/**********************************************************************
 * univariate normal model 
 * Peng Zeng @ Auburn University 
 * 2025-09-15 
 * 
 * model: 
 *    y ~ normal(mu, sigma) 
 * prior: 
 *    mu ~ normal(mu0, tau0) 
 *    sigma^2 ~ scaled inverse chi-square(v0, s0) 
 **********************************************************************/

data {
    int<lower=1> n;                // sample size 
    real y[n];                     // observations 
    real mu_mean;                  // prior - mu0 
    real<lower=0> mu_sd;           // prior - tau0 
    real sigma_df;                 // prior - v0 
    real<lower=0> sigma_scale;     // prior - s0, not s0^2  
}
parameters { 
    real mu;                       // mean
    real<lower=0> sigma;           // standard deviation 
}
model {
    mu ~ normal(mu_mean, mu_sd);    
    sigma^2 ~ scaled_inv_chi_square(sigma_df, sigma_scale); 
    y ~ normal(mu, sigma);   
}

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