Stat Colloquium [Virtual]: Dr. Debamita Kundu
University of Virginia
Title: Novel Bayesian Methodology in Multivariate Problems
This presentation involves into the development of novel Bayesian methodology for multivariate problems. Variable selection over a potentially large set of covariates in a linear model is quite popular. Within the Bayesian framework, common prior choices can lead to a posterior expectation of the regression coefficients that is a sparse (or nearly sparse) vector with a few nonzero components, those covariates that are most important. Our contribution lies in extending the "global-local" shrinkage concept to scenarios where multiple response variables are modeled simultaneously. In this context, we have developed a variable selection method for a K-outcome model (multivariate regression) that identifies the most important covariates across all outcomes. In another application, we have used “global-local” shrinkage prior in a way that shares the information between the main effects and interaction effects for estimating the complex relationship between environmental chemical mixtures and disease risk. Investigating health effects linked to exposure to environmental chemical mixtures is a challenging problem in epidemiology, toxicology, and exposure science. In particular, when there are a large number of chemicals under consideration it is difficult to estimate the interactive effects without incorporating reasonable prior information. Based on substantive considerations, researchers believe that true interactions between chemicals need to incorporate their corresponding main effects. In our work, we utilize this prior knowledge through a global-local shrinkage prior settings, which presumes that an interaction term can only occur when the corresponding main effects are present. We applied this methodology to the NCI-SEER NHL study to investigate the associations between exposures of pesticides and the risk of non-Hodgkin lymphoma (NHL).