Sampling Subsets from a Set

Modeling
1

Hello community,
I have a conceptual modelling question - I will attempt to abstract away as much as the details as possible.

Assume, you have a set \mathcal{T}. I wish to define a prior on the subsets of \mathcal{T}. Then, my paramater becomes simplex[$2^|T|$] theta (size equalling the powerset of \mathcal{T}).
The way I want to define this prior is via Bernoulli trials - for each element of \mathcal{T} perform a Bernoulli trial with success probability p and keep the ones that succeed.

What is a way to implement this distribution in STAN?

2

Can you provide more detail on what you mean here? How do you define p? And when you say “keep the ones that succeed”, how do you intend to define a prior from that?

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