chickens-no-corr-gp1.stan

data {
  int N;
  int J;
  vector[N] y;
  vector[N] z;
  vector[N] se;
  vector[J] x;
  int<lower=1, upper=J> expt_id[N];
}
transformed data {
  real delta = 1e-9;
  real x_array[J] = to_array_1d(x);
}
parameters {
  real mu_theta;
  real mu_b;
  real<lower=0> sigma_b;
  vector[J] eta_theta;
  vector[J] eta_b;
  real<lower=0> rho_theta;
  real<lower=0> alpha_theta;
}
transformed parameters {
  vector[J] theta;
  vector[J] b;
  b = mu_b + sigma_b * eta_b;
  {
    matrix[J, J] L_K_theta;
    matrix[J, J] K_theta =
      cov_exp_quad(x_array, alpha_theta, rho_theta);
    // diagonal elements
    for (j in 1:J)
      K_theta[j, j] = K_theta[j, j] + delta;
    L_K_theta = cholesky_decompose(K_theta);
    theta = mu_theta + L_K_theta * eta_theta;
  }
}
model {
  y ~ normal(b[expt_id] + theta[expt_id] .* z, se);
  eta_theta ~ normal(0, 1);
  eta_b ~ normal(0, 1);
  rho_theta ~ inv_gamma(5, 50);
}