Thomas Bayes' walk on manifolds

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.

References in corpus (2)

• Rates of contraction of posterior distributions based on Gaussian process priors
• Reproducing kernel Hilbert spaces of Gaussian priors