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Performance of variable selection methods in regression using variations of the Bayesian information criterion. (English) Zbl 1159.62301
Summary: 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. 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.

MSC:
62F15 Bayesian inference
62J05 Linear regression; mixed models
62H35 Image analysis in multivariate analysis
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