Bayesian Criterion Based Variable Selection: Comparisons and Applications

• Activity Number: 397 - Multiple Aspects of Bayesian Strategies for Variable Selection in Standard and Non-Standard Models
• Type: Topic Contributed
• Date/Time: Tuesday, July 30, 2019 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Sanjib Basu* and Arnab Kumar Maity and Santu Ghosh
• Companies: University of Illinois at Chicago and Texas A&M University and Augusta University
• Keywords: model selection; DIC; marginal likelihood; Bayes factor

Abstract

We consider criterion based variable selection in which selection is done by optimizing a criterion over the model space. These methods differ from many regularized methods that perform variable selection in the process of model fitting. The traditional Bayesian model selection criterion of marginal likelihood and Bayes factor can be difficult to estimate in complex models. The Deviance Information Criterion (DIC) is a popular Bayesian selection criterion based on penalized goodness of fit of a model. Another selection criterion is the Log Pseudo Marginal Likelihood (LPML) belonging to the broad class of cross-validation based selection methods. These criteria are often estimated in Markov Chain sampling settings. We investigate the theoretical performances of these criteria in selecting the data-generating model and obtain rather surprising results. These theoretical results are illustrated in extensive simulation studies. Criterion based model selection can be difficult to implement in high dimensional model space due to the computational limitations of an enumerative search. We propose a model space search methodology and compare its performance with other recent methods. We fur