Semiparametric Bernstein-von Mises theorems for reversible diffusions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908374315040768 |
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| author | Giordano, Matteo Ray, Kolyan |
| author_facet | Giordano, Matteo Ray, Kolyan |
| contents | We establish a general semiparametric Bernstein-von Mises theorem for Bayesian nonparametric priors based on continuous observations in a periodic reversible multidimensional diffusion model. We consider a wide range of functionals satisfying an approximate linearization condition, including several nonlinear functionals of the invariant measure. Our result is applied to Gaussian and Besov-Laplace priors, showing these can perform efficient semiparametric inference and thus justifying the corresponding Bayesian approach to uncertainty quantification. Our theoretical results are illustrated via numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16275 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semiparametric Bernstein-von Mises theorems for reversible diffusions Giordano, Matteo Ray, Kolyan Statistics Theory We establish a general semiparametric Bernstein-von Mises theorem for Bayesian nonparametric priors based on continuous observations in a periodic reversible multidimensional diffusion model. We consider a wide range of functionals satisfying an approximate linearization condition, including several nonlinear functionals of the invariant measure. Our result is applied to Gaussian and Besov-Laplace priors, showing these can perform efficient semiparametric inference and thus justifying the corresponding Bayesian approach to uncertainty quantification. Our theoretical results are illustrated via numerical simulations. |
| title | Semiparametric Bernstein-von Mises theorems for reversible diffusions |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2505.16275 |