data{
  int N;
  int y[N];
  real mu;
  real tau;
}
parameters{
  real<lower=0>lambda;
}
model{
  target+=poisson_lpmf(y|lambda);
  target+=lognormal_lpdf(lambda|mu, tau);
  //target+=normal_lpdf(log(lambda)|mu, tau);  // equivalent for lognormal
  //target+=-log(lambda);
}
generated quantities{
  vector[N] log_lik;
    for(n in 1:N){
      log_lik[n] = poisson_lpmf(y[n]|lambda);
    }
}