Statistical methods for expression quantitative trait loci (eQTL) mapping

This thesis focuses on developing statistical methods for expression quantitative trait loci (eQTL) mapping studies. Advances in microarray high-throughput technologies allow for the great opportunity to study variation at the level of gene expression. Much excitement abounds for this field of "genetical genomics"---identifying genetic polymorphisms that underlie the quantitative variation in gene expression. Although successful in many ways, the currently available methods used in the so called expression QTL (eQTL) studies to date are limited.In this thesis, we develolp a unified Bayesian statistical framework for eQTL mapping. The framework captures the linkage dependence among markers by imposing a mixture model on all the markers. The information shared among the transcripts is also utilized through Bayesian hierarchical modeling.We first develop a mixture model for the problem of mapping at the markers only. The model fit can be carried out using the EM algorithm. We then consider the need of eQTL interval mapping when the available marker density is coarse. The interval mapping uses the importance sampling idea. The "pseudomarkers" are generated at the desired mapping resolution. Then a weight is assigned to each sample of the pseudomarkers to reflect its "appropriateness" of explaining the variation in gene expression data. We illustrate the operating characteristics of the above method via simulations. Application on one case study of diabetes in mouse is also demonstrated.In the second part of the thesis, we consider the eQTL mapping problem when given dense marker maps in which case direct application of the mixture model becomes computationally prohibitive because the number of components in the mixture is too big. A Dirichlet process mixture model (DPMM) is proposed to address this problem. It is a natural extension of the finite mixture model. We develop a Markov chain Monte Carlo (MCMC) algorithm which utilizes Metropolis-Hastings proposals together with partial Gibbs sampling among certain states to simulate from the posterior distribution of the sampling variable. Simulation studies demonstrate the utility of this method. Application on the Berm et al. (2002) yeast data also reveals great potential.