A General Approach to Variable Section Using Bayesian Nonparametric Models

• Activity Number: 155
• Type: Invited
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Robert E. McCulloch*
• Companies: The University of Chicago
• Keywords: regression ; big data ; bayes ; nonparametric ; ensemble

Abstract

Over the last several years, dramatic advances in Bayesian modeling and computation have given us powerful tools for flexible fitting of high dimensional relationships. However, the flexibility and complexity of the modeling procedures comes at a price: we may have difficulty understanding what our models have found. In particular, we are often interested in finding a simple model that works well, with variable selection being an important special case. Traditionally Bayesian approaches to search for a simple model have emphasized the specification of priors on models and computation of the posterior on models. In this paper we emphasize the role of utility in choosing a model. We use fits of the posterior predictive using binary tree models to search for simple structure. Tree models are computationally fast and capable of capturing complex structure so that we can feasibly search for model simplificatons that are not too simple in that important variables and complexity (e.g. nonlinearity) are not lost.