Mixtures of g Priors for Bayesian Variable Selection

作者: Feng Liang , Rui Paulo , German Molina , Merlise A Clyde , Jim O Berger

DOI: 10.1198/016214507000001337

关键词: Mathematical optimizationDecision theoryg-priorModel selectionMathematicsBayes' theoremPrior probabilityConsistency (statistics)EconometricsFeature selectionCauchy distribution

摘要: Zellner's g prior remains a popular conventional for use in Bayesian variable selection, despite several undesirable consistency issues. In this article we study mixtures of priors as an alternative to default that resolve many the problems with original formulation while maintaining computational tractability has made so popular. We present theoretical properties mixture and provide real simulated examples compare fixed priors, empirical Bayes approaches, other procedures. Please see Arnold letter author's response.

参考文章(41)
Luis R. Pericchi, Julia A. Varshavsky, BAYES FACTORS AND MARGINAL DISTRIBUTIONS IN INVARIANT SITUATIONS Sankhya. Series A. ,vol. 60, pp. 307- 321 ,(2016)
Robert E. McCulloch, Edward I. George, APPROACHES FOR BAYESIAN VARIABLE SELECTION Statistica Sinica. ,vol. 7, pp. 339- 373 ,(1997)
Prem K. Goel, Arnold Zellner, Bruno De Finetti, Bayesian inference and decision techniques : essays in honor of Bruno de Finetti North-Holland. ,(1986)
Merlise A. Clyde, J. O. Berger, J. M. Bernardo, A. P. Dawid, Bayesian Model Averaging and Model Search Strategies ,(2007)
James O Berger, Luis R Pericchi, JK Ghosh, Tapas Samanta, Fulvio De Santis, JO Berger, LR Pericchi, Objective Bayesian Methods for Model Selection: Introduction and Comparison Institute of Mathematical Statistics. pp. 135- 207 ,(2001) , 10.1214/LNMS/1215540968
Morris L. Eaton, Group invariance applications in statistics Institute of Mathematical Statistics , American Statistical Association. ,(1989)
Chris T. Volinsky, Adrian E. Raftery, David Madigan, Jennifer A. Hoeting, Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors Statistical Science. ,vol. 14, pp. 382- 417 ,(1999) , 10.1214/SS/1009212519
Iain M. Johnstone, Bernard W. Silverman, Empirical Bayes selection of wavelet thresholds Annals of Statistics. ,vol. 33, pp. 1700- 1752 ,(2005) , 10.1214/009053605000000345
Alan J. Miller, Subset Selection in Regression ,(2002)