From 831d5cdc2d6f20147d4669e1c523adaf14b57be9 Mon Sep 17 00:00:00 2001
From: WawerOS <lion@waposta.com>
Date: Tue, 19 Apr 2022 03:28:42 -0500
Subject: [PATCH 1/2] Added a implementation of likelihood for the Student t
 distribution

---
 src/likelihoods/studentt.jl | 14 ++++++++++++++
 1 file changed, 14 insertions(+)
 create mode 100644 src/likelihoods/studentt.jl

diff --git a/src/likelihoods/studentt.jl b/src/likelihoods/studentt.jl
new file mode 100644
index 00000000..c672f703
--- /dev/null
+++ b/src/likelihoods/studentt.jl
@@ -0,0 +1,14 @@
+
+using SpecialFunctions :: logbeta
+using IrrationalConstants :: logπ, 
+
+struct StudentTLikelihood{T<:Real, Tn :: Real} <: AbstractLikelihood
+    σ²::Vector{T}
+    ν::Vector{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) )
+end
\ No newline at end of file

From f5d4d3e099b847242bda2dd4ff6c1d0f3be459cf Mon Sep 17 00:00:00 2001
From: WawerOS <lion@waposta.com>
Date: Tue, 19 Apr 2022 03:46:28 -0500
Subject: [PATCH 2/2] added come documentation

---
 src/likelihoods/studentt.jl | 19 +++++++++++++++++--
 1 file changed, 17 insertions(+), 2 deletions(-)

diff --git a/src/likelihoods/studentt.jl b/src/likelihoods/studentt.jl
index c672f703..fafd0046 100644
--- a/src/likelihoods/studentt.jl
+++ b/src/likelihoods/studentt.jl
@@ -2,6 +2,18 @@
 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
+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}
@@ -10,5 +22,8 @@ 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) )
-end
\ No newline at end of file
+    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))
+end
+
+
+default_expectation_method(::StudentTLikelihood) = AnalyticExpectation()
\ No newline at end of file