I am trying to follow the example posted in this blog

It seems to fit a multivariate gaussian mixture model using a lkj prior

as shown here

data {

int D; //number of dimensions

int K; //number of gaussians

int N; //number of data

vector[D] y[N]; //data

}

parameters {

simplex[K] theta; //mixing proportions

ordered[D] mu[K]; //mixture component means

cholesky_factor_corr[D] L[K]; //cholesky factor of covariance

}

model {

real ps[K];

for(k in 1:K){

mu[k] ~ normal(0,3);

L[k] ~ lkj_corr_cholesky(4);

}

for (n in 1:N){

for (k in 1:K){

ps[k] = log(theta[k])+multi_normal_cholesky_lpdf(y[n] | mu[k], L[k]); //increment log probability of the gaussian

}

target += log_sum_exp(ps);

}

}

I am confused by the fact that she samples

L[k] ~ lkj_corr_cholesky(4);

and then puts it into

multi_normal_cholesky_lpdf

I would have thought you need to also have a prior for the variance part of covariance matrix, is that not correct