/**********************************************************************
 * multivariate normal model 
 * Peng Zeng @ Auburn University 
 * 2025-09-15 
 * 
 * model: 
 *    y ~ multi_normal(mu, Sigma) 
 * prior: 
 *    mu ~ multi_normal(mu0, Lambda0) 
 *    Sigma ~ inverse Wishart(v0, S0) 
 **********************************************************************/

data {
    int<lower=1> n;                // sample size 
    int<lower=1> p;                // dimension of y
    array[n] vector[p] y;          // observations 
    vector[p] mu_mean;             // prior - mu0 
    cov_matrix[p] mu_cov;          // prior - Lambda0 
    real Sigma_df;                 // prior - v0 
    cov_matrix[p] Sigma_scale;     // prior - S0 
}
parameters { 
    vector[p] mu;                  // mean
    cov_matrix[p] Sigma;           // covariance matrix  
}
model {
    mu ~ multi_normal(mu_mean, mu_cov);    
    Sigma ~ inv_wishart(Sigma_df, Sigma_scale); 
    y ~ multi_normal(mu, Sigma);   
}

/**********************************************************************
 * THE END 
 **********************************************************************/