birats.stan

// http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/Vol2.pdf
// Page 23: Birats
//# 

data {
  int<lower=0> N;
  int<lower=0> T;
  array[T] real x;
  real xbar;
  array[N, T] real y;
  cov_matrix[2] Omega;
}
parameters {
  array[N] vector[2] beta;
  vector[2] mu_beta;
  real<lower=0> sigmasq_y;
  cov_matrix[2] Sigma_beta;
}
//  transformed parameters {
//    real rho; 
//    real alpha0; 
//    //rho <- Sigma_beta[1, 2] / sqrt(Sigma_beta[1, 1] * Sigma_beta[2, 2]);
//    //alpha0 <- mu_beta[1] - mu_beta[2] * xbar; 
//  }
transformed parameters {
  real<lower=0> sigma_y;
  sigma_y = sqrt(sigmasq_y);
}
model {
  sigmasq_y ~ inv_gamma(0.001, 0.001);
  mu_beta ~ normal(0, 100);
  Sigma_beta ~ inv_wishart(2, Omega);
  for (n in 1 : N) {
    beta[n] ~ multi_normal(mu_beta, Sigma_beta);
  }
  for (n in 1 : N) {
    for (t in 1 : T) {
      // centeralize x[] 
      // y[n,t] ~ normal(beta[n, 1] + beta[n, 2] * (x[t] - xbar), sqrt(sigmasq_y));
      
      // NOT-centeralize x[] 
      y[n, t] ~ normal(beta[n, 1] + beta[n, 2] * x[t], sigma_y);
    }
  }
}