Markov Chain Sampling Methods for Dirichlet Process Mixture Models

This article reviews Markov chain methods for sampling from the posterior distribution of a Dirichlet process mixture model and presents two new classes of methods. One new approach is to make Metropolis-Hastings updates of the indicators specifying which mixture component is associated with each observation, perhaps supplemented with a partial form of Gibbs sampling. The other new approach extends Gibbs sampling for these indicators by using a set of auxiliary parameters. These methods are simple to implement and are more efficient than previous ways of handling general Dirichlet process mixture models with non-conjugate priors.