I am going to study clustering methods in the Bayesian perspective. I understood how k-means works, and I found it pretty clear, due to the notion of distance and assignments to specific centers.
I am now turning the attention to the probabilistic approach and the use of mcmc methods.
I have read this question:
and a useful page:
However, I do not understand how to assign points to clusters. Which kind of posterior distribution should I compute? What is the meaning of sampling from the posterior distribution in layman's terms? Do I obtain a probability for each point to belong to any possible cluster?