A Bernstein--von-Mises theorem for the Calderón problem with piecewise constant conductivities (2206.08177v1)

Published 16 Jun 2022 in math.ST, math.AP, and stat.TH

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.

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Authors (1)

Jan Bohr

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