English

A Bernstein--von-Mises theorem for the Calder\'on problem with piecewise constant conductivities

Statistics Theory 2022-06-17 v1 Analysis of PDEs Statistics Theory

Abstract

This note considers a finite dimensional statistical model for the Calder\'on problem with piecewise constant conductivities. In this setting it is shown that injectivity of the forward map and its linearisation suffice to prove the invertibility of the information operator, resulting in a Bernstein--von-Mises theorem and optimality guarantees for estimation by Bayesian posterior means.

Keywords

Cite

@article{arxiv.2206.08177,
  title  = {A Bernstein--von-Mises theorem for the Calder\'on problem with piecewise constant conductivities},
  author = {Jan Bohr},
  journal= {arXiv preprint arXiv:2206.08177},
  year   = {2022}
}