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Separation measures and the geometry of Bayes factor selection for classification

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  • Jim Q. Smith
  • Paul E. Anderson
  • Silvia Liverani

Abstract

Conjugacy assumptions are often used in Bayesian selection over a partition because they allow the otherwise unfeasibly large model space to be searched very quickly. The implications of such models can be analysed algebraically. We use the explicit forms of the associated Bayes factors to demonstrate that such methods can be unstable under common settings of the associated hyperparameters. We then prove that the regions of instability can be removed by setting the hyperparameters in an unconventional way. Under this family of assignments we prove that model selection is determined by an implicit separation measure: a function of the hyperparameters and the sufficient statistics of clusters in a given partition. We show that this family of separation measures has plausible properties. The methodology proposed is illustrated through the selection of clusters of longitudinal gene expression profiles. Copyright (c) 2008 Royal Statistical Society.

Suggested Citation

  • Jim Q. Smith & Paul E. Anderson & Silvia Liverani, 2008. "Separation measures and the geometry of Bayes factor selection for classification," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 957-980.
  • Handle: RePEc:bla:jorssb:v:70:y:2008:i:5:p:957-980
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    References listed on IDEAS

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    1. Fernandez, Carmen & Ley, Eduardo & Steel, Mark F. J., 2001. "Benchmark priors for Bayesian model averaging," Journal of Econometrics, Elsevier, vol. 100(2), pages 381-427, February.
    2. Heard, Nicholas A. & Holmes, Christopher C. & Stephens, David A., 2006. "A Quantitative Study of Gene Regulation Involved in the Immune Response of Anopheline Mosquitoes: An Application of Bayesian Hierarchical Clustering of Curves," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 18-29, March.
    3. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
    4. Fernando A. Quintana & Pilar L. Iglesias, 2003. "Bayesian clustering and product partition models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 557-574.
    5. Shubhankar Ray & Bani Mallick, 2006. "Functional clustering by Bayesian wavelet methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 305-332.
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