Inverse Problems Seminar - Increasing Stability in an Inverse Boundary Value Problem and a Statistical Aspect

Motivated by the recent work of Abraham and Nickl on the statistical Calderón problem (Math. Stat. Learn., 2019), we revisit the increasing stability phenomenon in the inverse boundary value problem for the stationary wave equation with a potential, using a Bayesian framework. Instead of the commonly used Dirichlet-to-Neumann map, we consider boundary measurements given by the impedance-to-Neumann map, whose graph forms a subset of the Cauchy data. We establish the consistency of the posterior mean and derive a contraction rate that quantitatively captures the increasing stability phenomenon. This talk is prepared based on my work with Jenn-Nan Wang [1]. [1] Pu-Zhao Kow and Jenn-Nan Wang, Increasing stability in an inverse boundary value problem - Bayesian viewpoint, Taiwanese J. Math. 29 (2025), no. 1, 89-128. https://doi.org/10.11650/tjm/240704