Nonparametric Bayesian inference for reversible multidimensional diffusions
The Annals of Statistics · 2022 · Volume 50 · Issue 5
Abstract
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 in any dimension.
Keywords
60J60, 62F15, 62G20, Bayesian nonparametrics, Gaussian processes, Laplace prior, multidimensional diffusions, reversibility
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