I have been reading about discrete mixture models, and I know that in STAN it is necessary to marginalize over the latent categorical variables. It seems, however, that one can easily retrieve the latent discrete probabilities (or sample them with a random number generator) using the transformed parameter (usually called
lp in the user manual) that must be computed anyway.
My question is whether there is any disadvantage from inferring discrete latent parameters this way, as opposed to sampling them directly with other MCMC algorithms that allow for that.
Thank you for your attention