Student-T GP Augmented model model

studentt.jl

using Turing
using MLKernels
using LinearAlgebra

N=100
X = sort(rand(N,1),1) #Create some data
K = kernelmatrix(SquaredExponentialKernel(100.0),X) #Kernel matrix
y = rand(MvNormal(zeros(N),K+1e-1I)) #Sample from the GP prior with some noise

# Model representing Student-T Likelihood => Normal(y|f,omega)IG(omega|nu/2,nu/2)
@model augmentedmodel(K,y,nu,f=ones(N)) = begin
  omega = Vector{Real}(undef,N)
  for i in 1:N
    omega[i] ~ InverseGamma(0.5*(nu+1.0),0.5*(nu+(y[i]-f[i])^2))
  end
  Sigma = Symmetric(inv(Diagonal(inv.(omega))+inv(K+1e-3I))) #Jittering is added on K
  f ~ MvNormal(Sigma*(y./omega),Sigma)
end