functions {
  /*
  * Alternative to poisson_log_rng() that  avoids potential numerical problems during warmup
  */
  int poisson_log_safe_rng(real eta) {
    real pois_rate = exp(eta);
    if (pois_rate >= exp(20.79))
      return -9;
    return poisson_rng(pois_rate);
  }
}
data {
  int<lower=1> N;
  int<lower=0> complaints[N];
  vector<lower=0>[N] traps;
}
parameters {
  real alpha;
  real beta;
}
model {
  // weakly informative priors:
  // we expect negative slope on traps and a positive intercept,
  // but we will allow ourselves to be wrong
  beta ~ normal(-0.25, 1);
  alpha ~ normal(log(4), 1);
  
  // poisson_log(eta) is more efficient and stable alternative to poisson(exp(eta))
  complaints ~ poisson_log(alpha + beta * traps);
} 
generated quantities {
  // sample predicted values from the model for posterior predictive checks
  int y_rep[N];

  for (n in 1:N) {
    real eta_n = alpha + beta * traps[n];
    y_rep[n] = poisson_log_safe_rng(eta_n);
  }
}