data{
  int N;
  int y[N];
}
parameters{
  real lambda;
}
model{
  target+=poisson_lpmf(y|lambda);
  target+=gamma_lpdf(lambda|4.57, 1.43);
}
generated quantities{
  vector[N] log_lik;
    for(n in 1:N){
      log_lik[n] = poisson_lpmf(y[n]|lambda);
    }
}