Hello,

I have a simple Poisson mixture model that I am using to demonstrate some model checking techniques. I have been able to generate samples from the posterior predictive distribution, but I am running into some issues in creating the log likelihood in the generated quantities. Not sure how to translate the target syntax in the generated quantities block.

Here is the code

```
// Simple 3 component poisson mixture
data {
int N;
int<lower=0> y[N];
int n_groups;
}
parameters {
ordered[n_groups] mu;
simplex[n_groups] Theta;
}
model {
vector[n_groups] contributions;
// priors
mu ~ normal(0, 10);
Theta ~ dirichlet(rep_vector(2.0, n_groups));
// likelihood
for(n in 1:N) {
for(k in 1:n_groups) {
contributions[k] = log(Theta[k]) + poisson_log_lpmf(y[n] | mu[k]);
}
target += log_sum_exp(contributions);
}
}
generated quantities {
int z; // class index
int<lower=0> y_rep[N];
vector[N] log_lik;
for (n in 1:N) {
log_lik[n]= log_sum_exp(contributions); //stuck here
}
for (i in 1:N) {
z = categorical_rng(Theta);
y_rep[i] = poisson_log_rng(mu[z]);
}
}
```

Thanks for any help you can provide!!

-Patrick