Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm proposed by Green (1995) received much attention in recent years for its flexibility in performing model selection and parameter estimation simultaneously. Among various applications of the algorithm, Richardson and Green (1997) first applied the RJMCMC algorithm to fully Bayesian analysis of univariate Gaussian mixture models. They applied their algorithm in Bayesian semi-parametric density estimation and Bayesian classification problems. The success of their algorithm lies on the design of trans-dimensional moves that preserves moment conditions. In this thesis, we extend their algorithm to work on multivariate Gaussian mixtures. We applied Cholesky decomposition in designing our trains-dimensional moves that gives us elegant...[ Read more ]

Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm proposed by Green (1995) received much attention in recent years for its flexibility in performing model selection and parameter estimation simultaneously. Among various applications of the algorithm, Richardson and Green (1997) first applied the RJMCMC algorithm to fully Bayesian analysis of univariate Gaussian mixture models. They applied their algorithm in Bayesian semi-parametric density estimation and Bayesian classification problems. The success of their algorithm lies on the design of trans-dimensional moves that preserves moment conditions. In this thesis, we extend their algorithm to work on multivariate Gaussian mixtures. We applied Cholesky decomposition in designing our trains-dimensional moves that gives us elegant results. Besides plain applications to Gaussian mixtures, we also apply a modified version of our algorithm to linear mixed-effects model with random intercept and random slopes. Experimental results on simulated and real datasets demonstrate the efficacy of our algorithm.