I have recently read about mixture models, especially the cases in which we consider the number of components, k, as a random variables with posterior distribution.
I have read in different articles that the sampling of such posterior is pretty complicated, partly because the posterior’s dimensionality is changing with k.
Some authors proposed other sampling stategies, like reversible jumps Monte-Carlo, or the Fu and Wang’s algorithm, exploring the distribution of parameters conditional on K (2002,2007). Unfortunatly, I do not understand enough the different algorithms to recognize their similarities or dissimilarities with the ones implemented with STAN.
So I will ask the question very directly : is stan able to deal with those kind of problems, i.e. exploring a posterior distribution of changing dimension, given a random integer variable k?
Thank you very much!