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A note on some algorithms for the Gibbs posterior

Author

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  • Chen, Kun
  • Jiang, Wenxin
  • Tanner, Martin A.

Abstract

Jiang and Tanner (2008) consider a method of classification using the Gibbs posterior which is directly constructed from the empirical classification errors. They propose an algorithm to sample from the Gibbs posterior which utilizes a smoothed approximation of the empirical classification error, via a Gibbs sampler with augmented latent variables. In this paper, we note some drawbacks of this algorithm and propose an alternative method for sampling from the Gibbs posterior, based on the Metropolis algorithm. The numerical performance of the algorithms is examined and compared via simulated data. We find that the Metropolis algorithm produces good classification results at an improved speed of computation.

Suggested Citation

  • Chen, Kun & Jiang, Wenxin & Tanner, Martin A., 2010. "A note on some algorithms for the Gibbs posterior," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1234-1241, August.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:15-16:p:1234-1241
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    References listed on IDEAS

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    1. P. J. Brown & M. Vannucci & T. Fearn, 2002. "Bayes model averaging with selection of regressors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 519-536, August.
    2. Naijun Sha & Marina Vannucci & Mahlet G. Tadesse & Philip J. Brown & Ilaria Dragoni & Nick Davies & Tracy C. Roberts & Andrea Contestabile & Mike Salmon & Chris Buckley & Francesco Falciani, 2004. "Bayesian Variable Selection in Multinomial Probit Models to Identify Molecular Signatures of Disease Stage," Biometrics, The International Biometric Society, vol. 60(3), pages 812-819, September.
    3. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
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    Cited by:

    1. 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.

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