BAYESIAN MODELS FOR DNA MICROARRAY DATA ANALYSIS A Dissertation by KYEONG

Bayesian Models for DNA Microarray Data Analysis. (May 2004) Kyeong Eun Lee, B.A., Kyungpook National University, Korea; M.A., Seoul National University, Korea Co–Chairs of Advisory Committee: Dr. Bani K. Mallick Dr. James A. Calvin Selection of significant genes via expression patterns is important in a microarray problem. Owing to small sample size and large number of variables (genes), the selection process can be unstable. This research proposes a hierarchical Bayesian model for gene (variable) selection. We employ latent variables in a regression setting and use a Bayesian mixture prior to perform the variable selection. Due to the binary nature of the data, the posterior distributions of the parameters are not in explicit form, and we need to use a combination of truncated sampling and Markov Chain Monte Carlo (MCMC) based computation techniques to simulate the posterior distributions. The Bayesian model is flexible enough to identify the significant genes as well as to perform future predictions. The method is applied to cancer classification via cDNA microarrays. In particular, the genes BRCA1 and BRCA2 are associated with a hereditary disposition to breast cancer, and the method is used to identify the set of significant genes to classify BRCA1 and others. Microarray data can also be applied to survival models. We address the issue of how to reduce the dimension in building model by selecting significant genes as well as assessing the estimated survival curves. Additionally, we consider the well-