// Normal linear regressions with varying 
// priors for sigma to assess
// the influence of the prior for sigma

data {
  int<lower=0> n;
  vector[n] y;
  vector[n] x;
  real parssigma;    // parameters of gamma distribution
}

parameters {
  real beta0;
  real beta1;
  real<lower=0> invsigma2;
}

transformed parameters{
  real<lower=0> sigma;
  sigma <- 1/sqrt(invsigma2);
}

model {
  //priors
  beta0 ~ normal(0,5);
  beta1 ~ normal(0,5);
  invsigma2 ~ gamma(parssigma, parssigma);
  // likelihood
  y ~ normal(beta0 + beta1 * x, sigma);
}