Nonparametric Bayesian inference for reversible multi-dimensional diffusions

Autor:	Giordano, Matteo, Ray, Kolyan
Rok vydání:	2020
Předmět:	Mathematics - Statistics Theory Mathematics - Numerical Analysis Mathematics - Probability
Zdroj:	Ann. Statist. 50(5) (2022), 2872-2898
Druh dokumentu:	Working Paper
DOI:	10.1214/22-AOS2213
Popis:	We study nonparametric Bayesian models for reversible multi-dimensional diffusions with periodic drift. For continuous observation paths, reversibility is exploited to prove a general posterior contraction rate theorem for the drift gradient vector field under approximation-theoretic conditions on the induced prior for the invariant measure. The general theorem is applied to Gaussian priors and $p$-exponential priors, which are shown to converge to the truth at the minimax optimal rate over Sobolev smoothness classes in any dimension. Comment: 41 pages, 1 figure, to appear in the Annals of Statistics
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2012.12083 Zobrazit plný text záznamu View this record from Arxiv