I have the following model:

```
def model(counts_data, p):
sample_shape = counts_data.shape
counts_average = numpyro.sample('counts_average', dist.Uniform(0, 5,))
number_count = numpyro.sample('number_count', dist.Poisson(rate = counts_average), sample_shape = sample_shape)
numpyro.sample('data', dist.Binomial(total_count = number_count, probs = p), obs = counts_data)
```

Some hyper parameter (called `counts_average`

) determines the Poisson rate of the matrix `number_count`

, the entries of which are independent. For each entry of this matrix, the `counts_data`

variable is drawn from a Binomial distribution with (given) probability `p`

.

I have two problems.

**Problem 1:**

The Poisson distribution does not have `enumerate_support`

. Is there a way around this problem? (I am using the NUTS sampler).

**Problem 2:**

I can analytically marginalize over the `number_count`

value, but I would like to obtain posterior samples in the `number_count`

variable. Is this somehow possible?

Thank you very much!