Implement Analytic Likelihood for Student's T Distribution #81
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theogf
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Apr 19, 2022
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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) | ||
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| 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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| 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 |
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| 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 |
| 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
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