Bayesian mixture models

In this chapter, the authors discuss Bayesian mixture models and their implementation using Markov Chain Monte Carlo (MCMC) methods. The Bayesian approach offers advantages over the maximum likelihood method, especially when dealing with small sample sizes. However, the use of improper priors and the unknown number of components in the model pose challenges for Bayesian mixture models. The authors suggest solutions such as using partially proper priors and model selection criteria to choose the best number of components. Various methods for estimating mixture models simultaneously and addressing the issue of label switching are also discussed. The chapter includes examples of Bayesian univariate and multivariate normal mixture models, as well as the use of R for fitting mixture models.