From 7234054e22304f32fe091cb09363a038ab36482c Mon Sep 17 00:00:00 2001
From: Riccardo Buscicchio <riccardo.buscicchio@unimib.it>
Date: Mon, 7 Apr 2025 21:41:18 +0200
Subject: [PATCH] feat: univariate Gaussian likelihood in Gaussian prior

---
 src/models/Models.jl                     |  1 +
 src/models/univariategaussiangaussian.jl | 37 ++++++++++++++++++++++++
 2 files changed, 38 insertions(+)
 create mode 100644 src/models/univariategaussiangaussian.jl

diff --git a/src/models/Models.jl b/src/models/Models.jl
index a89a0ffc..369108de 100644
--- a/src/models/Models.jl
+++ b/src/models/Models.jl
@@ -15,5 +15,6 @@ using LogExpFunctions
 include("shells.jl")
 include("correlated.jl")
 include("eggbox.jl")
+include("univariagaussiangaussian.jl")
 
 end # module
diff --git a/src/models/univariategaussiangaussian.jl b/src/models/univariategaussiangaussian.jl
new file mode 100644
index 00000000..7c4f70c0
--- /dev/null
+++ b/src/models/univariategaussiangaussian.jl
@@ -0,0 +1,37 @@
+using Distributions
+using NestedSamplers
+using StatsBase
+
+@doc raw"""
+Models.UnivariateGaussianGaussian()
+
+Creates a model with Normal prior and Normal likelihood.
+
+```math
+\mathbf\theta \sim \mathcal{N}\left(\mu_p, \sigma_p\right)
+```
+```math
+\mathbf{d} \sim \mathcal{N}\left(\mathbf\theta, \sigma_d\right)
+```
+the analytical evidence of the model is
+
+```math
+Z = \mathcal{N}\left(\mu_p, \sqrt{\sigma_p^2 + \sigma_d^2}\right)
+```
+
+## Examples
+```jldoctest
+julia> model, lnZ = Models.UnivariateNormalNormal(2, 0.5, 1, 0);
+
+julia> lnZ
+-2.6305103088617776
+```
+"""
+
+function UnivariateGaussianGaussian(μp::Float64, σp::Float64, σd::Float64, d::Float64=0.0)
+    priors = [Normal(μp, σp)]                   # θ ~ N(μ, σ)
+    loglike(θ) = logpdf(Normal(d, σd),θ[1])     # d ~ N(θ, σd)
+    model = NestedModel(loglike, priors)
+    true_lnZ = logpdf(Normal(μp, sqrt(σp^2 + σd^2)), d) # lnZ is analytical in the data and the prior hyperparameters
+    return model, true_lnZ
+end