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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2511.11068 |
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| _version_ | 1866911265819983872 |
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| author | Kow, Pu-Zhao Nurminen, Janne Railo, Jesse |
| author_facet | Kow, Pu-Zhao Nurminen, Janne Railo, Jesse |
| contents | This paper investigates the consistency of a posterior distribution in the single-measurement fractional Calderón problem with additive Gaussian noise. We consider a Bayesian framework with rescaled and Gaussian sieve priors, using a collection of noisy, discrete observations taken from a suitable exterior domain. Our main result shows that the posterior distribution concentrates around the true parameter as the number of measurements increases. Furthermore, we establish tight convergence rates for the reconstruction error of the posterior mean. A central technical challenge is to obtain refined stability estimates for both the forward and inverse problems. In particular, the required forward estimates are delicate to obtain because the fractional elliptic problems do not enjoy as strong regularity theory as their classical counterparts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11068 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bayesian inference for the fractional Calderón problem with a single measurement Kow, Pu-Zhao Nurminen, Janne Railo, Jesse Statistics Theory Analysis of PDEs 35R30 (Primary) 35R11, 62G20 (Secondary) This paper investigates the consistency of a posterior distribution in the single-measurement fractional Calderón problem with additive Gaussian noise. We consider a Bayesian framework with rescaled and Gaussian sieve priors, using a collection of noisy, discrete observations taken from a suitable exterior domain. Our main result shows that the posterior distribution concentrates around the true parameter as the number of measurements increases. Furthermore, we establish tight convergence rates for the reconstruction error of the posterior mean. A central technical challenge is to obtain refined stability estimates for both the forward and inverse problems. In particular, the required forward estimates are delicate to obtain because the fractional elliptic problems do not enjoy as strong regularity theory as their classical counterparts. |
| title | Bayesian inference for the fractional Calderón problem with a single measurement |
| topic | Statistics Theory Analysis of PDEs 35R30 (Primary) 35R11, 62G20 (Secondary) |
| url | https://arxiv.org/abs/2511.11068 |