Non-centered parameterization of the multivariate student-t distribution

Modeling
8 
data {
  int<lower=1> p;
  vector[p] mu;
  cholesky_factor_cov[p,p] L;
  real<lower=0> nu;
}
parameters {
  vector[p] z;
  real<lower=0> u;
}
transformed parameters {
  vector[p] x;
  x = mu + sqrt(nu / u) * (L * z); // distributed multi_student_t
}
model {
  target += normal_lpdf(z | 0, 1);
  target += chi_square_lpdf(u | nu);
}
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