Data tracking and the understanding of Bayesian consistency

• 成果类型: Article
• 署名作者: Walker, SG; Lijoi, A; Prünster, I
• 署名单位: University of Kent; University of Pavia
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/92.4.765
• 发表日期: 2005
• 页码: 765778
• 关键词: density

摘要

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.