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.
Funding Statement
Kow was partially supported by the NCCU Office of research and development and the National Science and Technology Council of Taiwan, NSTC 112-2115-M-004-004-MY3. Wang was partially supported by the National Science and Technology Council of Taiwan, NSTC 112-2115-M-002-010-MY3.
Citation
Pu-Zhao Kow. Jenn-Nan Wang. "Increasing Stability in an Inverse Boundary Value Problem—Bayesian Viewpoint." Taiwanese J. Math. 29 (1) 89 - 128, February, 2025. https://doi.org/10.11650/tjm/240704
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