// 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;
  vector[3] priorparsigma; // parameters for folded t dist
}

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

model {
  //priors
  beta0 ~ normal(0,5);
  beta1 ~ normal(0,5);
  //increment_log_prob(student_t_log(sigma, priorparsigma[1], priorparsigma[2], priorparsigma[3]));
  sigma ~ student_t(priorparsigma[1], priorparsigma[2], priorparsigma[3]);

  // likelihood
  y ~ normal(beta0 + beta1 * x, sigma);
}