Bayesian variable selection for genetic and genomic studies

An important issue in high-dimensional regression problems is the accurate and efficient estimation of regression coefficients when, compared to the number of data points, a substantially larger number of potential predictors are present. Further complications arise with correlated predictors, leading to the breakdown of standard statistical models for inference; and the uncertain definition of the outcome variable, which is often a varying composition of several different observable traits. Examples of such problems arise in many scenarios in genomics- in determining expression patterns of genes that may be responsible for a type of cancer; and in determining which genetic mutations lead to higher risks for occurrence of a disease. This project involves developing broad and improved Bayesian methodologies for efficient inference in high-dimensional regression-type problems with complex outcomes, with a focus on genetic data applications. Further, we will extend this framework to a variety of latent class models, and investigate the operating characteristics and analytical properties of various priors in the context of high-dimensional variable selection problems.