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Performance of Variable Selection Methods in Regression Using Variations of the Bayesian Information Criterion
Authors:Tom Burr  Herb Fry  Brian McVey  Eric Sander  Joseph Cavanaugh  Andrew Neath
Institution:1. Statistical Sciences Group, Los Alamos National Laboratory , Los Alamos, New Mexico, USA tburr@lanl.gov;3. Physical Chemistry and Applied Spectroscopy Group, Los Alamos National Laboratory , Los Alamos, New Mexico, USA;4. Office of Defense Nuclear Nonproliferation, National Nuclear Security Administration , Washington, DC, USA;5. Department of Biostatistics , College of Public Health, The University of Iowa , Iowa City, Iowa, USA;6. Department of Mathematics and Statistics , Southern Illinois University-Edwardsville , Illinois, USA
Abstract:The Bayesian information criterion (BIC) is widely used for variable selection. We focus on the regression setting for which variations of the BIC have been proposed. A version that includes the Fisher Information matrix of the predictor variables performed best in one published study. In this article, we extend the evaluation, introduce a performance measure involving how closely posterior probabilities are approximated, and conclude that the version that includes the Fisher Information often favors regression models having more predictors, depending on the scale and correlation structure of the predictor matrix. In the image analysis application that we describe, we therefore prefer the standard BIC approximation because of its relative simplicity and competitive performance at approximating the true posterior probabilities.
Keywords:Approximate Bayesian posterior probabilities  Bayesian information criterion (BIC)  Image analysis  Variable selection
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