Data tracking and the understanding of Bayesian consistency

Stephen G. Walker, Antonio Lijoi and Igor Prunster

Biometrika, 2005, vol. 92, issue 4, 765-778

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.

Date: 2005
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