How to set up Hierarchical Poisson model where the *sum* of the rates at one level is controlled by a higher level

[jaharvey8]

Yeah that sounds like the basic idea I had in my head. I usually skip the dirichlet step and just plug each rate into separate binomials. You aren’t guaranteed that the rates sum to 1 in that case but it’s usually pretty close, much simpler, and samples faster. Then I just renormalize rates to 1 when making predictions. But adding in the dirichlet distribution would be more technically sound.