data {
  int<lower=0> N;
  real y[N];
  matrix[N,N] A;
  vector[N] mu_u_prior;
}

parameters{
 real beta0;
 vector[N] u;	
 real<lower=0> sig2_e;
 real<lower=0> sig2_u;	
} 


model {



  ##-----------------------------------------------
  ## likelihood	
  for(i in 1:N){
       y[i] ~ normal(beta0 + u[i], sqrt(sig2_e)); 
     }  


  ##---------------------------------
  ## priors
  
  u ~  multi_normal(mu_u_prior, A * sig2_u); 

  beta0 ~ normal(0,1000);

  sig2_e ~ scaled_inv_chi_square(2,0.25);
  sig2_u ~ scaled_inv_chi_square(2,0.25);	

}