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Bayesian inference for the fractional Calderón problem wi...
[Submitted on 14 Nov 2025 (v1), last revised 10 Sep 2026 (this v · 2025-11-14 · via stat updates on arXiv.org

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Abstract: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.

Submission history

From: Janne Nurminen [view email]
[v1] Fri, 14 Nov 2025 08:38:15 UTC (81 KB)
[v2] Thu, 10 Sep 2026 04:28:27 UTC (80 KB)