Increasing Stability in an Inverse Boundary Value Problem—Bayesian Viewpoint
Journal
Taiwanese Journal of Mathematics
Journal Volume
29
Journal Issue
1
ISSN
1027-5487
Date Issued
2025-01-17
Author(s)
Pu-Zhao Kow
Abstract
Motivated by the recent work of Abraham and Nickl on the statistical Calderón problem [2], we revisit the increasing stability phenomenon in the inverse boundary value problem for the stationary wave equation with a potential using the Bayesian approach. In this paper, rather than the Dirichlet-to-Neumann map, we consider another type of boundary measurements called the impedance-to-Neumann map. Its graph forms a subset of Cauchy data. We show the consistency of the posterior mean with a contraction rate demonstrating the phenomenon of increasing stability.
Publisher
The Mathematical Society of the Republic of China
Type
journal article