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- Title
Data tracking and the understanding of Bayesian consistency.
- Authors
Walker, Stephen G.; Lijoi, Antonio; Prünster, Igor
- 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 f0 depends on the prior mass assigned to the ‘pathological’ set of those densities that are close to f0, in a weak sense, and far apart from f0, 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.
- Subjects
BAYESIAN analysis; INCONSISTENCY (Logic); DENSITY functionals; EMPIRICAL research; ANALYSIS of variance; STUDY &; teaching of neighborhoods; EDUCATION
- Publication
Biometrika, 2005, Vol 92, Issue 4, p765
- ISSN
0006-3444
- Publication type
Article
- DOI
10.1093/biomet/92.4.765