Advances for Bayesian Model Selection and Inference

University Of Pennsylvania, Philadelphia PA

Investigators

Abstract

This project will develop new approaches that will unleash the potential of Bayesian methods for extracting meaningful structure in the "big data" that are of increasing interest and importance today. This will entail the creation of rapidly computable methods that enhance or bypass the much slower simulation methods upon which Bayesian methods have come to rely. By more efficiently harnessing the power of high-performance computing, our methods will provide a feasible vehicle for uncovering systematic associations in data across a variety of scientific disciplines. Examples include (a) genomics, where identifying the genetic determinants of diseases can substantially enhance targeted therapeutic decisions, (b) neuroimaging, where efficient methods will greatly facilitate understanding the complex brain architecture, and (c) environmental sciences, where identifying the determinants of climate change can better inform policy decisions. The main thrust of this research will be the development of a broad framework for fast deterministic search implementations for Bayesian model selection and inference. Building on new directions recently opened up by EMVS, a fast new alternative to stochastic search, this work will vastly increase the feasibility of general Bayesian implementations for large high-dimensional problems. This will entail the development of algorithms for classes of models that go beyond the canonical normal linear model. The speed of these algorithms will enable the broad application of new dynamic posterior exploration. Properties of the implicit selective shrinkage selection will be studied and asymptotic theory developed. New approaches to posterior reconstruction will provide new avenues for inference. Effectively, this project will lay the groundwork for a new paradigm for posterior exploration in large high-dimensional problems.