NONPARAMETRIC BAYESIAN INFERENCE FOR REVERSIBLE MULTIDIMENSIONAL DIFFUSIONS

• 成果类型: Article
• 署名作者: Giordano, Matteo; Ray, Kolyan
• 署名单位: University of Cambridge; Imperial College London
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/22-AOS2213
• 发表日期: 2022
• 页码: 2872-2898
• 关键词: posterior contraction rates; drift estimation; convergence-rates; Inverse problems; differential-equations; ergodic diffusions; scalar diffusions; besov priors; distributions

摘要

We study nonparametric Bayesian models for reversible multidimensional 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 optimal nonparametric rate over Sobolev smoothness classes