Example of applying the FSSD goodness-of-fit test to a ChiSq distribution using Log as as push-forward.

FSSD_gof_pushforward.jl

julia> using Bijectors

julia> using KernelGoodnessOfFit

julia> using Random; Random.seed!(123);

julia> using ForwardDiff

julia> function Distributions.gradlogpdf(d::ContinuousUnivariateDistribution, x::Real)
           ForwardDiff.derivative(z -> logpdf(d, z), x)
       end

julia> p = Chisq(2)         # true distribution
Chisq{Float64}(ν=2.0)

julia> td = transformed(p)    # transformed
Bijectors.TransformedDistribution{Chisq{Float64},Bijectors.Log{0},Univariate,0}(
dist: Chisq{Float64}(ν=2.0)
transform: Bijectors.Log{0}()
)

julia> α = 0.05               # size of the test
0.05

julia> n = 200                # number of samples
200

julia> num_experiments = 100  # number of experiments to run
100

julia> # Under H₀: p = q
       total = 0.0            # rejection ratio
0.0

julia> for i = 1:num_experiments
           xs = reshape(rand(p, n), 1, :)
           ys = td.transform.(xs)

           res = FSSDopt(ys, td; β_H₁ = 0.01)

           global total
           total += res.p_val ≤ α
       end

julia> total / num_experiments
0.05

julia> (total / num_experiments) ≤ α
true