Thomas Bayes' walk on manifolds

• 成果类型: Article
• 署名作者: Castillo, Ismael; Kerkyacharian, Gerard; Picard, Dominique
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0493-0
• 发表日期: 2014
• 页码: 665-710
• 关键词: entropy numbers; Metric Entropy; rates; CONVERGENCE; frames

摘要

Convergence of the Bayes posterior measure is considered in canonical statistical settings where observations sit on a geometrical object such as a compact manifold, or more generally on a compact metric space verifying some conditions. A natural geometric prior based on randomly rescaled solutions of the heat equation is considered. Upper and lower bound posterior contraction rates are derived.