A reversible jump MCMC for mixture of t factor analyzers

Abstract

This thesis explores the integration of Multivariate t-distribution within Factor Analysis and its extension through mixture models, emphasizing robust statistical methodologies for complex data analysis. We employ reversible jump Markov chain Monte Carlo for model selection, addressing the challenges of non-normal data behaviors such as outliers and heavy tails. The research contributes to the statistical field by enhancing model accuracy and flexibility, particularly in clustering and Bayesian inference. Through theoretical development and practical applications, including simulations and real-world datasets (wine and olive oil data), this study demonstrates the efficacy of these methodologies in uncovering latent structures and provides a comprehensive toolkit for advanced data analysis.