I have a dataset of a sequence of confirmed and suspected cases of COVID-19, the sum of which is the outcome of my model. What I want to consider is that only a proportion of the suspected cases will be actual cases. For example, say I have a sequence of suspected cases like this: 0 - 2 - 1 - 0 - 1. If the proportion of suspected being actual cases were 50%, then I could have the following possible sequences:

- 0 - 0 - 1 - 0 - 1
- 0 - 2 - 0 - 0 - 0
- 0 - 1 - 1 - 0 - 0
- …

If the proportion were 25% or 50%, there would be even more possible sequences. In other words, I have large number of possible outcome sequences.

What I could do is to simulate all possible outcome sequences and run my model on each of them individually, then summarizing the estimates for my parameters of interest. But I was wondering if there is a way that I can do this in a single stan model / program with probability distribution for the proportion of suspected cases being actual cases of COVID-19?