Data tracking and the understanding of Bayesian consistency

Walker, S.G. and Lijoi, A. and Prunster, I. (2005) Data tracking and the understanding of Bayesian consistency. Biometrika, 92 (4). pp. 765-778. ISSN 0006-3444. (The full text of this publication is not available from this repository)

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Official URL
http://dx.doi.org/10.1093/biomet/92.4.765

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(0) depends on the prior mass assigned to the 'pathological' set of those densities that are close to f(0), in a weak sense, and far apart from f(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.

Item Type: Article
Uncontrolled keywords: Bayesian consistency; Bayesian density estimation; Hellinger distance; Kullback-Leibler divergence; weak neighbourhood DENSITY
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Judith Broom
Date Deposited: 12 Sep 2008 23:32
Last Modified: 14 Jan 2010 14:40
Resource URI: http://kar.kent.ac.uk/id/eprint/10548 (The current URI for this page, for reference purposes)
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