Everything is subject to change, including type names and type hierarchy.
We try to cover a core set of usages common in HEP, namely, fitting one or multiple distributions to binned data, using Chi2 or Likelihood objective.
Conceptually, given user defined function ("shape"), we can treat it as if it's a PDF by numerically normalizing it at every evaluating point. We then package that with a user defined histogram using the FHist package which can be used with an optimization or plotting package.
The following code provides a framework for optimizing a single function with any number of parameters. The guess must be relatively close to the real parameters.
using BinnedDistributionFit, FHist, Optimization, ForwardDiff, ComponentArrays
function fit_pdf_to_hist(hist::Hist1D, pdf, guess::Vector)
support = extrema(binedges(hist))
NLL = LikelihoodSpec(ExtendPdf(pdf, support), hist)
opt_f = OptimizationFunction(NLL, AutoForwardDiff())
opt_p = OptimizationProblem(opt_f, ComponentArray(norms = integral(hist), p1 = guess))
sol = solve(opt_p, Optimization.LBFGS())
return sol.u
end
# Example
hist = Hist1D(; binedges=1:2:21, bincounts=[1:4; 1; 6:10])
pdf_input(x, ps) = ps[1]*x + ps[2]
guess = [5, 5]
fit_pdf_to_hist(hist, pdf_input, guess)
# output
ComponentVector{Float64}(norms = 51.0, p1 = [6.975319732308675, -0.8718290560996027])For main.py and main.jl (just the ExtendPdf)
if you change the observed bincounts from [2.0, 4.0] to [4.0, 8.0], the NLL becomes 1.3655798792934464
If on top of that, you also change p0 from 2.0 to 4.0, you get NLL -4.952186287425897
