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Implement Analytic Likelihood for Student's T Distribution #81

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Implement Analytic Likelihood for Student's T Distribution #81

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831d5cd
Added a implementation of likelihood for the Student t distribution
WawerOS Apr 19, 2022
f5d4d3e
added come documentation
WawerOS Apr 19, 2022
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29 changes: 29 additions & 0 deletions src/likelihoods/studentt.jl
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using SpecialFunctions :: logbeta
using IrrationalConstants :: logπ,
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You only need one :

Suggested change
using SpecialFunctions :: logbeta
using IrrationalConstants :: logπ,
using SpecialFunctions: logbeta
using IrrationalConstants: logπ,



"""
StudentTLikelihood(σ²,ν)

Student's T likelihood with `σ²` scale and ν degrees of freedom . This is to be used if we assume that the
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Suggested change
Student's T likelihood with `σ²` scale and ν degrees of freedom . This is to be used if we assume that the
Student's T likelihood with scale `σ²` and `ν` degrees of freedom. This is to be used if we assume that the

uncertainity associated with the data follows a Student's T distribution.

```math
p(y|f) = \\operatorname{Student}(y | f, σ², ν)
```
"""

struct StudentTLikelihood{T<:Real, Tn :: Real} <: AbstractLikelihood
σ²::Vector{T}
ν::Vector{Tn}
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We tend to change the implementation to avoid storing everything in Vector (I know it's not true for GaussianLikelihood but it should change).

Suggested change
σ²::Vector{T}
ν::Vector{Tn}
σ²::T
ν::Tn

end

function expected_loglikelihood( ::AnalyticExpectation,lik::StudentTLikelihood,q_f :: AbstractVector{<:Normal}, y :: AbstractVector{<:Real})
f_μ = mean.(q_f)
# Why?
return sum(-logbeta(0.5,0.5*lik.ν) .- 0.5*logπ .- 0.5*log(lik.ν) .- log(lik.σ²) .- (0.5*(lik.ν+1))*log.(1 .+ ((y .- f_μ).^2 + var.(q_f)) / lik.σ²))
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I am not sure that this is correct. The expectation of `log( (y - f)^2) is not available analytically I think

end


default_expectation_method(::StudentTLikelihood) = AnalyticExpectation()