On the Bayesian Mixture Model and Identifiability

This article is concerned with Bayesian mixture models and identifiability issues. There are two sources of unidentifiability: the well-known likelihood invariance under label switching and the perhaps less well-known parameter identifiability problem. When using latent allocation variables determined by the mixture model, these sources of unidentifiability create arbitrary labeling that renders estimation of the model very difficult. We endeavor to tackle these problems by proposing a prior distribution on the allocations, which provides an explicit interpretation for the labeling by removing gaps with high probability. We propose a Markov chain Monte Carlo (MCMC) estimation method and present supporting illustrations.