The Bernstein-von Mises theorem for the inverse scattering problem
Journal
Communications in Mathematical Sciences
Journal Volume
23
Journal Issue
4
Start Page
1023-1042
ISSN
1539-6746
1945-0796
Date Issued
2025
Author(s)
Furuya, Takashi
Abstract
In this work, we study the inverse scattering problem of determining an unknown refractive index from the far-field measurements using the Bayesian approach. Our aim is to prove the Bernstein-von Mises theorem for this inverse scattering problem when the unknown coefficient is in a class of piecewise constant functions. We also provide numerical simulations based on the MCMC algorithm combining with a Gibbs-type sampling and MALA to verify the Bernstein-von Mises theorem.
Publisher
International Press of Boston
Type
journal article