Bayesian methods in bioinformatics

This work is directed towards developing flexible Bayesian statistical methods in the semi- and nonparamteric regression modeling framework with special focus on analyzing data from biological and genetic experiments. This dissertation attempts to solve two such problems in this area. In the first part, we study penalized regression splines (P-splines), which are low-order basis splines with a penalty to avoid under- smoothing. Such P-splines are typically not spatially adaptive, and hence can have trouble when functions are varying rapidly. We model the penalty parameter inherent in the P-spline method as a heteroscedastic regression function. We develop a full Bayesian hierarchical structure to do this and use Markov Chain Monte Carlo tech- niques for drawing random samples from the posterior for inference. We show that the approach achieves very competitive performance as compared to other methods. The second part focuses on modeling DNA microarray data. Microarray technology enables us to monitor the expression levels of thousands of genes simultaneously and hence to obtain a better picture of the interactions between the genes. In order to understand the biological structure underlying these gene interactions, we present a hierarchical nonparametric Bayesian model based on Multivariate Adaptive Regres-sion Splines (MARS) to capture the functional relationship between genes and also between genes and disease status. The novelty of the approach lies in the attempt to capture the complex nonlinear dependencies between the genes which could otherwise be missed by linear approaches. The Bayesian model is flexible enough to identify significant genes of interest as well as model the functional relationships between the genes. The effectiveness of the proposed methodology is illustrated on leukemia and breast cancer datasets.