Mixture Models

4Bayesian mixture models

DOI: 10.1201/9781003038511-4

4.1 Introduction

A Bayesian approach to mixture analysis is usually implemented by simulating posterior distributions with Markov Chain Monte Carlo (MCMC) methods (Tanner and Wong, 1987; Gelfand and Smith, 1990). Important initial papers on Bayesian analysis of mixtures using MCMC methods include Diebolt and Robert (1994) and Escobar and West (1995). One main advantage of the Bayesian approach is that all statistical inferences about unknown parameters can be easily performed via the posterior distribution. When the posterior distribution of the unknown parameters is available, the Bayesian method can yield statistical inference without relying on the asymptotic normality. This is one ...