grp_prior_mean_var.stan

// Comparison of k groups with unequal variance and
// hierarchical priors for the mean and the variance
data {
  int<lower=0> N; // number of data points
  int<lower=0> K; // number of groups
  int<lower=1,upper=K> x[N]; // group indicator
  vector[N] y; //
}
parameters {
  real mu0;                 // prior mean
  real<lower=0> musigma0;   // prior std
  vector[K] mu;             // group means
  real lsigma0;             // prior mean
  real<lower=0> lsigma0s;   // prior std
  vector<lower=0>[K] sigma; // group stds
}
model {
  mu0 ~ normal(10, 10);       // weakly informative prior
  musigma0 ~ cauchy(0,10);    // weakly informative prior
  mu ~ normal(mu0, musigma0); // population prior with unknown parameters
  lsigma0 ~ normal(0,1);      // weakly informative prior
  lsigma0s ~ normal(0,1);     // weakly informative prior
  sigma ~ cauchy(lsigma0, lsigma0s); // population prior with unknown parameters
  y ~ normal(mu[x], sigma[x]);
}