//

// Gaussian prior on regression coeffs (linear regression)

//

data {

  // number of unpenalized columns in model matrix

  int U;

  // number of observations

  int N;

  // design matrix

  matrix[N, U] X;

  // continuous response variable

  vector[N] y;

  // prior standard deviation for the unpenalised variables

  real<lower=0> scale_u;

}

parameters {

  // unpenalized regression parameters

  vector[U] beta_u;

  // residual standard deviation

  real <lower=0> sigma;

}

model {

  // unpenalized coefficients including intercept

  beta_u ~ normal(0, scale_u);

  // noninformative gamma priors on scale parameter are not advised

  sigma ~ inv_gamma(1, 1);

  // likelihood

  y ~ normal_id_glm(X, 0, beta_u, sigma);

}