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Bayesian Model Selection in High-Dimensional Settings

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  • Valen E. Johnson
  • David Rossell

Abstract

Standard assumptions incorporated into Bayesian model selection procedures result in procedures that are not competitive with commonly used penalized likelihood methods. We propose modifications of these methods by imposing nonlocal prior densities on model parameters. We show that the resulting model selection procedures are consistent in linear model settings when the number of possible covariates p is bounded by the number of observations n , a property that has not been extended to other model selection procedures. In addition to consistently identifying the true model, the proposed procedures provide accurate estimates of the posterior probability that each identified model is correct. Through simulation studies, we demonstrate that these model selection procedures perform as well or better than commonly used penalized likelihood methods in a range of simulation settings. Proofs of the primary theorems are provided in the Supplementary Material that is available online.

Suggested Citation

  • Valen E. Johnson & David Rossell, 2012. "Bayesian Model Selection in High-Dimensional Settings," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 649-660, June.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:498:p:649-660
    DOI: 10.1080/01621459.2012.682536
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    File URL: http://hdl.handle.net/10.1080/01621459.2012.682536
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    Cited by:

    1. Thierry Chekouo & Francesco C. Stingo & James D. Doecke & Kim-Anh Do, 2015. "miRNA–target gene regulatory networks: A Bayesian integrative approach to biomarker selection with application to kidney cancer," Biometrics, The International Biometric Society, vol. 71(2), pages 428-438, June.
    2. repec:spr:testjl:v:26:y:2017:i:2:d:10.1007_s11749-016-0516-0 is not listed on IDEAS
    3. repec:bla:biomet:v:73:y:2017:i:2:p:615-624 is not listed on IDEAS
    4. Davide Altomare & Guido Consonni & Luca La Rocca, 2013. "Objective Bayesian Search of Gaussian Directed Acyclic Graphical Models for Ordered Variables with Non-Local Priors," Biometrics, The International Biometric Society, vol. 69(2), pages 478-487, June.
    5. Li, Cheng & Jiang, Wenxin, 2016. "On oracle property and asymptotic validity of Bayesian generalized method of moments," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 132-147.
    6. Latouche, Pierre & Mattei, Pierre-Alexandre & Bouveyron, Charles & Chiquet, Julien, 2016. "Combining a relaxed EM algorithm with Occam’s razor for Bayesian variable selection in high-dimensional regression," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 177-190.

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