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Data tracking and the understanding of Bayesian consistency

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  • Stephen G. Walker
  • Antonio Lijoi
  • Igor Prunster

Abstract

We deal with strong consistency for Bayesian density estimation. An awkward consequence of inconsistency is described. It is pointed out that consistency at some density f-sub-0 depends on the prior mass assigned to the 'pathological' set of those densities that are close to f-sub-0, in a weak sense, and far apart from f-sub-0, in a Hellinger sense. An analysis of these sets leads to the identification of the notion of 'data tracking'. Specific examples in which this phenomenon cannot occur are discussed. When it can happen, we show how and where things can go wrong, thus providing more intuition about the sources of inconsistency. Copyright 2005, Oxford University Press.

Suggested Citation

  • Stephen G. Walker & Antonio Lijoi & Igor Prunster, 2005. "Data tracking and the understanding of Bayesian consistency," Biometrika, Biometrika Trust, vol. 92(4), pages 765-778, December.
    • Handle: RePEc:oup:biomet:v:92:y:2005:i:4:p:765-778
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    File URL: http://hdl.handle.net/10.1093/biomet/92.4.765
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    Citations

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    Cited by:

    1. Pierpaolo De Blasi & Lancelot F. James & John W. Lau, 2007. "Bayesian Nonparametric Estimation and Consistency of Mixed Multinomial Logit Choice Models," ICER Working Papers - Applied Mathematics Series 15-2007, ICER - International Centre for Economic Research.
    2. Karabatsos, George & Walker, Stephen G., 2012. "Bayesian nonparametric mixed random utility models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1714-1722.

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