I am trying to fit a finite Gaussian mixture model with unknown mean and covariances using Stan. I am aware that as HMC can't be applied to sample from discrete distributions, the marginalization technique is usually used to infer mixture parameters using Stan. However, for my application, I need the data cluster assignments. What is the best way to infer them in Stan? Suggestions will be appreciated.
Chapter 13 of the Stan User Manual discusses this in some detail. In short, you can calculate (in the generated quantities block) the posterior probability that an observation falls in each of a finite number of categories and then use that vector of probabilities to draw a category realization from the categorical distribution.