// saved as 8schools.stan
data {
  int<lower=0> J;         // number of schools 
  real y[J];              // estimated treatment effects
  real<lower=0> sigma[J]; // standard error of effect estimates 
}
parameters {
  real mu;              // population treatment effect
  real<lower=0> tau;    // standard deviation in treatment effects
  vector[J] eta;        // unscaled deviation from mu by school
}
transformed parameters {
  vector[J] theta = mu + tau * eta;    // school treatment effects
}
model {
  eta ~ normal(0,1);          // prior 
  y ~ normal(theta, sigma);   //likelihood
}