lkj_turing_example.jl

using Turing
using Bijectors
using LinearAlgebra

Bijectors.bijector(d::LKJ) = PDBijector()

@model function correlation(y)
    N,D = size(y)
    
    mu ~ filldist(truncated(Normal(0, 100), -10, 10), D)
    sigma ~ filldist(truncated(Normal(0, 100), 0, 10), D)

    # prior on the correlation matrix
    rho ~ LKJ(D,D)
    L = Diagonal(sigma) * rho
    
    # Iterate through each datapoint, and observe its likelihood.
    for i in 1:N
        y[i,:] ~ MvNormal(mu , L*L')
    end
    return L*L'
end

cov = [ 4.94072998 -4.93536067; -4.93536067 5.99552455 ]
x = rand(MvNormal([0.0, 1.0], cov), 10)

model = correlation(x')
sample(model, HMC(0.01,5), 1000)