Gibbs Sampling Based Bayesian Analysis of Mixtures with Unknown Number of Components

For mixture models with unknown number of components, Bayesian approaches, as considered by Escobar and West (1995) and Richardson and Green (1997), are reconciled here through a simple Gibbs sampling approach. Specifically, we consider exactly the same direct set up as used by Richardson and Green (1997), but put Dirichlet process prior on the mixture components; the latter has also been used by Escobar and West (1995) albeit in a different set up. The reconciliation we propose here yields a simple Gibbs sampling scheme for learning about all the unknowns, including the unknown number of components. Thus, we completely avoid complicated reversible jump Markov chain Monte Carlo (RJMCMC) methods, yet tackle variable dimensionality simply and efficiently. Moreover, we demonstrate, using both simulated and real data sets, and pseudo-Bayes factors, that our proposed model outperforms that of Escobar and West (1995), while enjoying, at the same time, computational superiority over the methods proposed by Richardson and Green (1997) and Escobar and West (1995). We also discuss issues related to clustering and argue that in principle, our approach is capable of learning about the number of clusters in the sample as well as in the population, while the approach of Escobar and West (1995) is suitable for learning about the number of clusters in the sample only. AMS (2000) subject classification. Primary .