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October 2008 Gibbs posterior for variable selection in high-dimensional classification and data mining
Wenxin Jiang, Martin A. Tanner
Ann. Statist. 36(5): 2207-2231 (October 2008). DOI: 10.1214/07-AOS547


In the popular approach of “Bayesian variable selection” (BVS), one uses prior and posterior distributions to select a subset of candidate variables to enter the model. A completely new direction will be considered here to study BVS with a Gibbs posterior originating in statistical mechanics. The Gibbs posterior is constructed from a risk function of practical interest (such as the classification error) and aims at minimizing a risk function without modeling the data probabilistically. This can improve the performance over the usual Bayesian approach, which depends on a probability model which may be misspecified. Conditions will be provided to achieve good risk performance, even in the presence of high dimensionality, when the number of candidate variables “K” can be much larger than the sample size “n.” In addition, we develop a convenient Markov chain Monte Carlo algorithm to implement BVS with the Gibbs posterior.


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Wenxin Jiang. Martin A. Tanner. "Gibbs posterior for variable selection in high-dimensional classification and data mining." Ann. Statist. 36 (5) 2207 - 2231, October 2008.


Published: October 2008
First available in Project Euclid: 13 October 2008

zbMATH: 1274.62227
MathSciNet: MR2458185
Digital Object Identifier: 10.1214/07-AOS547

Primary: 62F99
Secondary: 82-08

Keywords: Data augmentation , data mining , Gibbs posterior , High-dimensional data , linear classification , Markov chain Monte Carlo , prior distribution , risk performance , Sparsity , Variable selection

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 5 • October 2008
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