Semi-parametric Bernstein-von Mises in Linear Inverse Problems
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916680649670656 |
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| author | Magra, Adel van der Vaart, Aad van Zanten, Harry |
| author_facet | Magra, Adel van der Vaart, Aad van Zanten, Harry |
| contents | We consider a Bayesian approach for the recovery of scalar parameters arising in inverse problems. We consider a general signal-in white noise model where we have access to two independent noisy observations of a function, and of a linear transformation of the function. The linear operator is unknown up to a scalar parameter. We present a Bernstein-von Mises theorem for the marginal posterior of the scalar under regularity assumptions of the operator. We further derive Bernstein-von Mises results for different priors and apply them to two concrete examples: the recovery of the thermal diffusivity in a heat equation problem, and the recovery of a location parameter in a semi-blind deconvolution problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_02883 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Semi-parametric Bernstein-von Mises in Linear Inverse Problems Magra, Adel van der Vaart, Aad van Zanten, Harry Statistics Theory 62F15, 62E20 We consider a Bayesian approach for the recovery of scalar parameters arising in inverse problems. We consider a general signal-in white noise model where we have access to two independent noisy observations of a function, and of a linear transformation of the function. The linear operator is unknown up to a scalar parameter. We present a Bernstein-von Mises theorem for the marginal posterior of the scalar under regularity assumptions of the operator. We further derive Bernstein-von Mises results for different priors and apply them to two concrete examples: the recovery of the thermal diffusivity in a heat equation problem, and the recovery of a location parameter in a semi-blind deconvolution problem. |
| title | Semi-parametric Bernstein-von Mises in Linear Inverse Problems |
| topic | Statistics Theory 62F15, 62E20 |
| url | https://arxiv.org/abs/2310.02883 |