Nonparametric Bayesian inference for reversible multi-dimensional diffusions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866910549249359872 |
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| author | Giordano, Matteo Ray, Kolyan |
| author_facet | Giordano, Matteo Ray, Kolyan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_12083 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Nonparametric Bayesian inference for reversible multi-dimensional diffusions Giordano, Matteo Ray, Kolyan Statistics Theory Numerical Analysis Probability 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. |
| title | Nonparametric Bayesian inference for reversible multi-dimensional diffusions |
| topic | Statistics Theory Numerical Analysis Probability |
| url | https://arxiv.org/abs/2012.12083 |