I’m trying to model a process in which I observe a sum of two binomials:

```
y~binomial(alpha*N,p_1)+binomial((1-alpha)*N,p_2)
```

Such that `y`

is observed, `N`

is known and I’m trying to infer `alpha,p_1`

and `p_2`

(I am aware that this isn’t “legitimate” Stan code, but I thought it’s a good way to describe the assumed data-generating process). I have informative priors for `p_1`

and `p_2`

(they should differ by an order of magnitude), and I hope this would help to deal with identifiability issues.

Is there any way to code something similar to this in Stan? Currently I’m using a poisson approximation to each, and then the sum is just another poisson… but I’m not sure this is a very good approximation here (both because `N`

is not very large, and because of possible correlations between them), and want to see if there’s “something better”.