Semi-parametric Bernstein-von Mises Theorem in a Parabolic PDE Problem
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915767017013248 |
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| author | Magra, Adel van der Meulen, Frank van der Vaart, Aad |
| author_facet | Magra, Adel van der Meulen, Frank van der Vaart, Aad |
| contents | We consider the heat equation with absorption in a bounded domain of $\mathbb{R}^d$, where both the scalar diffusivity and the absorption function are unknown. We investigate a Bayesian approach for recovering the diffusivity from a noisy observation of the solution to the PDE over the domain. Given a Gaussian process prior on the absorption function, we derive a Bernstein-von Mises theorem for the marginal posterior distribution of the diffusivity under assumptions on the prior and on smoothness properties of the absorption. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00889 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Semi-parametric Bernstein-von Mises Theorem in a Parabolic PDE Problem Magra, Adel van der Meulen, Frank van der Vaart, Aad Statistics Theory We consider the heat equation with absorption in a bounded domain of $\mathbb{R}^d$, where both the scalar diffusivity and the absorption function are unknown. We investigate a Bayesian approach for recovering the diffusivity from a noisy observation of the solution to the PDE over the domain. Given a Gaussian process prior on the absorption function, we derive a Bernstein-von Mises theorem for the marginal posterior distribution of the diffusivity under assumptions on the prior and on smoothness properties of the absorption. |
| title | Semi-parametric Bernstein-von Mises Theorem in a Parabolic PDE Problem |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2602.00889 |