Proposal Number: DMS PI: Merlise A. Clyde Institution: Duke University Project: Mode Uncertainty, Model Selection, and Robustness, with Applications in Environmental Sciences Abstract: Finding models to describe data and relationships among variables is a fundamental problem in statistics and science. Linear regression and its generalizations are some of the most commonly used statistical methods for data analysis. As scientists collect increasingly larger data sets, the fear of over-fitting the data by using all measured covariates leads to the standard approach of selecting a single ``best'' model based on a subset of the covariates, and then proceeding with scientific inferences and predictions as if that were the true model. This typical analysis ignores the uncertainty about which variables should be included in the model, potentially leading to overconfident inferences. Model uncertainty often significantly outweighs other sources of uncertainty in problems, but is generally ignored in standard statistical practice and teaching. This research focuses on Bayesian methods for incorporating model uncertainty into data analysis and decision making. In Bayesian model averaging, predictions and inferences are based on a set of models rather than a single model; each model contributes proportionally to the support it receives from the observed data. Novel methods of identifying promising models for use in Bayesian model averaging are studied. These can increase the applicability of Bayesian methods to realistic problems that involve a large number of variables. One of the major applications of the research is to estimate the effect of particulate matter on mortality in the elderly population and assess the potential impact of the EPA's new National Ambient Air Quality Standards for particulates. This and other case studies will be used to develop a new course in modern Baye sian statistical methods for environmental and biological science students at Duke University.
