Nonparametric Bayesian inference for reversible multi-dimensional diffusions
Autor: | Giordano, Matteo, Ray, Kolyan |
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Rok vydání: | 2020 |
Předmět: | |
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 |
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