Efficient algorithms for fitting Bayesian mixture models.

摘要

Mixture distributions have been given considerable attention due to their flexible form and convenience of use. Markov Chain Monte Carlo (MCMC) methods enable us to generate samples from a target distribution from which it is difficult to sample directly by simulating a Markov chain. However, practical difficulties arise when MCMC methods are implemented to fit mixture distributions with several isolated modes. Most MCMC sampling methods have difficulties transitioning between the isolated modal regions and the inferences based on the samples generated by these methods can be unreliable. This motivated us to develop efficient algorithms for fitting Bayesian mixture models. Our approach hinges on the premise that a preliminary understanding of some essential features of the posterior distribution is needed to make sampling more efficient.;In this thesis we introduce two algorithms that rely on an initial identification of possible isolated modes of the mixture distribution. The algorithms are applied to fit four different models: a Bayesian univariate normal mixture model; a Bayesian univariate outlier accommodation model; a Bayesian linear regression model; and a hierarchical Bayesian regression model for repeated measures data. Their performance is compared to that of other methods including the Gibbs sampler and an MCMC tempering transition method by examining the accuracy of inferences and the ease of transition between isolated modal regions of the posterior distributions for the Bayesian models. The results show that the proposed algorithms outperform the Gibbs sampler and the tempering transition method.