Bayesian Formulations for Model Uncertainty

University Of Pennsylvania, Philadelphia PA

Investigators

Abstract

The investigator and his colleagues consider new directions for the development of default model uncertainty input specifications for Bayesian model selection and model averaging. For the problem of model space prior specification, distributions are developed that dilute probability within neighborhoods of redundant models, thereby providing a more appropriate representation of ignorance. For the problem of parameter space prior specification, the predictive properties of model averaging are investigated for various prior formulations. In particular, focusing on the frequentist consequences of prior misspecification, new formulations are developed that maintain near-minimax behavior with only a minor degradation of predictive potential. For Bayesian modeling of large data sets, new adaptive formulations are developed that accommodate local as well as global structure. This includes new adaptive hierarchical modeling formulations as well as a new framework for simultaneous model and data selection. The goals of theoretical optimality and practical feasibility are considered throughout. The ultimate objective of this research is to enhance the potential of Bayesian statistical methods for discovering and modeling systematic relationships between variables in large multi-variable data sets. The explosive growth of information technologies has led to the proliferation of such data sets across widely diverse fields in business and science. Such methods offer a general approach towards improving explanations and predictions of many varied phenomenon such as, for example, consumer behavior, disease incidence, financial turbulence, industrial pollution and school efficiency. Bayesian statistical methods, in particular, offer the promise of optimally distinguishing systematic structure from random noise, which is of critical importance for effective mining of large, detailed data sets. The main thrust of this research is on the development of automatic implementations and richer formulations of these methods that will more fully exploit their statistical potential.