nc\" source"},{"id":341,"pagetitle":"Home","title":"ArviZExampleData","ref":"/ArviZExampleData/stable/#ArviZExampleData","content":" ArviZExampleData This package provides utilities for loading datasets defined in the arviz_example_data repository. The resulting objects are InferenceObjects.jl 's InferenceData . These utilities are used in ArviZ.jl ."},{"id":344,"pagetitle":"API","title":"API","ref":"/ArviZExampleData/stable/api/#API","content":" API"},{"id":345,"pagetitle":"API","title":"ArviZExampleData.describe_example_data","ref":"/ArviZExampleData/stable/api/#ArviZExampleData.describe_example_data","content":" ArviZExampleData.describe_example_data — Function describe_example_data() -> String Return a string containing descriptions of all available datasets. Examples julia> describe_example_data(\"radon\") |> println\nradon\n=====\n\nRadon is a radioactive gas that enters homes through contact points with the ground. It is a carcinogen that is the primary cause of lung cancer in non-smokers. Radon levels vary greatly from household to household.\n\nThis example uses an EPA study of radon levels in houses in Minnesota to construct a model with a hierarchy over households within a county. The model includes estimates (gamma) for contextual effects of the uranium per household.\n\nSee Gelman and Hill (2006) for details on the example, or https://docs.pymc.io/notebooks/multilevel_modeling.html by Chris Fonnesbeck for details on this implementation.\n\nremote: http://ndownloader.figshare.com/files/24067472 source"},{"id":346,"pagetitle":"API","title":"ArviZExampleData.load_example_data","ref":"/ArviZExampleData/stable/api/#ArviZExampleData.load_example_data","content":" ArviZExampleData.load_example_data — Function load_example_data(name; kwargs...) -> InferenceObjects.InferenceData\nload_example_data() -> Dict{String,AbstractFileMetadata} Load a local or remote pre-made dataset. kwargs are forwarded to InferenceObjects.from_netcdf . Pass no parameters to get a Dict listing all available datasets. Data files are handled by DataDeps.jl. A file is downloaded only when it is requested and then cached for future use. Examples julia> keys(load_example_data())\nKeySet for a OrderedCollections.OrderedDict{String, ArviZExampleData.AbstractFileMetadata} with 9 entries. Keys:\n \"centered_eight\"\n \"non_centered_eight\"\n \"radon\"\n \"rugby\"\n \"regression1d\"\n \"regression10d\"\n \"classification1d\"\n \"classification10d\"\n \"glycan_torsion_angles\"\n\njulia> load_example_data(\"centered_eight\")\nInferenceData with groups:\n > posterior\n > posterior_predictive\n > log_likelihood\n > sample_stats\n > prior\n > prior_predictive\n > observed_data\n > constant_data source"},{"id":349,"pagetitle":"Datasets","title":"Datasets","ref":"/ArviZExampleData/stable/datasets/#Datasets","content":" Datasets The following shows the currently available example datasets: using ArviZExampleData\n\nprintln(describe_example_data()) centered_eight\n==============\n\nA centered parameterization of the eight schools model. Provided as an example of a model that NUTS has trouble fitting. Compare to `non_centered_eight`.\n\nThe eight schools model is a hierarchical model used for an analysis of the effectiveness of classes that were designed to improve students' performance on the Scholastic Aptitude Test.\n\nSee Bayesian Data Analysis (Gelman et. al.) for more details.\n\nlocal: /home/runner/.julia/artifacts/1a48fb48ab2b35cdeeb84e0dcdcda134e24a1c20/arviz_example_data-0.1.1/data/centered_eight.nc\n\nnon_centered_eight\n==================\n\nA non-centered parameterization of the eight schools model. This is a hierarchical model where sampling problems may be fixed by a non-centered parametrization. Compare to `centered_eight`.\n\nThe eight schools model is a hierarchical model used for an analysis of the effectiveness of classes that were designed to improve students' performance on the Scholastic Aptitude Test.\n\nSee Bayesian Data Analysis (Gelman et. al.) for more details.\n\nlocal: /home/runner/.julia/artifacts/1a48fb48ab2b35cdeeb84e0dcdcda134e24a1c20/arviz_example_data-0.1.1/data/non_centered_eight.nc\n\nradon\n=====\n\nRadon is a radioactive gas that enters homes through contact points with the ground. It is a carcinogen that is the primary cause of lung cancer in non-smokers. Radon levels vary greatly from household to household.\n\nThis example uses an EPA study of radon levels in houses in Minnesota to construct a model with a hierarchy over households within a county. The model includes estimates (gamma) for contextual effects of the uranium per household.\n\nSee Gelman and Hill (2006) for details on the example, or https://docs.pymc.io/notebooks/multilevel_modeling.html by Chris Fonnesbeck for details on this implementation.\n\nremote: http://ndownloader.figshare.com/files/24067472\n\nrugby\n=====\n\nThe Six Nations Championship is a yearly rugby competition between Italy, Ireland, Scotland, England, France and Wales. Fifteen games are played each year, representing all combinations of the six teams.\n\nThis example uses and includes results from 2014 - 2017, comprising 60 total games. It models latent parameters for each team's attack and defense, as well as a parameter for home team advantage.\n\nSee https://docs.pymc.io/notebooks/rugby_analytics.html by Peader Coyle for more details and references.\n\nremote: http://ndownloader.figshare.com/files/16254359\n\nregression1d\n============\n\nA synthetic one dimensional linear regression dataset with latent slope, intercept, and noise (\"eps\"). One hundred data points, fit with PyMC3.\n\nTrue slope and intercept are included as deterministic variables.\n\nremote: http://ndownloader.figshare.com/files/16254899\n\nregression10d\n=============\n\nA synthetic multi-dimensional (10 dimensions) linear regression dataset with latent weights (\"w\"), intercept, and noise (\"eps\"). Five hundred data points, fit with PyMC3.\n\nTrue weights and intercept are included as deterministic variables.\n\nremote: http://ndownloader.figshare.com/files/16255736\n\nclassification1d\n================\n\nA synthetic one dimensional logistic regression dataset with latent slope and intercept, passed into a Bernoulli random variable. One hundred data points, fit with PyMC3.\n\nTrue slope and intercept are included as deterministic variables.\n\nremote: http://ndownloader.figshare.com/files/16256678\n\nclassification10d\n=================\n\nA synthetic multi dimensional (10 dimensions) logistic regression dataset with latent weights (\"w\") and intercept, passed into a Bernoulli random variable. Five hundred data points, fit with PyMC3.\n\nTrue weights and intercept are included as deterministic variables.\n\nremote: http://ndownloader.figshare.com/files/16256681\n\nglycan_torsion_angles\n=====================\n\nTorsion angles phi and psi are critical for determining the three dimensional structure of bio-molecules. Combinations of phi and psi torsion angles that produce clashes between atoms in the bio-molecule result in high energy, unlikely structures.\n\nThis model uses a Von Mises distribution to propose torsion angles for the structure of a glycan molecule (pdb id: 2LIQ), and a Potential to estimate the proposed structure's energy. Said Potential is bound by Boltzman's law.\n\nremote: http://ndownloader.figshare.com/files/22882652"},{"id":352,"pagetitle":"For developers","title":"For developers","ref":"/ArviZExampleData/stable/for_developers/#For-developers","content":" For developers This package has arviz_example_data as a data dependency, which is included as an artifact . When arviz_example_data is updated, and a new release is made, Artifacts.toml should be updated to point to the new tarball corresponding to the release: julia> using ArtifactUtils\n\njulia> version = v\"0.1.0\";\n\njulia> tarball_url = \"https://github.com/arviz-devs/arviz_example_data/archive/refs/tags/v$version.tar.gz\";\n\njulia> add_artifact!(\"Artifacts.toml\", \"arviz_example_data\", tarball_url; force=true);"},{"id":357,"pagetitle":"DimensionalData.jl","title":"DimensionalData ¤","ref":"/DimensionalData/stable/#dimensionaldata","content":" DimensionalData ¤ DimensionalData.jl provides tools and abstractions for working with datasets that have named dimensions, and optionally a lookup index. DimensionalData is a pluggable, generalised version of AxisArrays.jl with a cleaner syntax, and additional functionality found in NamedDims.jl. It has similar goals to pythons xarray , and is primarily written for use with spatial data in Rasters.jl ."},{"id":358,"pagetitle":"DimensionalData.jl","title":"Goals ¤","ref":"/DimensionalData/stable/#goals","content":" Goals ¤ Clean, readable syntax. Minimise required parentheses, minimise of exported Zero-cost dimensional indexing a[Y(4), X(5)] of a single value. methods, and instead extend Base methods whenever possible. Plotting is easy: data should plot sensibly and correctly with useful labels, by default. Least surprise: everything works the same as in Base, but with named dims. If a method accepts numeric indices or dims=X in base, you should be able to use DimensionalData.jl dims. Minimal interface: implementing a dimension-aware type should be easy. Maximum extensibility: always use method dispatch. Regular types over special syntax. Recursion over @generated. Always dispatch on abstract types. Type stability: dimensional methods should be type stable more often than Base methods Functional style: structs are always rebuilt, and other than the array data, fields are not mutated in place."},{"id":359,"pagetitle":"DimensionalData.jl","title":"For package developers ¤","ref":"/DimensionalData/stable/#for-package-developers","content":" For package developers ¤"},{"id":360,"pagetitle":"DimensionalData.jl","title":"Data types and the interface ¤","ref":"/DimensionalData/stable/#data-types-and-the-interface","content":" Data types and the interface ¤ DimensionalData.jl provides the concrete DimArray type. But its behaviours are intended to be easily applied to other array types. more The main requirement for extending DimensionalData.jl is to define a dims method\nthat returns a Tuple of Dimension that matches the dimension order\nand axis values of your data. Define rebuild and base methods for similar \nand parent if you want the metadata to persist through transformations (see\nthe DimArray and AbstractDimArray types). A refdims method\nreturns the lost dimensions of a previous transformation, passed in to the\n rebuild method. refdims can be discarded, the main loss being plot labels\nand ability to reconstruct dimensions in cat . Inheriting from AbstractDimArray in this way will give nearly all the functionality\nof using DimArray ."},{"id":361,"pagetitle":"DimensionalData.jl","title":"LookupArrays and Dimensions ¤","ref":"/DimensionalData/stable/#lookuparrays-and-dimensions","content":" LookupArrays and Dimensions ¤ Sub modules LookupArrays and Dimensions define the behviour of dimensions and their lookup index. LookupArrays and Dimensions"},{"id":364,"pagetitle":"Crash course - DimensionalData.jl","title":"Dimensions and DimArrays ¤","ref":"/DimensionalData/stable/crash/generated/course/course/#dimensions-and-dimarrays","content":" Dimensions and DimArrays ¤ The core type of DimensionalData.jl is the Dimension and the types that inherit from it, such as Ti , X , Y , Z , the generic Dim{:x} , or others that you define manually using the @dim macro. Dimension s are primarily used in DimArray , other AbstractDimArray . We can use dimensions without a value index - these simply label the axis. A DimArray with labelled dimensions is constructed by: using DimensionalData \n A = rand ( X ( 5 ), Y ( 5 )) \n 5×5 DimArray{Float64,2} with dimensions: X, Y\n 0.0257194 0.0545864 0.668622 0.990097 0.652228\n 0.44662 0.762548 0.954042 0.497596 0.000702532\n 0.980668 0.583562 0.190779 0.233336 0.298915\n 0.313727 0.392187 0.54035 0.644368 0.940491\n 0.723664 0.83586 0.834754 0.0447846 0.45741\n get value A [ Y ( 1 ), X ( 2 )] \n 0.44661950368409176\n As shown above, Dimension s can be used to construct arrays in rand , ones , zeros and fill with either a range for a lookup index or a number for the dimension length. Or we can use the Dim{X} dims by using Symbol s, and indexing with keywords: A = DimArray ( rand ( 5 , 5 ), ( :a , :b )) \n 5×5 DimArray{Float64,2} with dimensions: Dim{:a}, Dim{:b}\n 0.262882 0.664631 0.533606 0.734399 0.832567\n 0.760415 0.700901 0.331099 0.768394 0.23546\n 0.81808 0.436833 0.769763 0.867433 0.0349366\n 0.157131 0.589521 0.798718 0.463894 0.188219\n 0.486978 0.486446 0.437844 0.816005 0.460578\n get value A [ a = 3 , b = 5 ] \n 0.03493658137331457\n Often, we want to provide a lookup index for the dimension: using Dates \n t = DateTime ( 2001 ) : Month ( 1 ) : DateTime ( 2001 , 12 ) \n x = 10 : 10 : 100 \n A = rand ( X ( x ), Ti ( t )) \n 10×12 DimArray{Float64,2} with dimensions: \n X Sampled{Int64} 10:10:100 ForwardOrdered Regular Points,\n Ti Sampled{DateTime} DateTime(\"2001-01-01T00:00:00\"):Month(1):DateTime(\"2001-12-01T00:00:00\") ForwardOrdered Regular Points\n 2001-01-01T00:00:00 … 2001-12-01T00:00:00\n 10 0.220572 0.272713\n 20 0.383863 0.308758\n 30 0.0220933 0.211049\n 40 0.475009 0.835277\n 50 0.733425 … 0.991225\n 60 0.713087 0.0849085\n 70 0.38453 0.558929\n 80 0.523681 0.277764\n 90 0.767148 0.848079\n 100 0.125821 … 0.598359\n Here both X and Ti are dimensions from DimensionalData . The currently exported dimensions are X, Y, Z, Ti ( Ti is shortening of Time ). The length of each dimension index has to match the size of the corresponding array axis. This can also be done with Symbol , using Dim{X} : A2 = DimArray ( rand ( 12 , 10 ), ( time = t , distance = x )) \n 12×10 DimArray{Float64,2} with dimensions: \n Dim{:time} Sampled{DateTime} DateTime(\"2001-01-01T00:00:00\"):Month(1):DateTime(\"2001-12-01T00:00:00\") ForwardOrdered Regular Points,\n Dim{:distance} Sampled{Int64} 10:10:100 ForwardOrdered Regular Points\n … 80 90 100\n 2001-01-01T00:00:00 0.776826 0.446688 0.758554\n 2001-02-01T00:00:00 0.380958 0.696744 0.905861\n 2001-03-01T00:00:00 0.864697 0.318554 0.441301\n 2001-04-01T00:00:00 0.618603 0.753646 0.0732071\n 2001-05-01T00:00:00 … 0.698003 0.106475 0.611565\n 2001-06-01T00:00:00 0.487678 0.394129 0.878072\n 2001-07-01T00:00:00 0.102116 0.476639 0.895151\n 2001-08-01T00:00:00 0.659545 0.144719 0.792332\n 2001-09-01T00:00:00 0.433718 0.0994015 0.614477\n 2001-10-01T00:00:00 … 0.668483 0.796421 0.179683\n 2001-11-01T00:00:00 0.686543 0.935012 0.663855\n 2001-12-01T00:00:00 0.436568 0.745237 0.87978\n Symbols can be more convenient to use than defining custom dims with @dim , but have some downsides. They don't inherit from a specific Dimension type, so plots will not know what axis to put them on. They also cannot use the basic constructor methods like rand or zeros , as we cannot dispatch on Symbol for Base methods without \"type-piracy\"."},{"id":365,"pagetitle":"Crash course - DimensionalData.jl","title":"Indexing the array by name and index ¤","ref":"/DimensionalData/stable/crash/generated/course/course/#indexing-the-array-by-name-and-index","content":" Indexing the array by name and index ¤ Dimensions can be used to index the array by name, without having to worry about the order of the dimensions. The simplest case is to select a dimension by index. Let's say every 2nd point of the Ti dimension and every 3rd point of the X dimension. This is done with the simple Ti(range) syntax like so: A [ X ( 1 : 3 : 11 ), Ti ( 1 : 2 : 11 )] \n 4×6 DimArray{Float64,2} with dimensions: \n X Sampled{Int64} 10:30:100 ForwardOrdered Regular Points,\n Ti Sampled{DateTime} DateTime(\"2001-01-01T00:00:00\"):Month(2):DateTime(\"2001-11-01T00:00:00\") ForwardOrdered Regular Points\n 2001-01-01T00:00:00 … 2001-11-01T00:00:00\n 10 0.220572 0.435993\n 40 0.475009 0.446399\n 70 0.38453 0.863633\n 100 0.125821 0.639194\n When specifying only one dimension, all elements of the other dimensions are assumed to be included: A [ X ( 1 : 3 : 10 )] \n 4×12 DimArray{Float64,2} with dimensions: \n X Sampled{Int64} 10:30:100 ForwardOrdered Regular Points,\n Ti Sampled{DateTime} DateTime(\"2001-01-01T00:00:00\"):Month(1):DateTime(\"2001-12-01T00:00:00\") ForwardOrdered Regular Points\n 2001-01-01T00:00:00 … 2001-12-01T00:00:00\n 10 0.220572 0.272713\n 40 0.475009 0.835277\n 70 0.38453 0.558929\n 100 0.125821 0.598359\n Indexing Indexing AbstractDimArray s works with getindex , setindex! and view . The result is still an AbstracDimArray , unless using all single Int or Selector s that resolve to Int . Dimension s can be used to construct arrays in rand , ones , zeros and fill with either a range for a lookup index or a number for the dimension length. using DimensionalData \n A1 = ones ( X ( 1 : 40 ), Y ( 50 )) \n 40×50 DimArray{Float64,2} with dimensions: \n X Sampled{Int64} 1:40 ForwardOrdered Regular Points,\n Y\n 1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 … 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n 2 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n 3 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n 4 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n 5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n 6 1.0 1.0 1.0 1.0 1.0 1.0 1.0 … 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n ⋮ ⋮ ⋱ ⋮ ⋮ \n 35 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n 36 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n 37 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n 38 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n 39 1.0 1.0 1.0 1.0 1.0 1.0 1.0 … 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n 40 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n We can also use dim wrappers for indexing, so that the dimension order in the underlying array does not need to be known: A1 [ Y ( 1 ), X ( 1 : 10 )] \n 10-element DimArray{Float64,1} with dimensions: \n X Sampled{Int64} 1:10 ForwardOrdered Regular Points\nand reference dimensions: Y\n 1 1.0\n 2 1.0\n 3 1.0\n 4 1.0\n 5 1.0\n 6 1.0\n 7 1.0\n 8 1.0\n 9 1.0\n 10 1.0\n"},{"id":366,"pagetitle":"Crash course - DimensionalData.jl","title":"Indexing Performance ¤","ref":"/DimensionalData/stable/crash/generated/course/course/#indexing-performance","content":" Indexing Performance ¤ Indexing with Dimension has no runtime cost: A2 = ones ( X ( 3 ), Y ( 3 )) \n 3×3 DimArray{Float64,2} with dimensions: X, Y\n 1.0 1.0 1.0\n 1.0 1.0 1.0\n 1.0 1.0 1.0\n time ? using BenchmarkTools \n\n println ( @btime $ A2 [ X ( 1 ), Y ( 2 )]) \n 43.920 ns (0 allocations: 0 bytes)\n1.0\n and println ( @btime parent ( $ A2 )[ 1 , 2 ]) \n 3.095 ns (0 allocations: 0 bytes)\n1.0\n"},{"id":367,"pagetitle":"Crash course - DimensionalData.jl","title":"Specifying dims keyword arguments with Dimension ¤","ref":"/DimensionalData/stable/crash/generated/course/course/#specifying-dims-keyword-arguments-with-dimension","content":" Specifying dims keyword arguments with Dimension ¤ In many Julia functions like size or sum , you can specify the dimension along which to perform the operation as an Int . It is also possible to do this using Dimension types with AbstractDimArray : A3 = rand ( X ( 3 ), Y ( 4 ), Ti ( 5 )); \n sum ( A3 ; dims = Ti ) \n 3×4×1 DimArray{Float64,3} with dimensions: X, Y, Ti\n[:, :, 1]\n 2.86333 3.42363 2.38244 1.3045\n 1.47257 2.43555 2.6565 2.27314\n 3.24374 2.10504 2.27636 2.93816\n This also works in methods from Statistics : using Statistics \n mean ( A3 ; dims = Ti ) \n 3×4×1 DimArray{Float64,3} with dimensions: X, Y, Ti\n[:, :, 1]\n 0.572667 0.684727 0.476489 0.2609\n 0.294513 0.48711 0.5313 0.454629\n 0.648749 0.421008 0.455273 0.587633\n"},{"id":368,"pagetitle":"Crash course - DimensionalData.jl","title":"Methods where dims, dim types, or Symbol s can be used to indicate the array dimension: ¤","ref":"/DimensionalData/stable/crash/generated/course/course/#methods-where-dims-dim-types-or-symbols-can-be-used-to-indicate-the-array-dimension","content":" Methods where dims, dim types, or Symbol s can be used to indicate the array dimension: ¤ size , axes , firstindex , lastindex cat , reverse , dropdims reduce , mapreduce sum , prod , maximum , minimum , mean , median , extrema , std , var , cor , cov permutedims , adjoint , transpose , Transpose mapslices , eachslice"},{"id":369,"pagetitle":"Crash course - DimensionalData.jl","title":"LookupArrays and Selectors ¤","ref":"/DimensionalData/stable/crash/generated/course/course/#lookuparrays-and-selectors","content":" LookupArrays and Selectors ¤ Indexing by value in DimensionalData is done with Selectors . IntervalSets.jl is now used for selecting ranges of values (formerly Between ). Selector Description At(x) get the index exactly matching the passed in value(s) Near(x) get the closest index to the passed in value(s) Contains(x) get indices where the value x falls within an interval Where(f) filter the array axis by a function of the dimension index values. [ Not(x) ] get all indices not selected by x , which can be another selector. [ a..b ] get all indices between two values, inclusively. [ OpenInterval(a, b) ] get all indices between a and b , exclusively. [ Interval{A,B}(a, b) ] get all indices between a and b , as :closed or :open . Selectors find indices in the LookupArray , for each dimension. Here we use an Interval to select a range between integers and DateTime : A [ X ( 12 .. 35 ), Ti ( Date ( 2001 , 5 ) .. Date ( 2001 , 7 ))] \n 2×3 DimArray{Float64,2} with dimensions: \n X Sampled{Int64} 20:10:30 ForwardOrdered Regular Points,\n Ti Sampled{DateTime} DateTime(\"2001-05-01T00:00:00\"):Month(1):DateTime(\"2001-07-01T00:00:00\") ForwardOrdered Regular Points\n 2001-05-01T00:00:00 … 2001-07-01T00:00:00\n 20 0.57611 0.535862\n 30 0.642167 0.457967\n To select intervals in DimArrays (e.g. A2 ) you need to specify dimname=a .. b : A2 [ distance = 12 .. 35 , time = Date ( 2001 , 5 ) .. Date ( 2001 , 7 )] \n 3×3 DimArray{Float64,2} with dimensions: X, Y\n 1.0 1.0 1.0\n 1.0 1.0 1.0\n 1.0 1.0 1.0\n Selectors can be used in getindex , setindex! and view to select indices matching the passed in value(s) We can use selectors inside dim wrappers, here selecting values from DateTime and Int : using Dates \n timespan = DateTime ( 2001 , 1 ) : Month ( 1 ) : DateTime ( 2001 , 12 ) \n A4 = rand ( Ti ( timespan ), X ( 10 : 10 : 100 )) \n A4 [ X ( Near ( 35 )), Ti ( At ( DateTime ( 2001 , 5 )))] \n 0.9138958993339432\n Without dim wrappers selectors must be in the right order, and specify all axes: using Unitful \n A5 = rand ( Y (( 1 : 10 : 100 ) u \"m\" ), Ti (( 1 : 5 : 100 ) u \"s\" )); \n A5 [ 10.5 u \"m\" .. 50.5 u \"m\" , Near ( 23 u \"s\" )] \n 4-element DimArray{Float64,1} with dimensions: \n Y Sampled{Quantity{Int64, 𝐋, Unitful.FreeUnits{(m,), 𝐋, nothing}}} (11:10:41) m ForwardOrdered Regular Points\nand reference dimensions: \n Ti Sampled{Quantity{Int64, 𝐓, Unitful.FreeUnits{(s,), 𝐓, nothing}}} (21:5:21) s ForwardOrdered Regular Points\n 11 m 0.270118\n 21 m 0.191835\n 31 m 0.767381\n 41 m 0.117902\n We can also use Linear indices as in standard Array : A5 [ 1 : 5 ] \n 5-element Vector{Float64}:\n 0.4403938161748643\n 0.116883355447569\n 0.18929453007416674\n 0.33024233140041537\n 0.6230648314878906\n But unless the DimArray is one dimensional, this will return a regular Array . It is not possible to keep the LookupArray or even Dimension s after linear indexing is used."},{"id":370,"pagetitle":"Crash course - DimensionalData.jl","title":"LookupArrays and traits ¤","ref":"/DimensionalData/stable/crash/generated/course/course/#lookuparrays-and-traits","content":" LookupArrays and traits ¤ Using a regular range or Vector as a lookup index has a number of downsides. We cannot use searchsorted for fast searches without knowing the order of the array, and this is slow to compute at runtime. It also means reverse or rotations cannot be used while keeping the DimArray wrapper. Step sizes are also a problem. Some ranges like LinRange lose their step size with a length of 1 . Often, instead of a range, multi-dimensional data formats provide a Vector of evenly spaced values for a lookup, with a step size specified separately. Converting to a range introduces floating point errors that means points may not be selected with At without setting tolerances. This means using a lookup wrapper with traits is more generally robust and versatile than simply using a range or vector. DimensionalData provides types for specifying details about the dimension index, in the LookupArrays sub-module: using DimensionalData \n using . LookupArrays \n The main LookupArray are : Sampled Categorical , NoLookup Each comes with specific traits that are either fixed or variable, depending on the contained index. These enable optimisations with Selector s, and modified behaviours, such as: Selection of Intervals or Points , which will give slightly different results for selectors like .. - as whole intervals are selected, and have different bounds values. Tracking of lookup order. A reverse order is labelled ReverseOrdered and will still work with searchsorted , and for plots to always be the right way up when either the index or the array is backwards. Reversing a DimArray will reverse the LookupArray for that dimension, swapping ReverseOrdered to ForwardOrdered . Sampled Intervals can have index located at a Locus of: Start , Center End Which specifies the point of the interval represented in the index, to match different data standards, e.g. GeoTIFF ( Start ) and NetCDF ( Center ). A Span specifies the gap between Points or the size of Intervals . This may be: Regular , in the case of a range and equally spaced vector, Irregular for unequally spaced vectors Explicit for the case where all interval start and end points are specified explicitly - as is common in the NetCDF standard. These traits all for subtypes of Aligned . Unaligned also exists to handle dimensions with an index that is rotated or otherwise transformed in relation to the underlying array, such as Transformed ."},{"id":371,"pagetitle":"Crash course - DimensionalData.jl","title":"LookupArray detection ¤","ref":"/DimensionalData/stable/crash/generated/course/course/#lookuparray-detection","content":" LookupArray detection ¤ Aligned types will be detected automatically if not specified - which usually isn't required. An empty Dimension or a Type or Symbol will be assigned NoLookup - this behaves as a simple named dimension without a lookup index. A Dimension containing and index of String , Char , Symbol or mixed types will be given the Categorical mode, A range will be assigned Sampled , defaulting to Regular , Points Other AbstractVector will be assigned Sampled Irregular Points . In all cases the Order of ForwardOrdered or ReverseOrdered will be be detected, otherwise Unordered for an unsorted Array . See the LookupArray API docs for more detail."},{"id":372,"pagetitle":"Crash course - DimensionalData.jl","title":"Referenced dimensions ¤","ref":"/DimensionalData/stable/crash/generated/course/course/#referenced-dimensions","content":" Referenced dimensions ¤ The reference dimensions record the previous dimensions that an array was selected from. These can be use for plot labelling, and tracking array changes so that cat can reconstruct the lookup array from previous dimensions that have been sliced."},{"id":373,"pagetitle":"Crash course - DimensionalData.jl","title":"Warnings ¤","ref":"/DimensionalData/stable/crash/generated/course/course/#warnings","content":" Warnings ¤ Indexing with unordered or reverse-ordered arrays has undefined behaviour. It will trash the dimension index, break searchsorted and nothing will make sense any more. So do it at you own risk. However, indexing with sorted vectors of Int can be useful, so it's allowed. But it may do strange things to interval sizes for Intervals that are not Explicit . This selects the first 5 entries of the underlying array. In the case that A has only one dimension, it will be retained. Multidimensional AbstracDimArray indexed this way will return a regular array. This page was generated using Literate.jl ."},{"id":376,"pagetitle":"Reference - DimensionalData.jl","title":"API ¤","ref":"/DimensionalData/stable/reference/#api","content":" API ¤"},{"id":377,"pagetitle":"Reference - DimensionalData.jl","title":"Arrays ¤","ref":"/DimensionalData/stable/reference/#arrays","content":" Arrays ¤ # DimensionalData.AbstractDimArray — Type . AbstractDimArray <: AbstractArray \n Abstract supertype for all \"dim\" arrays. These arrays return a Tuple of Dimension from a dims method, and can be rebuilt using rebuild . parent must return the source array. They should have metadata , name and refdims methods, although these are optional. A rebuild method for AbstractDimArray must accept data , dims , refdims , name , metadata arguments. Indexing AbstractDimArray with non-range AbstractArray has undefined effects on the Dimension index. Use forward-ordered arrays only\" source # DimensionalData.DimArray — Type . DimArray <: AbstractDimArray \n\n DimArray ( data , dims , refdims , name , metadata ) \n DimArray ( data , dims :: Tuple ; refdims = (), name = NoName (), metadata = NoMetadata ()) \n The main concrete subtype of AbstractDimArray . DimArray maintains and updates its Dimension s through transformations and moves dimensions to reference dimension refdims after reducing operations (like e.g. mean ). Arguments data : An AbstractArray . dims : A Tuple of Dimension name : A string name for the array. Shows in plots and tables. refdims : refence dimensions. Usually set programmatically to track past slices and reductions of dimension for labelling and reconstruction. metadata : Dict or Metadata object, or NoMetadata() Indexing can be done with all regular indices, or with Dimension s and/or Selector s. Indexing AbstractDimArray with non-range AbstractArray has undefined effects on the Dimension index. Use forward-ordered arrays only\" Example: using Dates , DimensionalData \n\n ti = ( Ti ( DateTime ( 2001 ) : Month ( 1 ) : DateTime ( 2001 , 12 )), \n x = X ( 10 : 10 : 100 )) \n A = DimArray ( rand ( 12 , 10 ), ( ti , x ), \"example\" ) \n\n julia > A [ X ( Near ([ 12 , 35 ])), Ti ( At ( DateTime ( 2001 , 5 )))]; \n\n julia > A [ Near ( DateTime ( 2001 , 5 , 4 )), Between ( 20 , 50 )]; \n source"},{"id":378,"pagetitle":"Reference - DimensionalData.jl","title":"Multi-array datasets ¤","ref":"/DimensionalData/stable/reference/#multi-array-datasets","content":" Multi-array datasets ¤ # DimensionalData.AbstractDimStack — Type . AbstractDimStack \n Abstract supertype for dimensional stacks. These have multiple layers of data, but share dimensions. Notably, their behaviour lies somewhere between a DimArray and a NamedTuple : indexing with a Symbol as in dimstack[:symbol] returns a DimArray layer. iteration amd map are apply over array layers, as indexed with a Symbol . getindex and many base methods are applied as for DimArray - to avoid the need to allways use map . This design gives very succinct code when working with many-layered, mixed-dimension objects. But it may be jarring initially - the most surprising outcome is that dimstack[1] will return a NamedTuple of values for the first index in all layers, while first(dimstack) will return the first value of the iterator - the DimArray for the first layer. See DimStack for the concrete implementation. Most methods are defined on the abstract type. To extend AbstractDimStack , implement argument and keyword version of rebuild and also rebuild_from_arrays . The constructor of an AbstractDimStack must accept a NamedTuple . source # DimensionalData.DimStack — Type . DimStack <: AbstractDimStack \n\n DimStack ( data :: AbstractDimArray ... ) \n DimStack ( data :: Tuple { Vararg { AbstractDimArray }}) \n DimStack ( data :: NamedTuple { Keys , Vararg { AbstractDimArray }}) \n DimStack ( data :: NamedTuple , dims :: DimTuple ; metadata = NoMetadata ()) \n DimStack holds multiple objects sharing some dimensions, in a NamedTuple . Notably, their behaviour lies somewhere between a DimArray and a NamedTuple : indexing with a Symbol as in dimstack[:symbol] returns a DimArray layer. iteration amd map are apply over array layers, as indexed with a Symbol . getindex or view with Int , Dimension s or Selector s that resolve to Int will return a NamedTuple of values from each layer in the stack. This has very good performace, and avoids the need to always use map . getindex or view with a Vector or Colon will return another DimStack where all data layers have been sliced. setindex! must pass a Tuple or NamedTuple maching the layers. many base and Statistics methods ( sum , mean etc) will work as for a DimArray again removing the need to use map . For example, here we take the mean over the time dimension for all layers : mean ( mydimstack ; dims = Ti ) \n And this equivalent to: map ( A -> mean ( A ; dims = Ti ), mydimstack ) \n This design gives succinct code when working with many-layered, mixed-dimension objects. But it may be jarring initially - the most surprising outcome is that dimstack[1] will return a NamedTuple of values for the first index in all layers, while first(dimstack) will return the first value of the iterator - the DimArray for the first layer. DimStack can be constructed from multiple AbstractDimArray or a NamedTuple of AbstractArray and a matching dims tuple. Most Base and Statistics methods that apply to AbstractArray can be used on all layers of the stack simulataneously. The result is a DimStack , or a NamedTuple if methods like mean are used without dims arguments, and return a single non-array value. Example julia> using DimensionalData \n\n julia> A = [ 1.0 2.0 3.0 ; 4.0 5.0 6.0 ]; \n\n julia> dimz = ( X ([ :a , :b ]), Y ( 10.0 : 10.0 : 30.0 )) \n X Symbol[:a, :b], \n Y 10.0:10.0:30.0 \n\n julia> da1 = DimArray ( 1 A , dimz ; name = :one ); \n\n julia> da2 = DimArray ( 2 A , dimz ; name = :two ); \n\n julia> da3 = DimArray ( 3 A , dimz ; name = :three ); \n\n julia> s = DimStack ( da1 , da2 , da3 ); \n\n julia> s [ At ( :b ), At ( 10.0 )] \n (one = 4.0, two = 8.0, three = 12.0) \n\n julia> s [ X ( At ( :a ))] isa DimStack \n true \n source"},{"id":379,"pagetitle":"Reference - DimensionalData.jl","title":"Dimension indices generators ¤","ref":"/DimensionalData/stable/reference/#dimension-indices-generators","content":" Dimension indices generators ¤ # DimensionalData.DimIndices — Type . DimIndices <: AbstractArray \n\n DimIndices ( x ) \n DimIndices ( dims :: Tuple ) \n DimIndices ( dims :: Dimension ) \n Like CartesianIndices , but for Dimension s. Behaves as an Array of Tuple of Dimension(i) for all combinations of the axis indices of dims . This can be used to view/index into arbitrary dimensions over an array, and is especially useful when combined with otherdims , to iterate over the indices of unknown dimension. source # DimensionalData.DimKeys — Type . DimKeys <: AbstractArray \n\n DimKeys ( x ) \n DimKeys ( dims :: Tuple ) \n DimKeys ( dims :: Dimension ) \n Like CartesianIndices , but for the lookup values of Dimensions. Behaves as an Array of Tuple of Dimension(At(lookupvalue)) for all combinations of the lookup values of dims . source # DimensionalData.DimPoints — Type . DimPoints <: AbstractArray \n\n DimPoints ( x ; order ) \n DimPoints ( dims :: Tuple ; order ) \n DimPoints ( dims :: Dimension ; order ) \n Like CartesianIndices , but for the point values of the dimension index. Behaves as an Array of Tuple lookup values (whatever they are) for all combinations of the lookup values of dims . Either a Dimension , a Tuple of Dimension or an object that defines a dims method can be passed in. Keywords order : determines the order of the points, the same as the order of dims by default. source"},{"id":380,"pagetitle":"Reference - DimensionalData.jl","title":"Tables.jl/TableTraits.jl interface ¤","ref":"/DimensionalData/stable/reference/#tablesjltabletraitsjl-interface","content":" Tables.jl/TableTraits.jl interface ¤ # DimensionalData.AbstractDimTable — Type . AbstractDimTable <: Tables . AbstractColumns \n Abstract supertype for dim tables source # DimensionalData.DimTable — Type . DimTable <: AbstractDimTable \n\n DimTable ( s :: AbstractDimStack ; mergedims = nothing ) \n DimTable ( x :: AbstractDimArray ; layersfrom = nothing , mergedims = nothing ) \n DimTable ( xs :: Vararg { AbstractDimArray }; layernames = nothing , mergedims = nothing ) \n Construct a Tables.jl/TableTraits.jl compatible object out of an AbstractDimArray or AbstractDimStack . This table will have columns for the array data and columns for each Dimension index, as a [ DimColumn ]. These are lazy, and generated as required. Column names are converted from the dimension types using DimensionalData.dim2key . This means type Ti becomes the column name :Ti , and Dim{:custom} becomes :custom . To get dimension columns, you can index with Dimension ( X() ) or Dimension type ( X ) as well as the regular Int or Symbol . Keywords mergedims : Combine two or more dimensions into a new dimension. layersfrom : Treat a dimension of an AbstractDimArray as layers of an AbstractDimStack . Example julia> a = DimArray ( rand ( 32 , 32 , 3 ), ( X , Y , Dim { :band })); \n\n julia> DimTable ( a , layersfrom = Dim { :band }, mergedims = ( X , Y ) =>: geometry ) \n DimTable with 1024 rows, 4 columns, and schema: \n :geometry Tuple{Int64, Int64} \n :band_1 Float64 \n :band_2 Float64 \n :band_3 Float64 \n source # DimensionalData.DimColumn — Type . DimColumn { T , D <: Dimension } <: AbstractVector { T } \n\n DimColumn ( dim :: Dimension , dims :: Tuple { Vararg { DimTuple }}) \n DimColumn ( dim :: DimColumn , length :: Int , dimstride :: Int ) \n A table column based on a Dimension and it's relationship with other Dimension s in dims . length is the product of all dim lengths (usually the length of the corresponding array data), while stride is the product of the preceding dimension lengths, which may or may not be the real stride of the corresponding array depending on the data type. For A isa Array , the dimstride will match the stride . When the second argument is a Tuple of Dimension , the length and dimstride fields are calculated from the dimensions, relative to the column dimension dim . This object will be returned as a column of DimTable . source"},{"id":381,"pagetitle":"Reference - DimensionalData.jl","title":"Common methods ¤","ref":"/DimensionalData/stable/reference/#common-methods","content":" Common methods ¤ Common functions for obtaining information from objects: # DimensionalData.Dimensions.dims — Function . dims ( x , [ dims :: Tuple ]) => Tuple { Vararg { Dimension }} \n dims ( x , dim ) => Dimension \n Return a tuple of Dimension s for an object, in the order that matches the axes or columns of the underlying data. dims can be Dimension , Dimension types, or Symbols for Dim{Symbol} . The default is to return nothing . source # DimensionalData.Dimensions.refdims — Function . refdims ( x , [ dims :: Tuple ]) => Tuple { Vararg { Dimension }} \n refdims ( x , dim ) => Dimension \n Reference dimensions for an array that is a slice or view of another array with more dimensions. slicedims(a, dims) returns a tuple containing the current new dimensions and the new reference dimensions. Refdims can be stored in a field or disgarded, as it is mostly to give context to plots. Ignoring refdims will simply leave some captions empty. The default is to return an empty Tuple () . source # DimensionalData.Dimensions.LookupArrays.metadata — Function . metadata ( x ) => ( object metadata ) \n metadata ( x , dims :: Tuple ) => Tuple ( Dimension metadata ) \n metadata ( xs :: Tuple ) => Tuple \n Returns the metadata for an object or for the specified dimension(s) Second argument dims can be Dimension s, Dimension types, or Symbols for Dim{Symbol} . source # DimensionalData.Dimensions.name — Function . name ( x ) => Symbol \n name ( xs : Tuple ) => NTuple { N , Symbol } \n name ( x , dims :: Tuple ) => NTuple { N , Symbol } \n name ( x , dim ) => Symbol \n Get the name of an array or Dimension, or a tuple of of either as a Symbol. Second argument dims can be Dimension s, Dimension types, or Symbols for Dim{Symbol} . source Utility methods for transforming DimensionalData objects: # DimensionalData.Dimensions.LookupArrays.set — Function . set ( x , val ) \n set ( x , args :: Pairs ... ) => x with updated field / s \n set ( x , args ... ; kw ... ) => x with updated field / s \n set ( x , args :: Tuple { Vararg { Dimension }}; kw ... ) => x with updated field / s \n\n set ( dim :: Dimension , index :: AbstractArray ) => Dimension \n set ( dim :: Dimension , lookup :: LookupArray ) => Dimension \n set ( dim :: Dimension , lookupcomponent :: LookupArrayTrait ) => Dimension \n set ( dim :: Dimension , metadata :: AbstractMetadata ) => Dimension \n Set the properties of an object, its internal data or the traits of its dimensions and lookup index. As DimensionalData is so strongly typed you do not need to specify what field of a LookupArray to set - there is no ambiguity. To set fields of a LookupArray you need to specify the dimension. This can be done using X => val pairs, X = val keyword arguments, or X(val) wrapped arguments. When a Dimension or LookupArray is passed to set to replace the existing ones, fields that are not set will keep their original values. Notes: Changing a lookup index range/vector will also update the step size and order where applicable. Setting the Order like ForwardOrdered will not reverse the array or dimension to match. Use reverse and reorder to do this. Examples julia> using DimensionalData ; const DD = DimensionalData \n DimensionalData \n\n julia> da = DimArray ( zeros ( 3 , 4 ), ( custom = 10.0 : 010.0 : 30.0 , Z =- 20 : 010.0 : 10.0 )); \n\n julia> set ( da , ones ( 3 , 4 )) \n 3×4 DimArray{Float64,2} with dimensions: \n Dim{:custom} Sampled{Float64} 10.0:10.0:30.0 ForwardOrdered Regular Points, \n Z Sampled{Float64} -20.0:10.0:10.0 ForwardOrdered Regular Points \n -20.0 -10.0 0.0 10.0 \n 10.0 1.0 1.0 1.0 1.0 \n 20.0 1.0 1.0 1.0 1.0 \n 30.0 1.0 1.0 1.0 1.0 \n Change the Dimension wrapper type: julia> set ( da , :Z => Ti , :custom => Z ) \n 3×4 DimArray{Float64,2} with dimensions: \n Z Sampled{Float64} 10.0:10.0:30.0 ForwardOrdered Regular Points, \n Ti Sampled{Float64} -20.0:10.0:10.0 ForwardOrdered Regular Points \n -20.0 -10.0 0.0 10.0 \n 10.0 0.0 0.0 0.0 0.0 \n 20.0 0.0 0.0 0.0 0.0 \n 30.0 0.0 0.0 0.0 0.0 \n Change the lookup Vector : julia> set ( da , Z => [ :a , :b , :c , :d ], :custom => [ 4 , 5 , 6 ]) \n 3×4 DimArray{Float64,2} with dimensions: \n Dim{:custom} Sampled{Int64} Int64[4, 5, 6] ForwardOrdered Regular Points, \n Z Sampled{Symbol} Symbol[:a, :b, :c, :d] ForwardOrdered Regular Points \n :a :b :c :d \n 4 0.0 0.0 0.0 0.0 \n 5 0.0 0.0 0.0 0.0 \n 6 0.0 0.0 0.0 0.0 \n Change the LookupArray type: julia> set ( da , Z = DD . NoLookup (), custom = DD . Sampled ()) \n 3×4 DimArray{Float64,2} with dimensions: \n Dim{:custom} Sampled{Float64} 10.0:10.0:30.0 ForwardOrdered Regular Points, \n Z \n 10.0 0.0 0.0 0.0 0.0 \n 20.0 0.0 0.0 0.0 0.0 \n 30.0 0.0 0.0 0.0 0.0 \n Change the Sampling trait: julia> set ( da , :custom => DD . Irregular ( 10 , 12 ), Z => DD . Regular ( 9.9 )) \n 3×4 DimArray{Float64,2} with dimensions: \n Dim{:custom} Sampled{Float64} 10.0:10.0:30.0 ForwardOrdered Irregular Points, \n Z Sampled{Float64} -20.0:10.0:10.0 ForwardOrdered Regular Points \n -20.0 -10.0 0.0 10.0 \n 10.0 0.0 0.0 0.0 0.0 \n 20.0 0.0 0.0 0.0 0.0 \n 30.0 0.0 0.0 0.0 0.0 \n source # DimensionalData.Dimensions.LookupArrays.rebuild — Function . rebuild ( x , args ... ) \n rebuild ( x ; kw ... ) \n Rebuild an object struct with updated field values. x can be a AbstractDimArray , a Dimension , LookupArray or other custom types. This is an abstraction that alows inbuilt and custom types to be rebuilt to update their fields, as most objects in DimensionalData.jl are immutable. The arguments version can be concise but depends on a fixed order defined for some DimensionalData objects. It should be defined based on the object type in DimensionalData, adding the fields specific to your object. The keyword version ignores order, and is mostly automated using ConstructionBase.setproperties . It should only be defined if your object has missing fields or fields with different names to DimensionalData objects. The arguments required are defined for the abstract type that has a rebuild method. source # DimensionalData.modify — Function . modify ( f , A :: AbstractDimArray ) => AbstractDimArray \n modify ( f , s :: AbstractDimStack ) => AbstractDimStack \n modify ( f , dim :: Dimension ) => Dimension \n modify ( f , x , lookupdim :: Dimension ) => typeof ( x ) \n Modify the parent data, rebuilding the object wrapper without change. f must return a AbstractArray of the same size as the original. This method is mostly useful as a way of swapping the parent array type of an object. Example If we have a previously-defined DimArray , we can copy it to an Nvidia GPU with: A = DimArray ( rand ( 100 , 100 ), ( X , Y )) \n modify ( CuArray , A ) \n This also works for all the data layers in a DimStack . source # DimensionalData.broadcast_dims — Function . broadcast_dims ( f , sources :: AbstractDimArray ... ) => AbstractDimArray \n Broadcast function f over the AbstractDimArray s in sources , permuting and reshaping dimensions to match where required. The result will contain all the dimensions in all passed in arrays in the order in which they are found. Arguments sources : AbstractDimArrays to broadcast over with f . This is like broadcasting over every slice of A if it is sliced by the dimensions of B . source # DimensionalData.broadcast_dims! — Function . broadcast_dims! ( f , dest :: AbstractDimArray , sources :: AbstractDimArray ... ) => dest \n Broadcast function f over the AbstractDimArray s in sources , writing to dest . sources are permuting and reshaping dimensions to match where required. The result will contain all the dimensions in all passed in arrays, in the order in which they are found. Arguments dest : AbstractDimArray to update. sources : AbstractDimArrays to broadcast over with f . source # DimensionalData.mergedims — Function . mergedims ( old_dims => new_dim ) => Dimension \n Return a dimension new_dim whose indices are a MergedLookup of the indices of old_dims . source mergedims(dims, old_dims => new_dim, others::Pair...) => dims_new\n If dimensions old_dims , new_dim , etc. are found in dims , then return new dims_new where all dims in old_dims have been combined into a single dim new_dim . The returned dimension will keep only the name of new_dim . Its coords will be a MergedLookup of the coords of the dims in old_dims . New dimensions are always placed at the end of dims_new . others contains other dimension pairs to be merged. Example julia> ds = ( X ( 0 : 0.1 : 0.4 ), Y ( 10 : 10 : 100 ), Ti ([ 0 , 3 , 4 ])); \n julia> mergedims ( ds , Ti => :time , ( X , Y ) => :space ) \n Dim{:time} MergedLookup{Tuple{Int64}} Tuple{Int64}[(0,), (3,), (4,)] Ti, \n Dim{:space} MergedLookup{Tuple{Float64, Int64}} Tuple{Float64, Int64}[(0.0, 10), (0.1, 10), …, (0.3, 100), (0.4, 100)] X, Y \n source mergedims(A::AbstractDimArray, dim_pairs::Pair...) => AbstractDimArray\nmergedims(A::AbstractDimStack, dim_pairs::Pair...) => AbstractDimStack\n Return a new array or stack whose dimensions are the result of mergedims(dims(A), dim_pairs) . source # DimensionalData.unmergedims — Function . unmergedims ( merged_dims :: Tuple { Vararg { Dimension }}) => Tuple { Vararg { Dimension }} \n Return the unmerged dimensions from a tuple of merged dimensions. However, the order of the original dimensions are not necessarily preserved. source unmergedims(A::AbstractDimArray, original_dims) => AbstractDimArray\nunmergedims(A::AbstractDimStack, original_dims) => AbstractDimStack\n Return a new array or stack whose dimensions are restored to their original prior to calling mergedims(A, dim_pairs) . source # DimensionalData.reorder — Function . reorder ( A :: Union { AbstractDimArray , AbstractDimStack }, order :: Pair ... ) \n reorder ( A :: Union { AbstractDimArray , AbstractDimStack }, order ) \n reorder ( A :: Dimension , order :: Order ) \n Reorder every dims index/array to order , or reorder index for the the given dimension(s) in order . order can be an Order , Dimension => Order pairs. A Tuple of Dimensions or any object that defines dims can be used in which case dimensions are If no axis reversal is required the same objects will be returned, without allocation. Example **Create a DimArray**\n\nda = DimArray([1 2 3; 4 5 6], (X(10:10:20), Y(300:-100:100)))\n\n**Reverse it**\n\nrev = reverse(da, dims=Y)\n\n**using `da` in reorder will return it to the original order**\n\nreorder(rev, da) == da\n\n**output**\n\ntrue\n\n\nsource
        \n\n#\n**`Base.cat`** — *Function*.\n\n\n\n```julia\nBase.cat(stacks::AbstractDimStack...; [keys=keys(stacks[1])], dims)\n Concatenate all or a subset of layers for all passed in stacks. Keywords keys : Tuple of Symbol for the stack keys to concatenate. dims : Dimension of child array to concatenate on. Example Concatenate the :sea surface temp and :humidity layers in the time dimension: cat ( stacks ... ; keys = ( :sea_surface_temp , :humidity ), dims = Ti ) \n source # Base.map — Function . Base . map ( f , stacks :: AbstractDimStack ... ) \n Apply function f to each layer of the stacks . If f returns DimArray s the result will be another DimStack . Other values will be returned in a NamedTuple . source # Base.copy! — Function . Base . copy! ( dst :: AbstractArray , src :: AbstractGimStack , key :: Key ) \n Copy the stack layer key to dst , which can be any AbstractArray . Example Copy the :humidity layer from stack to array . copy! ( array , stack , :humidity ) \n source Base.copy!(dst::AbstractDimStack, src::AbstractDimStack, [keys=keys(dst)])\n Copy all or a subset of layers from one stack to another. Example Copy just the :sea_surface_temp and :humidity layers from src to dst . copy! ( dst :: AbstractDimStack , src :: AbstractDimStack , keys = ( :sea_surface_temp , :humidity )) \n source # Base.eachslice — Function . Base . eachslice ( stack :: AbstractDimStack ; dims ) \n Create a generator that iterates over dimensions dims of stack , returning stacks that select all the data from the other dimensions in stack using views. The generator has size and axes equivalent to those of the provided dims . Examples julia > ds = DimStack (( \n x = DimArray ( randn ( 2 , 3 , 4 ), ( X ([ :x1 , :x2 ]), Y ( 1 : 3 ), Z )), \n y = DimArray ( randn ( 2 , 3 , 5 ), ( X ([ :x1 , :x2 ]), Y ( 1 : 3 ), Ti )) \n )); \n\n julia > slices = eachslice ( ds ; dims = ( Z , X )); \n\n julia > size ( slices ) \n ( 4 , 2 ) \n\n julia > map ( dims , axes ( slices )) \n Z , \n X Categorical { Symbol } Symbol [ x1 , x2 ] ForwardOrdered \n\n julia > first ( slices ) \n DimStack with dimensions : \n Y Sampled { Int64 } 1 : 3 ForwardOrdered Regular Points , \n Ti \n and 2 layers : \n :x Float64 dims : Y ( 3 ) \n :y Float64 dims : Y , Ti ( 3 × 5 ) \n source Most base methods work as expected, using Dimension wherever a dims keyword is used. They are not allspecifically documented here. Shorthand constructors: # Base.fill — Function . Base . fill ( x , dims :: Dimension ... ; kw ... ) => DimArray \n Base . fill ( x , dims :: Tuple { Vararg { Dimension }}; kw ... ) => DimArray \n Create a DimArray with a fill value of x . There are two kinds of Dimension value acepted: A Dimension holding an AbstractVector will set the dimension index to that AbstractVector , and detect the dimension lookup. A Dimension holding an Integer will set the length of the axis, and set the dimension lookup to NoLookup . Keywords are the same as for DimArray . Example ```@doctest\njulia> using DimensionalData julia> rand(Bool, X(2), Y(4))\n2×4 DimArray{Bool,2} with dimensions: X, Y\n 1 0 0 1\n 1 0 1 1\n source
        \n\n#\n**`Base.rand`** — *Function*.\n\n\n\n```julia\nBase.rand(x, dims::Dimension...; kw...) => DimArray\nBase.rand(x, dims::Tuple{Vararg{Dimension}}; kw...) => DimArray\nBase.rand(r::AbstractRNG, x, dims::Tuple{Vararg{Dimension}}; kw...) => DimArray\nBase.rand(r::AbstractRNG, x, dims::Dimension...; kw...) => DimArray\n Create a DimArray of random values. There are two kinds of Dimension value acepted: A Dimension holding an AbstractVector will set the dimension index to that AbstractVector , and detect the dimension lookup. A Dimension holding an Integer will set the length of the axis, and set the dimension lookup to NoLookup . Keywords are the same as for DimArray . Example julia > using DimensionalData \n\n julia > rand ( Bool , X ( 2 ), Y ( 4 )) \n 2 × 4 DimArray { Bool , 2 } with dimensions : X , Y \n 1 0 0 1 \n 1 0 1 1 \n\n julia > rand ( X ([ :a , :b , :c ]), Y ( 100.0 : 50 : 200.0 )) \n 3 × 3 DimArray { Float64 , 2 } with dimensions : \n X : Symbol [ a , b , c ] Categorical : Unordered , \n Y : 100.0 : 50.0 : 200.0 Sampled : Ordered Regular Points \n 0.43204 0.835111 0.624231 \n 0.752868 0.471638 0.193652 \n 0.484558 0.846559 0.455256 \n source # Base.zeros — Function . Base . zeros ( x , dims :: Dimension ... ; kw ... ) => DimArray \n Base . zeros ( x , dims :: Tuple { Vararg { Dimension }}; kw ... ) => DimArray \n Create a DimArray of zeros. There are two kinds of Dimension value acepted: A Dimension holding an AbstractVector will set the dimension index to that AbstractVector , and detect the dimension lookup. A Dimension holding an Integer will set the length of the axis, and set the dimension lookup to NoLookup . Keywords are the same as for DimArray . Example ```@doctest\njulia> using DimensionalData julia> zeros(Bool, X(2), Y(4))\n2×4 DimArray{Bool,2} with dimensions: X, Y\n 0 0 0 0\n 0 0 0 0 julia> zeros(X([:a, :b, :c]), Y(100.0:50:200.0))\n3×3 DimArray{Float64,2} with dimensions:\n X: Symbol[a, b, c] Categorical: Unordered,\n Y: 100.0:50.0:200.0 Sampled: Ordered Regular Points\n 0.0 0.0 0.0\n 0.0 0.0 0.0\n 0.0 0.0 0.0\n source
        \n\n#\n**`Base.ones`** — *Function*.\n\n\n\n```julia\nBase.ones(x, dims::Dimension...; kw...) => DimArray\nBase.ones(x, dims::Tuple{Vararg{Dimension}}; kw...) => DimArray\n Create a DimArray of ones. There are two kinds of Dimension value acepted: A Dimension holding an AbstractVector will set the dimension index to that AbstractVector , and detect the dimension lookup. A Dimension holding an Integer will set the length of the axis, and set the dimension lookup to NoLookup . Keywords are the same as for DimArray . Example ```@doctest\njulia> using DimensionalData julia> ones(Bool, X(2), Y(4))\n2×4 DimArray{Bool,2} with dimensions: X, Y\n 1 1 1 1\n 1 1 1 1 julia> ones(X([:a, :b, :c]), Y(100.0:50:200.0))\n3×3 DimArray{Float64,2} with dimensions:\n X: Symbol[a, b, c] Categorical: Unordered,\n Y: 100.0:50.0:200.0 Sampled: Ordered Regular Points\n 1.0 1.0 1.0\n 1.0 1.0 1.0\n 1.0 1.0 1.0\n source
        \n\n\n\n\n\n\n# Dimensions\n\n\nHandling of Dimensions is kept in a sub-module `Dimensions`.\n\n#\n**`DimensionalData.Dimensions`** — *Module*.\n\n\n\nDimensions\n\nSub-module for [`Dimension`](reference.md#DimensionalData.Dimensions.Dimension)s wrappers, and operations on them used in DimensionalData.jl.\n\nTo load `Dimensions` types and methods into scope:\n\n```julia\nusing DimensionalData\nusing DimensionalData.Dimensions\n source Dimensions have a type-heirarchy that organises plotting and dimension matching. # DimensionalData.Dimensions.Dimension — Type . Dimension \n Abstract supertype of all dimension types. Example concrete implementations are X , Y , Z , Ti (Time), and the custom [ Dim ]@ref) dimension. Dimension s label the axes of an AbstractDimArray , or other dimensional objects, and are used to index into the array. They may also provide an alternate index to lookup for each array axis. This may be any AbstractVector matching the array axis length, or a Val holding a tuple for compile-time index lookups. Dimension s also have lookup and metadata fields. lookup gives more details about the dimension, such as that it is Categorical or Sampled as Points or Intervals along some transect. DimensionalData will attempt to guess the lookup from the passed-in index value. Example: using DimensionalData , Dates \n\n x = X ( 2 : 2 : 10 ) \n y = Y ([ 'a' , 'b' , 'c' ]) \n ti = Ti ( DateTime ( 2021 , 1 ) : Month ( 1 ) : DateTime ( 2021 , 12 )) \n\n A = DimArray ( zeros ( 3 , 5 , 12 ), ( y , x , ti )) \n\n # output \n\n 3 × 5 × 12 DimArray { Float64 , 3 } with dimensions : \n Y Categorical { Char } Char [ 'a' , 'b' , 'c' ] ForwardOrdered , \n X Sampled { Int64 } 2 : 2 : 10 ForwardOrdered Regular Points , \n Ti Sampled { DateTime } DateTime ( \"2021-01-01T00:00:00\" ) : Month ( 1 ) : DateTime ( \"2021-12-01T00:00:00\" ) ForwardOrdered Regular Points \n [ : , : , 1 ] \n 2 4 6 8 10 \n 'a' 0.0 0.0 0.0 0.0 0.0 \n 'b' 0.0 0.0 0.0 0.0 0.0 \n 'c' 0.0 0.0 0.0 0.0 0.0 \n [ and 11 more slices ... ] \n For simplicity, the same Dimension types are also used as wrappers in getindex , like: x = A [ X ( 2 ), Y ( 3 )] \n\n # output \n\n 12 - element DimArray { Float64 , 1 } with dimensions : \n Ti Sampled { DateTime } DateTime ( \"2021-01-01T00:00:00\" ) : Month ( 1 ) : DateTime ( \"2021-12-01T00:00:00\" ) ForwardOrdered Regular Points \n and reference dimensions : \n Y Categorical { Char } Char [ 'c' ] ForwardOrdered , \n X Sampled { Int64 } 4 : 2 : 4 ForwardOrdered Regular Points \n 2021 - 01 - 01 T00 : 00 : 00 0.0 \n 2021 - 02 - 01 T00 : 00 : 00 0.0 \n 2021 - 03 - 01 T00 : 00 : 00 0.0 \n 2021 - 04 - 01 T00 : 00 : 00 0.0 \n ⋮ \n 2021 - 10 - 01 T00 : 00 : 00 0.0 \n 2021 - 11 - 01 T00 : 00 : 00 0.0 \n 2021 - 12 - 01 T00 : 00 : 00 0.0 \n A Dimension can also wrap Selector . x = A [ X ( Between ( 3 , 4 )), Y ( At ( 'b' ))] \n\n # output \n\n 1 × 12 DimArray { Float64 , 2 } with dimensions : \n X Sampled { Int64 } 4 : 2 : 4 ForwardOrdered Regular Points , \n Ti Sampled { DateTime } DateTime ( \"2021-01-01T00:00:00\" ) : Month ( 1 ) : DateTime ( \"2021-12-01T00:00:00\" ) ForwardOrdered Regular Points \n and reference dimensions : \n Y Categorical { Char } Char [ 'b' ] ForwardOrdered \n 2021 - 01 - 01 T00 : 00 : 00 … 2021 - 12 - 01 T00 : 00 : 00 \n 4 0.0 0.0 \n Dimension objects may have lookup and metadata fields to track additional information about the data and the index, and their relationship. source # DimensionalData.Dimensions.DependentDim — Type . DependentDim <: Dimension \n Abstract supertype for Dependent dimensions. These will plot on the Y axis. source # DimensionalData.Dimensions.IndependentDim — Type . IndependentDim <: Dimension \n Abstract supertype for independent dimensions. Thise will plot on the X axis. source # DimensionalData.Dimensions.XDim — Type . XDim <: IndependentDim \n Abstract supertype for all X dimensions. source # DimensionalData.Dimensions.YDim — Type . YDim <: DependentDim \n Abstract supertype for all Y dimensions. source # DimensionalData.Dimensions.ZDim — Type . ZDim <: DependentDim \n Abstract supertype for all Z dimensions. source # DimensionalData.Dimensions.TimeDim — Type . TimeDim <: IndependentDim \n Abstract supertype for all time dimensions. In a TimeDime with Interval sampling the locus will automatically be set to Start() . Dates and times generally refer to the start of a month, hour, second etc., not the central point as is more common with spatial data. ` source # DimensionalData.Dimensions.X — Type . X <: XDim \n\n X ( val =: ) \n X Dimension . X <: XDim <: IndependentDim Example: xdim = X ( 2 : 2 : 10 ) \n # Or \n val = A [ X ( 1 )] \n # Or \n mean ( A ; dims = X ) \n source # DimensionalData.Dimensions.Y — Type . Y <: YDim \n\n Y ( val =: ) \n Y Dimension . Y <: YDim <: DependentDim Example: ydim = Y ([ 'a' , 'b' , 'c' ]) \n # Or \n val = A [ Y ( 1 )] \n # Or \n mean ( A ; dims = Y ) \n source # DimensionalData.Dimensions.Z — Type . Z <: ZDim \n\n Z ( val =: ) \n Z Dimension . Z <: ZDim <: Dimension Example: zdim = Z ( 10 : 10 : 100 ) \n # Or \n val = A [ Z ( 1 )] \n # Or \n mean ( A ; dims = Z ) \n source # DimensionalData.Dimensions.Ti — Type . m Ti <: TimeDim Ti(val=:)\n Time Dimension . Ti <: TimeDim <: IndependentDim Time is already used by Dates, and T is a common type parameter, We use Ti to avoid clashes. Example: timedim = Ti ( DateTime ( 2021 , 1 ) : Month ( 1 ) : DateTime ( 2021 , 12 )) \n # Or \n val = A [ Ti ( 1 )] \n # Or \n mean ( A ; dims = Ti ) \n source # DimensionalData.Dimensions.Dim — Type . Dim { S }( val =: ) \n A generic dimension. For use when custom dims are required when loading data from a file. Can be used as keyword arguments for indexing. Dimension types take precedence over same named Dim types when indexing with symbols, or e.g. creating Tables.jl keys. using DimensionalData \n\n dim = Dim { :custom }([ 'a' , 'b' , 'c' ]) \n\n # output \n\n Dim { :custom } Char [ 'a' , 'b' , 'c' ] \n source # DimensionalData.Dimensions.Coord — Type . Coord <: Dimension \n A coordinate dimension itself holds dimensions. This allows combining point data with other dimensions, such as time. Example julia > using DimensionalData \n\n julia > dim = Coord ([( 1.0 , 1.0 , 1.0 ), ( 1.0 , 2.0 , 2.0 ), ( 3.0 , 4.0 , 4.0 ), ( 1.0 , 3.0 , 4.0 )], ( X (), Y (), Z ())) \n Coord :: \n val : Tuple { Float64 , Float64 , Float64 }[( 1.0 , 1.0 , 1.0 ), ( 1.0 , 2.0 , 2.0 ), ( 3.0 , 4.0 , 4.0 ), ( 1.0 , 3.0 , \n 4.0 )] \n lookup : MergedLookup \n Coord { Vector { Tuple { Float64 , Float64 , Float64 }}, DimensionalData . MergedLookup { Tuple { X { Colon , AutoLookup { Auto \n Order }, NoMetadata }, Y { Colon , AutoLookup { AutoOrder }, NoMetadata }, Z { Colon , AutoLookup { AutoOrder }, NoMetada \n ta }}}, NoMetadata } \n\n julia > da = DimArray ( 0.1 : 0.1 : 0.4 , dim ) \n 4 - element DimArray { Float64 , 1 } with dimensions : \n Coord () : Tuple { Float64 , Float64 , Float64 }[( 1.0 , 1.0 , 1.0 ), ( 1.0 , 2.0 , 2.0 ), ( 3.0 , 4.0 , 4.0 ), ( 1.0 , \n 3.0 , 4.0 )] \n MergedLookup \n 0.1 \n 0.2 \n 0.3 \n 0.4 \n\n julia > da [ Coord ( Z ( At ( 1.0 )), Y ( Between ( 1 , 3 )))] \n 1 - element DimArray { Float64 , 1 } with dimensions : \n Coord () : Tuple { Float64 , Float64 , Float64 }[( 1.0 , 1.0 , 1.0 )] MergedLookup \n 0.1 \n\n julia > da [ Coord ( 4 )] == 0.4 \n true \n\n julia > da [ Coord ( Between ( 1 , 5 ), : , At ( 4.0 ))] \n 2 - element DimArray { Float64 , 1 } with dimensions : \n Coord () : Tuple { Float64 , Float64 , Float64 }[( 3.0 , 4.0 , 4.0 ), ( 1.0 , 3.0 , 4.0 )] MergedLookup \n 0.3 \n 0.4 \n source # DimensionalData.Dimensions.AnonDim — Type . AnonDim <: Dimension \n\n AnonDim () \n Anonymous dimension. Used when extra dimensions are created, such as during transpose of a vector. source # DimensionalData.Dimensions.@dim — Macro . @dim typ [ supertype = Dimension ] [ name :: String = string ( typ )] \n Macro to easily define new dimensions. The supertype will be inserted into the type of the dim. The default is simply YourDim <: Dimension . Making a Dimesion inherit from XDim , YDim , ZDim or TimeDim will affect automatic plot layout and other methods that dispatch on these types. <: YDim are plotted on the Y axis, <: XDim on the X axis, etc. Example: using DimensionalData \n using DimensionalData : @dim , YDim , XDim \n @dim Lat YDim \"latitude\" \n @dim Lon XDim \"Longitude\" \n # output \n source"},{"id":382,"pagetitle":"Reference - DimensionalData.jl","title":"Exported methods ¤","ref":"/DimensionalData/stable/reference/#exported-methods","content":" Exported methods ¤ # DimensionalData.Dimensions.hasdim — Function . hasdim ([ f ], x , query :: Tuple ) => NTUple { Bool } \n hasdim ([ f ], x , query ... ) => NTUple { Bool } \n hasdim ([ f ], x , query ) => Bool \n Check if an object x has dimensions that match or inherit from the query dimensions. Arguments x : any object with a dims method, a Tuple of Dimension or a single Dimension . query : Tuple or single Dimension or dimension Type . f : <: by default, but can be >: to match abstract types to concrete types. Check if an object or tuple contains an Dimension , or a tuple of dimensions. Example julia> using DimensionalData \n\n julia> A = DimArray ( ones ( 10 , 10 , 10 ), ( X , Y , Z )); \n\n julia> hasdim ( A , X ) \n true \n\n julia> hasdim ( A , ( Z , X , Y )) \n (true, true, true) \n\n julia> hasdim ( A , Ti ) \n false \n source # DimensionalData.Dimensions.dimnum — Function . dimnum ( x , query :: Tuple ) => NTuple { Int } \n dimnum ( x , query ) => Int \n Get the number(s) of Dimension (s) as ordered in the dimensions of an object. Arguments x : any object with a dims method, a Tuple of Dimension or a single Dimension . query : Tuple, Array or single Dimension or dimension Type . The return type will be a Tuple of Int or a single Int , depending on wether query is a Tuple or single Dimension . Example julia> using DimensionalData \n\n julia> A = DimArray ( ones ( 10 , 10 , 10 ), ( X , Y , Z )); \n\n julia> dimnum ( A , ( Z , X , Y )) \n (3, 1, 2) \n\n julia> dimnum ( A , Y ) \n 2 \n source"},{"id":383,"pagetitle":"Reference - DimensionalData.jl","title":"Non-exported methods ¤","ref":"/DimensionalData/stable/reference/#non-exported-methods","content":" Non-exported methods ¤ # DimensionalData.Dimensions.lookup — Function . lookup ( x :: Dimension ) => LookupArray \n lookup ( x , [ dims :: Tuple ]) => Tuple { Vararg { LookupArray }} \n lookup ( x :: Tuple ) => Tuple { Vararg { LookupArray }} \n lookup ( x , dim ) => LookupArray \n Returns the LookupArray of a dimension. This dictates properties of the dimension such as array axis and index order, and sampling properties. dims can be a Dimension , a dimension type, or a tuple of either. source # DimensionalData.Dimensions.label — Function . label ( x ) => String \n label ( x , dims :: Tuple ) => NTuple { N , String } \n label ( x , dim ) => String \n label ( xs :: Tuple ) => NTuple { N , String } \n Get a plot label for data or a dimension. This will include the name and units if they exist, and anything else that should be shown on a plot. Second argument dims can be Dimension s, Dimension types, or Symbols for Dim{Symbol} . source # DimensionalData.Dimensions.dim2key — Function . dim2key ( dim :: Dimension ) => Symbol \n dim2key ( dims :: Type { <: Dimension }) => Symbol \n dim2key ( dims :: Tuple ) => Tuple { Symbol , Vararg } \n Convert a dimension object to a simbol. X() , Y() , Ti() etc will be converted. to :X , :Y , :Ti , as with any other dims generated with the @dim macro. All other Dim{S}() dimensions will generate Symbol s S . source # DimensionalData.Dimensions.key2dim — Function . key2dim ( s :: Symbol ) => Dimension \n key2dim ( dims ... ) => Tuple { Dimension , Vararg } \n key2dim ( dims :: Tuple ) => Tuple { Dimension , Vararg } \n Convert a symbol to a dimension object. :X , :Y , :Ti etc will be converted. to X() , Y() , Ti() , as with any other dims generated with the @dim macro. All other Symbol s S will generate Dim{S}() dimensions. source # DimensionalData.Dimensions.dims2indices — Function . dims2indices ( dim :: Dimension , I ) => NTuple { Union { Colon , AbstractArray , Int }} \n Convert a Dimension or Selector I to indices of Int , AbstractArray or Colon . source # DimensionalData.Dimensions.LookupArrays.selectindices — Function . selectindices ( lookups , selectors ) \n Converts Selector to regular indices. source # DimensionalData.Dimensions.format — Function . format ( dims , x ) => Tuple { Vararg { Dimension , N }} \n Format the passed-in dimension(s) dims to match the object x . Errors are thrown if dims don't match the array dims or size, and any fields holding Auto- objects are filled with guessed objects. If a LookupArray hasn't been specified, a lookup is chosen based on the type and element type of the index. source # DimensionalData.Dimensions.reducedims — Function . reducedims ( x , dimstoreduce ) => Tuple { Vararg { Dimension }} \n Replace the specified dimensions with an index of length 1. This is usually to match a new array size where an axis has been reduced with a method like mean or reduce to a length of 1, but the number of dimensions has not changed. LookupArray traits are also updated to correspond to the change in cell step, sampling type and order. source # DimensionalData.Dimensions.swapdims — Function . swapdims ( x :: T , newdims ) => T \n swapdims ( dims :: Tuple , newdims ) => Tuple { Vararg { Dimension }} \n Swap dimensions for the passed in dimensions, in the order passed. Passing in the Dimension types rewraps the dimension index, keeping the index values and metadata, while constructed Dimension objectes replace the original dimension. nothing leaves the original dimension as-is. Arguments x : any object with a dims method or a Tuple of Dimension . newdim : Tuple of Dimension or dimension Type . Example using DimensionalData \n A = ones ( X ( 2 ), Y ( 4 ), Z ( 2 )) \n Dimensions . swapdims ( A , ( Dim { :a }, Dim { :b }, Dim { :c })) \n\n # output \n 2 × 4 × 2 DimArray { Float64 , 3 } with dimensions : Dim { :a }, Dim { :b }, Dim { :c } \n [ : , : , 1 ] \n 1.0 1.0 1.0 1.0 \n 1.0 1.0 1.0 1.0 \n [ and 1 more slices ... ] \n source # DimensionalData.Dimensions.slicedims — Function . slicedims ( x , I ) => Tuple { Tuple , Tuple } \n slicedims ( f , x , I ) => Tuple { Tuple , Tuple } \n Slice the dimensions to match the axis values of the new array. All methods return a tuple conatining two tuples: the new dimensions, and the reference dimensions. The ref dimensions are no longer used in the new struct but are useful to give context to plots. Called at the array level the returned tuple will also include the previous reference dims attached to the array. Arguments f : a function getindex , view or dotview . This will be used for slicing getindex is the default if f is not included. x : An AbstractDimArray , Tuple of Dimension , or Dimension I : A tuple of Integer , Colon or AbstractArray source # DimensionalData.Dimensions.comparedims — Function . comparedims ( A :: AbstractDimArray ... ; kw ... ) \n comparedims ( A :: Tuple ... ; kw ... ) \n comparedims ( A :: Dimension ... ; kw ... ) \n comparedims ( :: Type { Bool }, args ... ; kw ... ) \n Check that dimensions or tuples of dimensions passed as each argument are the same, and return the first valid dimension. If AbstractDimArray s are passed as arguments their dimensions are compared. Empty tuples and nothing dimension values are ignored, returning the Dimension value if it exists. Passing Bool as the first argument means true / false will be returned, rather than throwing an error. Keywords These are all Bool flags: type : compare dimension type, true by default. valtype : compare wrapped value type, false by default. val : compare wrapped values, false by default. order : compare order, false by default. length : compare lengths, true by default. ignore_length_one : ignore length 1 in comparisons, and return whichever dimension is not length 1, if any. This is useful in e.g. broadcasting comparisons. false by default. warn : a String or nothing . Used only for Bool methods, to give a warning for false values and include warn in the warning text. source # DimensionalData.Dimensions.combinedims — Function . combinedims ( xs ; check = true ) \n Combine the dimensions of each object in xs , in the order they are found. source # DimensionalData.Dimensions.otherdims — Function . otherdims ( x , query ) => Tuple { Vararg { Dimension , N }} \n Get the dimensions of an object not in query . Arguments x : any object with a dims method, a Tuple of Dimension . query : Tuple or single Dimension or dimension Type . f : <: by default, but can be >: to match abstract types to concrete types. A tuple holding the unmatched dimensions is always returned. Example julia> using DimensionalData , DimensionalData . Dimensions \n\n julia> A = DimArray ( ones ( 10 , 10 , 10 ), ( X , Y , Z )); \n\n julia> otherdims ( A , X ) \n Y, Z \n\n julia> otherdims ( A , ( Y , Z )) \n X \n source # DimensionalData.Dimensions.commondims — Function . commondims ([ f ], x , query ) => Tuple { Vararg { Dimension }} \n This is basically dims(x, query) where the order of the original is kept, unlike dims where the query tuple determines the order Also unlike dims , commondims always returns a Tuple , no matter the input. No errors are thrown if dims are absent from either x or query . f is <: by default, but can be >: to sort abstract types by concrete types. julia> using DimensionalData , . Dimensions \n\n julia> A = DimArray ( ones ( 10 , 10 , 10 ), ( X , Y , Z )); \n\n julia> commondims ( A , X ) \n X \n\n julia> commondims ( A , ( X , Z )) \n X, Z \n\n julia> commondims ( A , Ti ) \n () \n source # DimensionalData.Dimensions.sortdims — Function . sortdims ([ f ], tosort , order ) => Tuple \n Sort dimensions tosort by order . Dimensions in order but missing from tosort are replaced with nothing . tosort and order can be Tuple s or Vector s or Dimension or dimension type. Abstract supertypes like TimeDim can be used in order . f is <: by default, but can be >: to sort abstract types by concrete types. source # DimensionalData.Dimensions.LookupArrays.basetypeof — Function . basetypeof ( x ) => Type \n Get the \"base\" type of an object - the minimum required to define the object without it's fields. By default this is the full UnionAll for the type. But custom basetypeof methods can be defined for types with free type parameters. In DimensionalData this is primariliy used for comparing Dimension s, where Dim{:x} is different from Dim{:y} . source # DimensionalData.Dimensions.setdims — Function . setdims ( X , newdims ) => AbstractArray \n setdims ( :: Tuple , newdims ) => Tuple { Vararg { Dimension , N }} \n Replaces the first dim matching <: basetypeof(newdim) with newdim, and returns a new object or tuple with the dimension updated. Arguments x : any object with a dims method, a Tuple of Dimension or a single Dimension . newdim : Tuple or single Dimension , Type or Symbol . Example using DimensionalData , DimensionalData . Dimensions , DimensionalData . LookupArrays \n A = ones ( X ( 10 ), Y ( 10 : 10 : 100 )) \n B = setdims ( A , Y ( Categorical ( 'a' : 'j' ; order = ForwardOrdered ()))) \n lookup ( B , Y ) \n # output \n Categorical { Char } ForwardOrdered \n wrapping : 'a' : 1 : 'j' \n source # DimensionalData.Dimensions.dimsmatch — Function . dimsmatch ([ f ], dim , query ) => Bool \n dimsmatch ([ f ], dims :: Tuple , query :: Tuple ) => Bool \n Compare 2 dimensions or Tuple of Dimension are of the same base type, or are at least rotations/transformations of the same type. f is <: by default, but can be >: to match abstract types to concrete types. source # DimensionalData.Dimensions.dimstride — Function . dimstride ( x , dim ) => Int \n Get the stride of the dimension relative to the other dimensions. This may or may not be equal to the stride of the related array, although it will be for Array . Arguments x is any object with a dims method, or a Tuple of Dimension . dim is a Dimension , Dimension type, or and Int . Using an Int is not type-stable. source # DimensionalData.refdims_title — Function . refdims_title ( A :: AbstractDimArray ) \n refdims_title ( refdims :: Tuple ) \n refdims_title ( refdim :: Dimension ) \n Generate a title string based on reference dimension values. source # DimensionalData.rebuild_from_arrays — Function . rebuild_from_arrays ( s :: AbstractDimStack , das :: NamedTuple { <: Any , <: Tuple { Vararg { AbstractDimArray }}}; kw ... ) \n Rebuild an AbstractDimStack from a Tuple or NamedTuple of AbstractDimArray and an existing stack. Keywords Keywords are simply the fields of the stack object: data dims refdims metadata layerdims layermetadata source"},{"id":384,"pagetitle":"Reference - DimensionalData.jl","title":"LookupArrays ¤","ref":"/DimensionalData/stable/reference/#lookuparrays","content":" LookupArrays ¤ # DimensionalData.Dimensions.LookupArrays — Module . LookupArrays \n Module for LookupArrays and [ Selector ]s used in DimensionalData.jl LookupArrays defines traits and AbstractArray wrappers that give specific behaviours for a lookup index when indexed with Selector . For example, these allow tracking over array order so fast indexing works evne when the array is reversed. To load LookupArrays types and methods into scope: using DimensionalData \n using DimensionalData . LookupArrays \n source"},{"id":385,"pagetitle":"Reference - DimensionalData.jl","title":"Selectors ¤","ref":"/DimensionalData/stable/reference/#selectors","content":" Selectors ¤ # DimensionalData.Dimensions.LookupArrays.Selector — Type . Selector \n Abstract supertype for all selectors. Selectors are wrappers that indicate that passed values are not the array indices, but values to be selected from the dimension index, such as DateTime objects for a Ti dimension. Selectors provided in DimensionalData are: At Between Touches Near Where Contains source # DimensionalData.Dimensions.LookupArrays.IntSelector — Type . IntSelector <: Selector \n Abstract supertype for Selector s that return a single Int index. IntSelectors provided by DimensionalData are: At Contains Near source # DimensionalData.Dimensions.LookupArrays.ArraySelector — Type . ArraySelector <: Selector \n Abstract supertype for Selector s that return an AbstractArray . ArraySelectors provided by DimensionalData are: Between Touches Where source # DimensionalData.Dimensions.LookupArrays.At — Type . At <: IntSelector \n\n At ( x , atol , rtol ) \n At ( x ; atol = nothing , rtol = nothing ) \n Selector that exactly matches the value on the passed-in dimensions, or throws an error. For ranges and arrays, every intermediate value must match an existing value - not just the end points. x can be any value or Vector of values. atol and rtol are passed to isapprox . For Number rtol will be set to Base.rtoldefault , otherwise nothing , and wont be used. Example using DimensionalData \n\n A = DimArray ([ 1 2 3 ; 4 5 6 ], ( X ( 10 : 10 : 20 ), Y ( 5 : 7 ))) \n A [ X ( At ( 20 )), Y ( At ( 6 ))] \n\n # output \n\n 5 \n source # DimensionalData.Dimensions.LookupArrays.Near — Type . Near <: IntSelector \n\n Near ( x ) \n Selector that selects the nearest index to x . With Points this is simply the index values nearest to the x , however with Intervals it is the interval center nearest to x . This will be offset from the index value for Start and End loci. Example using DimensionalData \n\n A = DimArray ([ 1 2 3 ; 4 5 6 ], ( X ( 10 : 10 : 20 ), Y ( 5 : 7 ))) \n A [ X ( Near ( 23 )), Y ( Near ( 5.1 ))] \n\n # output \n 4 \n source # DimensionalData.Dimensions.LookupArrays.Between — Type . Between <: ArraySelector \n\n Between ( a , b ) \n Depreciated: use a..b instead of Between(a, b) . Other Interval objects from IntervalSets.jl, like `OpenInterval(a, b) will also work, giving the correct open/closed boundaries. Between will e removed in furture to avoid clashes with DataFrames.Between . Selector that retreive all indices located between 2 values, evaluated with >= for the lower value, and < for the upper value. This means the same value will not be counted twice in 2 adjacent Between selections. For Intervals the whole interval must be lie between the values. For Points the points must fall between the values. Different Sampling types may give different results with the same input - this is the intended behaviour. Between for Irregular intervals is a little complicated. The interval is the distance between a value and the next (for Start locus) or previous (for End locus) value. For Center , we take the mid point between two index values as the start and end of each interval. This may or may not make sense for the values in your indes, so use Between with Irregular Intervals(Center()) with caution. Example using DimensionalData \n\n A = DimArray ([ 1 2 3 ; 4 5 6 ], ( X ( 10 : 10 : 20 ), Y ( 5 : 7 ))) \n A [ X ( Between ( 15 , 25 )), Y ( Between ( 4 , 6.5 ))] \n\n # output \n\n 1 × 2 DimArray { Int64 , 2 } with dimensions : \n X Sampled { Int64 } 20 : 10 : 20 ForwardOrdered Regular Points , \n Y Sampled { Int64 } 5 : 6 ForwardOrdered Regular Points \n 5 6 \n 20 4 5 \n source # DimensionalData.Dimensions.LookupArrays.Touches — Type . Touches <: ArraySelector \n\n Touches ( a , b ) \n Selector that retreives all indices touching the closed interval 2 values, for the maximum possible area that could interact with the supplied range. This can be better than .. when e.g. subsetting an area to rasterize, as you may wish to include pixels that just touch the area, rather than those that fall within it. Touches is different to using closed intervals when the lookups also contain intervals - if any of the intervals touch, they are included. With .. they are discarded unless the whole cell interval falls inside the selector interval. Example using DimensionalData \n\n A = DimArray ([ 1 2 3 ; 4 5 6 ], ( X ( 10 : 10 : 20 ), Y ( 5 : 7 ))) \n A [ X ( Touches ( 15 , 25 )), Y ( Touches ( 4 , 6.5 ))] \n\n # output \n 1 × 2 DimArray { Int64 , 2 } with dimensions : \n X Sampled { Int64 } 20 : 10 : 20 ForwardOrdered Regular Points , \n Y Sampled { Int64 } 5 : 6 ForwardOrdered Regular Points \n 5 6 \n 20 4 5 \n source # DimensionalData.Dimensions.LookupArrays.Contains — Type . Contains <: IntSelector \n\n Contains ( x ) \n Selector that selects the interval the value is contained by. If the interval is not present in the index, an error will be thrown. Can only be used for Intervals or Categorical . For Categorical it falls back to using At . Contains should not be confused with Base.contains - use Where(contains(x)) to check for if values are contain in categorical values like strings. Example using DimensionalData ; const DD = DimensionalData \n dims_ = X ( 10 : 10 : 20 ; sampling = DD . Intervals ( DD . Center ())), \n Y ( 5 : 7 ; sampling = DD . Intervals ( DD . Center ())) \n A = DimArray ([ 1 2 3 ; 4 5 6 ], dims_ ) \n A [ X ( Contains ( 8 )), Y ( Contains ( 6.8 ))] \n\n # output \n 3 \n source # DimensionalData.Dimensions.LookupArrays.Where — Type . Where <: ArraySelector \n\n Where ( f :: Function ) \n Selector that filters a dimension lookup by any function that accepts a single value and returns a Bool . Example using DimensionalData \n\n A = DimArray ([ 1 2 3 ; 4 5 6 ], ( X ( 10 : 10 : 20 ), Y ( 19 : 21 ))) \n A [ X ( Where ( x -> x > 15 )), Y ( Where ( x -> x in ( 19 , 21 )))] \n\n # output \n\n 1 × 2 DimArray { Int64 , 2 } with dimensions : \n X Sampled { Int64 } Int64 [ 20 ] ForwardOrdered Regular Points , \n Y Sampled { Int64 } Int64 [ 19 , 21 ] ForwardOrdered Regular Points \n 19 21 \n 20 4 6 \n source # DimensionalData.Dimensions.LookupArrays.All — Type . All <: Selector \n\n All ( selectors :: Selector ... ) \n Selector that combines the results of other selectors. The indices used will be the union of all result sorted in ascending order. Example using DimensionalData , Unitful \n\n dimz = X ( 10.0 : 20 : 200.0 ), Ti ( 1 u \"s\" : 5 u \"s\" : 100 u \"s\" ) \n A = DimArray (( 1 : 10 ) * ( 1 : 20 ) ' , dimz ) \n A [ X = All ( At ( 10.0 ), At ( 50.0 )), Ti = All ( 1 u \"s\" .. 10 u \"s\" , 90 u \"s\" .. 100 u \"s\" )] \n\n # output \n\n 2 × 4 DimArray { Int64 , 2 } with dimensions : \n X Sampled { Float64 } Float64 [ 10.0 , 50.0 ] ForwardOrdered Regular Points , \n Ti Sampled { Quantity { Int64 , 𝐓 , Unitful . FreeUnits {( s ,), 𝐓 , nothing }}} Quantity { Int64 , 𝐓 , Unitful . FreeUnits {( s ,), 𝐓 , nothing }}[ 1 s , 6 s , 91 s , 96 s ] ForwardOrdered Regular Points \n 1 s 6 s 91 s 96 s \n 10.0 1 2 19 20 \n 50.0 3 6 57 60 \n source Lookup properties: # DimensionalData.Dimensions.LookupArrays.bounds — Function . bounds ( xs , [ dims :: Tuple ]) => Tuple { Vararg { Tuple { T , T }}} \n bounds ( xs :: Tuple ) => Tuple { Vararg { Tuple { T , T }}} \n bounds ( x , dim ) => Tuple { T , T } \n bounds ( dim :: Union { Dimension , LookupArray }) => Tuple { T , T } \n Return the bounds of all dimensions of an object, of a specific dimension, or of a tuple of dimensions. If bounds are not known, one or both values may be nothing . dims can be a Dimension , a dimension type, or a tuple of either. source # DimensionalData.Dimensions.LookupArrays.val — Function . val ( x ) \n val ( dims :: Tuple ) => Tuple \n Return the contained value of a wrapper object. dims can be Dimension , Dimension types, or Symbols for Dim{Symbol} . Objects that don't define a val method are returned unaltered. source # DimensionalData.Dimensions.LookupArrays.LookupArray — Type . LookupArray \n Types defining the behaviour of a lookup index, how it is plotted and how Selector s like Between work. A LookupArray may be NoLookup indicating that the index is just the underlying array axis, Categorical for ordered or unordered categories, or a Sampled index for Points or Intervals . source # DimensionalData.Dimensions.LookupArrays.Aligned — Type . Aligned <: LookupArray \n Abstract supertype for LookupArray s where the index is aligned with the array axes. This is by far the most common supertype for LookupArray . source # DimensionalData.Dimensions.LookupArrays.AbstractSampled — Type . AbstractSampled <: Aligned \n Abstract supertype for LookupArray s where the index is aligned with the array, and is independent of other dimensions. Sampled is provided by this package. AbstractSampled must have order , span and sampling fields, or a rebuild method that accpts them as keyword arguments. source # DimensionalData.Dimensions.LookupArrays.Sampled — Type . Sampled <: AbstractSampled \n\n Sampled ( data :: AbstractVector , order :: Order , span :: Span , sampling :: Sampling , metadata ) \n Sampled ( data = AutoIndex (); order = AutoOrder (), span = AutoSpan (), sampling = Points (), metadata = NoMetadata ()) \n A concrete implementation of the LookupArray AbstractSampled . It can be used to represent Points or Intervals . Sampled is capable of representing gridded data from a wide range of sources, allowing correct bounds and Selector s for points or intervals of regular, irregular, forward and reverse indexes. On AbstractDimArray construction, Sampled lookup is assigned for all lookups of AbstractRange not assigned to Categorical . Arguments data : An AbstractVector of index values, matching the length of the curresponding array axis. order : Order ) indicating the order of the index, AutoOrder by default, detected from the order of data to be ForwardOrdered , ReverseOrdered or Unordered . These can be provided explicitly if they are known and performance is important. span : indicates the size of intervals or distance between points, and will be set to Regular for AbstractRange and Irregular for AbstractArray , unless assigned manually. sampling : is assigned to Points , unless set to Intervals manually. Using Intervals will change the behaviour of bounds and Selectors s to take account for the full size of the interval, rather than the point alone. metadata : a Dict or Metadata wrapper that holds any metadata object adding more information about the array axis - useful for extending DimensionalData for specific contexts, like geospatial data in GeoData.jl. By default it is NoMetadata() . Example Create an array with [ Interval ] sampling, and Regular span for a vector with known spacing. We set the Locus of the Intervals to Start specifying that the index values are for the positions at the start of each interval. using DimensionalData , DimensionalData . LookupArrays \n\n x = X ( Sampled ( 100 :- 20 : 10 ; sampling = Intervals ( Start ()))) \n y = Y ( Sampled ([ 1 , 4 , 7 , 10 ]; span = Regular ( 3 ), sampling = Intervals ( Start ()))) \n A = ones ( x , y ) \n\n # output \n 5 × 4 DimArray { Float64 , 2 } with dimensions : \n X Sampled { Int64 } 100 :- 20 : 20 ReverseOrdered Regular Intervals , \n Y Sampled { Int64 } Int64 [ 1 , 4 , 7 , 10 ] ForwardOrdered Regular Intervals \n 1 4 7 10 \n 100 1.0 1.0 1.0 1.0 \n 80 1.0 1.0 1.0 1.0 \n 60 1.0 1.0 1.0 1.0 \n 40 1.0 1.0 1.0 1.0 \n 20 1.0 1.0 1.0 1.0 \n source # DimensionalData.Dimensions.LookupArrays.AbstractCyclic — Type . AbstractCyclic <: AbstractSampled end \n An abstract supertype for cyclic lookups. These are AbstractSampled lookups that are cyclic for Selectors . source # DimensionalData.Dimensions.LookupArrays.Cyclic — Type . Cyclic <: AbstractCyclic \n\n Cyclic ( data ; order = AutoOrder (), span = AutoSpan (), sampling = Points (), metadata = NoMetadata (), cycle ) \n A Cyclic lookup is similar to Sampled but out of range Selectors At , Near , Contains will cycle the values to typemin or typemax over the length of cycle . Where and .. work as for Sampled . This is useful when we are using mean annual datasets over a real time-span, or for wrapping longitudes so that -360 and 360 are the same. Arguments data : An AbstractVector of index values, matching the length of the curresponding array axis. order : Order ) indicating the order of the index, AutoOrder by default, detected from the order of data to be ForwardOrdered , ReverseOrdered or Unordered . These can be provided explicitly if they are known and performance is important. span : indicates the size of intervals or distance between points, and will be set to Regular for AbstractRange and Irregular for AbstractArray , unless assigned manually. sampling : is assigned to Points , unless set to Intervals manually. Using Intervals will change the behaviour of bounds and Selectors s to take account for the full size of the interval, rather than the point alone. metadata : a Dict or Metadata wrapper that holds any metadata object adding more information about the array axis - useful for extending DimensionalData for specific contexts, like geospatial data in GeoData.jl. By default it is NoMetadata() . cycle : the length of the cycle. This does not have to exactly match the data, the step size is Week(1) the cycle can be Years(1) . Notes If you use dates and e.g. cycle over a Year , every year will have the number and spacing of Week s and Day s as the cycle year. Using At may not be reliable in terms of exact dates, as it will be applied to the specified date plus or minus n years. Indexing into a Cycled with any AbstractArray or AbstractRange will return a Sampled as the full cycle is likely no longer available. .. or Between selectors do not work in a cycled way: they work as for Sampled . This may change in future to return cycled values, but there are problems with this, such as leap years breaking correct date cycling of a single year. If you actually need this behaviour, please make a GitHub issue. source # DimensionalData.Dimensions.LookupArrays.AbstractCategorical — Type . AbstractCategorical <: Aligned \n LookupArray s where the values are categories. Categorical is the provided concrete implementation. but this can easily be extended - all methods are defined for AbstractCategorical . All AbstractCategorical must provide a rebuild method with data , order and metadata keyword arguments. source # DimensionalData.Dimensions.LookupArrays.Categorical — Type . Categorical <: AbstractCategorical \n\n Categorical ( o :: Order ) \n Categorical (; order = Unordered ()) \n An LookupArray where the values are categories. This will be automatically assigned if the index contains AbstractString , Symbol or Char . Otherwise it can be assigned manually. Order will be determined automatically where possible. Arguments data : An AbstractVector of index values, matching the length of the curresponding array axis. order : Order ) indicating the order of the index, AutoOrder by default, detected from the order of data to be ForwardOrdered , ReverseOrdered or Unordered . Can be provided if this is known and performance is important. metadata : a Dict or Metadata wrapper that holds any metadata object adding more information about the array axis - useful for extending DimensionalData for specific contexts, like geospatial data in GeoData.jl. By default it is NoMetadata() . Example Create an array with [ Interval ] sampling. using DimensionalData \n\n ds = X ([ \"one\" , \"two\" , \"three\" ]), Y ([ :a , :b , :c , :d ]) \n A = DimArray ( rand ( 3 , 4 ), ds ) \n Dimensions . lookup ( A ) \n\n # output \n\n Categorical { String } String [ \"one\" , \"two\" , \"three\" ] Unordered , \n Categorical { Symbol } Symbol [ :a , :b , :c , :d ] ForwardOrdered \n source # DimensionalData.Dimensions.LookupArrays.Unaligned — Type . Unaligned <: LookupArray \n Abstract supertype for LookupArray where the index is not aligned to the grid. Indexing an Unaligned with Selector s must provide all other Unaligned dimensions. source # DimensionalData.Dimensions.LookupArrays.Transformed — Type . Transformed <: Unaligned \n\n Transformed ( f , dim :: Dimension ; metadata = NoMetadata ()) \n LookupArray that uses an affine transformation to convert dimensions from dims(lookup) to dims(array) . This can be useful when the dimensions are e.g. rotated from a more commonly used axis. Any function can be used to do the transformation, but transformations from CoordinateTransformations.jl may be useful. Arguments f : transformation function dim : a dimension to transform to. Keyword Arguments metdata : Example using DimensionalData , DimensionalData . LookupArrays , CoordinateTransformations \n\n m = LinearMap ([ 0.5 0.0 ; 0.0 0.5 ]) \n A = [ 1 2 3 4 \n 5 6 7 8 \n 9 10 11 12 ]; \n da = DimArray ( A , ( t1 = Transformed ( m , X ), t2 = Transformed ( m , Y ))) \n\n da [ X ( At ( 6 )), Y ( At ( 2 ))] \n\n # output \n 9 \n source # DimensionalData.Dimensions.MergedLookup — Type . MergedLookup <: LookupArray \n\n MergedLookup ( data , dims ; [ metadata ]) \n A LookupArray that holds multiple combined dimensions. MergedLookup can be indexed with Selector s like At , Between , and Where although Near has undefined meaning. Arguments data : A Vector of Tuple . dims : A Tuple of Dimension indicating the dimensions in the tuples in data . Keywords metadata : a Dict or Metadata object to attach dimension metadata. source # DimensionalData.Dimensions.LookupArrays.NoLookup — Type . NoLookup <: LookupArray \n\n NoLookup () \n A LookupArray that is identical to the array axis. Selector s can't be used on this lookup. Example Defining a DimArray without passing an index to the dimensions, it will be assigned NoLookup : using DimensionalData \n\n A = DimArray ( rand ( 3 , 3 ), ( X , Y )) \n Dimensions . lookup ( A ) \n\n # output \n\n NoLookup , NoLookup \n Which is identical to: using . LookupArrays \n A = DimArray ( rand ( 3 , 3 ), ( X ( NoLookup ()), Y ( NoLookup ()))) \n Dimensions . lookup ( A ) \n\n # output \n\n NoLookup , NoLookup \n source # DimensionalData.Dimensions.LookupArrays.AutoLookup — Type . AutoLookup <: LookupArray \n\n AutoLookup () \n AutoLookup ( index = AutoIndex (); kw ... ) \n Automatic LookupArray , the default lookup. It will be converted automatically to another LookupArray when it is possible to detect it from the index. Keywords will be used in the detected LookupArray constructor. source # DimensionalData.Dimensions.LookupArrays.AutoIndex — Type . AutoIndex \n Detect a LookupArray index from the context. This is used in NoLookup to simply use the array axis as the index when the array is constructed, and in set to change the LookupArray type without changing the index values. source"},{"id":386,"pagetitle":"Reference - DimensionalData.jl","title":"Metadata ¤","ref":"/DimensionalData/stable/reference/#metadata","content":" Metadata ¤ # DimensionalData.Dimensions.LookupArrays.AbstractMetadata — Type . AbstractMetadata { X , T } \n Abstract supertype for all metadata wrappers. Metadata wrappers allow tracking the contents and origin of metadata. This can facilitate conversion between metadata types (for saving a file to a differenet format) or simply saving data back to the same file type with identical metadata. Using a wrapper instead of Dict or NamedTuple also lets us pass metadata objects to set without ambiguity about where to put them. source # DimensionalData.Dimensions.LookupArrays.Metadata — Type . Metadata <: AbstractMetadata \n\n Metadata { X }( val :: Union { Dict , NamedTuple }) \n Metadata { X }( pairs :: Pair ... ) => Metadata { Dict } \n Metadata { X }(; kw ... ) => Metadata { NamedTuple } \n General Metadata object. The X type parameter categorises the metadata for method dispatch, if required. source # DimensionalData.Dimensions.LookupArrays.NoMetadata — Type . NoMetadata <: AbstractMetadata \n\n NoMetadata () \n Indicates an object has no metadata. But unlike using nothing , get , keys and haskey will still work on it, get always returning the fallback argument. keys returns () while haskey always returns false . source"},{"id":387,"pagetitle":"Reference - DimensionalData.jl","title":"LookupArray traits ¤","ref":"/DimensionalData/stable/reference/#lookuparray-traits","content":" LookupArray traits ¤ # DimensionalData.Dimensions.LookupArrays.LookupArrayTrait — Type . LookupArrayTrait \n Abstract supertype of all traits of a LookupArray . These modify the behaviour of the lookup index. The term \"Trait\" is used loosely - these may be fields of an object of traits hard-coded to specific types. source"},{"id":388,"pagetitle":"Reference - DimensionalData.jl","title":"Order ¤","ref":"/DimensionalData/stable/reference/#order","content":" Order ¤ # DimensionalData.Dimensions.LookupArrays.Order — Type . Order <: LookupArrayTrait \n Traits for the order of a LookupArray . These determine how searchsorted finds values in the index, and how objects are plotted. source # DimensionalData.Dimensions.LookupArrays.Ordered — Type . Ordered <: Order \n Supertype for the order of an ordered LookupArray , including ForwardOrdered and ReverseOrdered . source # DimensionalData.Dimensions.LookupArrays.ForwardOrdered — Type . ForwardOrdered <: Ordered \n\n ForwardOrdered () \n Indicates that the LookupArray index is in the normal forward order. source # DimensionalData.Dimensions.LookupArrays.ReverseOrdered — Type . ReverseOrdered <: Ordered \n\n ReverseOrdered () \n Indicates that the LookupArray index is in the reverse order. source # DimensionalData.Dimensions.LookupArrays.Unordered — Type . Unordered <: Order \n\n Unordered () \n Indicates that LookupArray is unordered. This means the index cannot be searched with searchsortedfirst or similar optimised methods - instead it will use findfirst . source # DimensionalData.Dimensions.LookupArrays.AutoOrder — Type . AutoOrder <: Order \n\n AutoOrder () \n Specifies that the Order of a LookupArray will be found automatically where possible. source"},{"id":389,"pagetitle":"Reference - DimensionalData.jl","title":"Span ¤","ref":"/DimensionalData/stable/reference/#span","content":" Span ¤ # DimensionalData.Dimensions.LookupArrays.Span — Type . Span <: LookupArrayTrait \n Defines the type of span used in a Sampling index. These are Regular or Irregular . source # DimensionalData.Dimensions.LookupArrays.Regular — Type . Regular <: Span \n\n Regular ( step = AutoStep ()) \n Points or Intervals that have a fixed, regular step. source # DimensionalData.Dimensions.LookupArrays.Irregular — Type . Irregular <: Span \n\n Irregular ( bounds :: Tuple ) \n Irregular ( lowerbound , upperbound ) \n Points or Intervals that have an Irrigular step size. To enable bounds tracking and accuract selectors, the starting bounds are provided as a 2 tuple, or 2 arguments. (nothing, nothing) is acceptable input, the bounds will be guessed from the index, but may be innaccurate. source # DimensionalData.Dimensions.LookupArrays.Explicit — Type . Explicit ( bounds :: AbstractMatix ) \n Intervals where the span is explicitly listed for every interval. This uses a matrix where with length 2 columns for each index value, holding the lower and upper bounds for that specific index. source # DimensionalData.Dimensions.LookupArrays.AutoSpan — Type . AutoSpan <: Span \n\n AutoSpan () \n The span will be guessed and replaced in format or set . source"},{"id":390,"pagetitle":"Reference - DimensionalData.jl","title":"Sampling ¤","ref":"/DimensionalData/stable/reference/#sampling","content":" Sampling ¤ # DimensionalData.Dimensions.LookupArrays.Sampling — Type . Sampling <: LookupArrayTrait \n Indicates the sampling method used by the index: Points or Intervals . source # DimensionalData.Dimensions.LookupArrays.Points — Type . Points <: Sampling \n\n Points () \n Sampling lookup where single samples at exact points. These are always plotted at the center of array cells. source # DimensionalData.Dimensions.LookupArrays.Intervals — Type . Intervals <: Sampling \n\n Intervals ( locus :: Locus ) \n Sampling specifying that sampled values are the mean (or similar) value over an interval , rather than at one specific point. Intervals require a Locus of Start , Center or End to define the location in the interval that the index values refer to. source"},{"id":391,"pagetitle":"Reference - DimensionalData.jl","title":"Loci ¤","ref":"/DimensionalData/stable/reference/#loci","content":" Loci ¤ # DimensionalData.Dimensions.LookupArrays.Locus — Type . Locus <: LookupArrayTrait Abstract supertype of types that indicate the position of index values where they represent Intervals . These allow for values array cells to align with the Start , Center , or End of values in the lookup index. This means they can be plotted with correct axis markers, and allows automatic converrsions to between formats with different standards (such as NetCDF and GeoTiff). source # DimensionalData.Dimensions.LookupArrays.Center — Type . Center <: Locus \n\n Center () \n Indicates a lookup value is for the center of its corresponding array cell. source # DimensionalData.Dimensions.LookupArrays.Start — Type . Start <: Locus \n\n Start () \n Indicates a lookup value is for the start of its corresponding array cell, in the direction of the lookup index order. source # DimensionalData.Dimensions.LookupArrays.End — Type . End <: Locus \n\n End () \n Indicates a lookup value is for the end of its corresponding array cell, in the direction of the lookup index order. source # DimensionalData.Dimensions.LookupArrays.AutoLocus — Type . AutoLocus <: Locus \n\n AutoLocus () \n Indicates a interval where the index position is not yet known. This will be filled with a default value on object construction. source"},{"id":392,"pagetitle":"Reference - DimensionalData.jl","title":"LookupArrays methods ¤","ref":"/DimensionalData/stable/reference/#lookuparrays-methods","content":" LookupArrays methods ¤ # DimensionalData.Dimensions.LookupArrays.hasselection — Function . hasselection ( x , selector ) => Bool \n hasselection ( x , selectors :: Tuple ) => Bool \n Check if indexing into x with selectors can be performed, where x is some object with a dims method, and selectors is a Selector or Dimension or a tuple of either. source # DimensionalData.Dimensions.LookupArrays.shiftlocus — Function . shiftlocus ( locus :: Locus , x ) \n Shift the index of x from the current locus to the new locus. We only shift Sampled , Regular or Explicit , Intervals . source # DimensionalData.Dimensions.LookupArrays.sampling — Function . sampling ( x , [ dims :: Tuple ]) => Tuple \n sampling ( x , dim ) => Sampling \n sampling ( xs :: Tuple ) => Tuple { Vararg { Sampling }} \n sampling ( x : Union { Dimension , LookupArray }) => Sampling \n Return the Sampling for each dimension. Second argument dims can be Dimension s, Dimension types, or Symbols for Dim{Symbol} . source # DimensionalData.Dimensions.LookupArrays.span — Function . span ( x , [ dims :: Tuple ]) => Tuple \n span ( x , dim ) => Span \n span ( xs :: Tuple ) => Tuple { Vararg { Span , N }} \n span ( x :: Union { Dimension , LookupArray }) => Span \n Return the Span for each dimension. Second argument dims can be Dimension s, Dimension types, or Symbols for Dim{Symbol} . source # DimensionalData.Dimensions.LookupArrays.order — Function . order ( x , [ dims :: Tuple ]) => Tuple \n order ( xs :: Tuple ) => Tuple \n order ( x :: Union { Dimension , LookupArray }) => Order \n Return the Ordering of the dimension index for each dimension: ForwardOrdered , ReverseOrdered , or Unordered Second argument dims can be Dimension s, Dimension types, or Symbols for Dim{Symbol} . source # DimensionalData.Dimensions.LookupArrays.index — Function . index ( x ) => Tuple { Vararg { AbstractArray }} \n index ( x , dims :: Tuple ) => Tuple { Vararg { AbstractArray }} \n index ( dims :: Tuple ) => Tuple { Vararg { AbstractArray }} } \n index ( x , dim ) => AbstractArray \n index ( dim :: Dimension ) => AbstractArray \n Return the contained index of a Dimension . Only valid when a Dimension contains an AbstractArray or a Val tuple like Val{(:a, :b)}() . The Val is unwrapped to return just the Tuple dims can be a Dimension , or a tuple of Dimension . source # DimensionalData.Dimensions.LookupArrays.locus — Function . locus ( x , [ dims :: Tuple ]) => Tuple \n locus ( x , dim ) => Locus \n locus ( xs :: Tuple ) => Tuple { Vararg { Locus , N }} \n locus ( x :: Union { Dimension , LookupArray }) => Locus \n Return the Locus for each dimension. Second argument dims can be Dimension s, Dimension types, or Symbols for Dim{Symbol} . source # DimensionalData.Dimensions.LookupArrays.units — Function . units ( x ) => Union { Nothing , Any } \n units ( xs : Tuple ) => Tuple \n unit ( A :: AbstractDimArray , dims :: Tuple ) => Tuple \n unit ( A :: AbstractDimArray , dim ) => Union { Nothing , Any } \n Get the units of an array or Dimension , or a tuple of of either. Units do not have a set field, and may or may not be included in metadata . This method is to facilitate use in labels and plots when units are available, not a guarantee that they will be. If not available, nothing is returned. Second argument dims can be Dimension s, Dimension types, or Symbols for Dim{Symbol} . source"},{"id":393,"pagetitle":"Reference - DimensionalData.jl","title":"Name ¤","ref":"/DimensionalData/stable/reference/#name","content":" Name ¤ # DimensionalData.AbstractName — Type . AbstractName \n Abstract supertype for name wrappers. source # DimensionalData.Name — Type . Name <: AbstractName \n\n Name ( name :: Union { Symbol , Name ) => Name \n Name ( name :: NoName ) => NoName \n Name wrapper. This lets arrays keep symbol names when the array wrapper neeeds to be `isbits, like for use on GPUs. It makes the name a property of the type. It's not necessary to use in normal use, a symbol is probably easier. source # DimensionalData.NoName — Type . NoName <: AbstractName \n\n NoName () \n NoName specifies an array is not named, and is the default name value for all AbstractDimArray s. source"}] \ No newline at end of file diff --git a/search-data/content.map.json b/search-data/content.map.json index bb17d517b..8ef38d23b 100644 --- a/search-data/content.map.json +++ b/search-data/content.map.json @@ -1 +1 @@ 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