Sampling path in in the tree structure

I have a naive question: I have a model which has a tree structure and I would like to sample the probability of each path and levels in my model. The levels create due to some endogenous and exogenous parts which have different priors. What is the best way to sample this algorithm?

I would simulate from the priors and do forward pass random generation.

Well in some papers, the stratified sampling is used for some tree structures. I was wondering whether it can be extended to any kind of tree structure?