Efficient Bayesian Inference in Strictly Semi-parametric Linear Inverse Problems
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918317683376128 |
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| author | Magra, Adel van der Vaart, Aad |
| author_facet | Magra, Adel van der Vaart, Aad |
| contents | We consider the efficient inference of finite dimensional parameters arising in the context of inverse problems. Our setup is the observation of a transformation of an unknown infinite dimensional signal $f$ corrupted by statistical noise, with the transformation $K_θ$ being linear but unknown up to a scalar $θ$. We adopt a Bayesian approach and put a prior on the pair $(θ,f)$ and prove a Bernstein-von Mises theorem for the marginal posterior of $θ$ under regularity conditions on the operators $K_θ$ and on the prior. We apply our results to the recovery of location parameters in semi-blind deconvolution problems and to the recovery of attenuation constants in X-ray tomography. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00901 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Efficient Bayesian Inference in Strictly Semi-parametric Linear Inverse Problems Magra, Adel van der Vaart, Aad Statistics Theory We consider the efficient inference of finite dimensional parameters arising in the context of inverse problems. Our setup is the observation of a transformation of an unknown infinite dimensional signal $f$ corrupted by statistical noise, with the transformation $K_θ$ being linear but unknown up to a scalar $θ$. We adopt a Bayesian approach and put a prior on the pair $(θ,f)$ and prove a Bernstein-von Mises theorem for the marginal posterior of $θ$ under regularity conditions on the operators $K_θ$ and on the prior. We apply our results to the recovery of location parameters in semi-blind deconvolution problems and to the recovery of attenuation constants in X-ray tomography. |
| title | Efficient Bayesian Inference in Strictly Semi-parametric Linear Inverse Problems |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2602.00901 |