//

// Gaussian prior on regression coeffs (logistic regression)

//

data {

  // number of unpenalized columns in model matrix

  int U;

  // number of observations

  int N;

  // prior standard deviation for the unpenalised variables

  real <lower=0> scale_u;

  // design matrix

  matrix[N, U] X;

  // binary response variable

  array[N] int<lower=0, upper=1> y;

}

parameters {

  // unpenalized regression parameters

  vector[U] beta_u;

}

model {

  // unpenalized coefficients including intercept

  beta_u ~ normal(0, scale_u);

  // likelihood

  y ~ bernoulli_logit_glm(X, 0, beta_u);

}