functions{
  vector inv_logit_vector(vector x){
    vector[rows(x)] value;
    int n;
    
    n <- rows(x);
    for(i in 1:n){
      value[i] <- inv_logit(x[i]);
    }
    return value;
  }
}


data{
  int<lower=0> n; //number of samples
  int<lower=0> p; //input dimension
  
  matrix[n,p] x; //input samples
  real<lower=0, upper=1> y[n]; //output samples
  
  real hy_center;
  real<lower=0> hy_sd;
}

parameters{
  vector[p] beta;
}

model{
  //for prior
  beta ~ normal(hy_center, hy_sd); //ridge
  //beta ~ double_exponential(hy_center, hy_sd); //lasso
  
  increment_log_prob(to_vector(y)'*x*beta + sum(log(1-inv_logit_vector(x*beta))));
}