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NONPARAMETRIC BAYESIAN INFERENCE FOR REVERSIBLE MULTIDIMENSIONAL DIFFUSIONS
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DOI：10.1214/22-AOS2213.png)
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Abstract
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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
Keywords:
Bayesian nonparametrics
multidimensional diffusions
reversibility
Gaussian processes
Laplace prior
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