Hi, the model I am trying to build has a vector parameter such that the sum of its elements cannot exceed 1. So the sum must be less than or equal to 1. What kind of prior would be appropriate?

I am thinking the Dirichlet may work but I would like to hear people’s thoughts. Thank you.

There’s probably a few different ways to get the constraints you want.

You could do a simplex and then scale it by a parameter constrained [0, 1], or you could take a simplex and then just ignore the last entry (the N - 1 other entries sum to something between zero and one). You could also do something totally unconstrained, pass it through a softmax to get a simplex, and scale that by something [0, 1].

I don’t know how to do the priors though. You’ll probably need to make prior predictions and calibrate the quantiles of these predictions against things you know. Does that make sense? Sorta like the thing here: https://youtu.be/ZRpo41l02KQ?t=2695