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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.00901 |
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Table of 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.