Mixture distributions have been given considerable attention due totheir 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.