I want to do Bayesian MCMC on a Gaussian Mixture Model. But, I want to update the means, weights, and covariance matrix for a single component separate from the others. Would there be the issue of variables not updating often enough? Like, if I have four components, then each variable can only be updated every four iterations at most. But then again, I can’t see how this would compromise detailed balance. Is there literature on this? Thanks!