Thomas Bayes' walk on manifolds

2012/06/03 by Ismael Castillo, Ismaël Castillo, Gérard Kerkyacharian +5 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #62G05 #62G20 #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Statistical Mechanics and Entropy #Statistics Theory (math.ST) #math.ST #msc:62G05 #msc:62G20 #stat.TH

paper · pdf · doi:10.48550/arxiv.1206.0459

arxiv created 2012/06/03 · openalex publication_date 2012/06/03 · arxiv updated 2012/06/05 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

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.

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