Nonparametric Bayesian inference for reversible multi-dimensional diffusions
File(s)
Accepted version
Supporting information
Author(s)
Giordano, Matteo
Ray, Kolyan
Type
Journal Article
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.
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.
Date Issued
2022-10-01
Date Acceptance
2022-07-18
Citation
Annals of Statistics, 2022, 50 (5), pp.2872-2898
ISSN
0090-5364
Publisher
Institute of Mathematical Statistics
Start Page
2872
End Page
2898
Journal / Book Title
Annals of Statistics
Volume
50
Issue
5
Copyright Statement
© 2022 Institute of Mathematical Statistics.
Publication Status
Published