A Bernstein–von-Mises theorem for the Calderón problem with piecewise constant conductivities
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IOP Publishing
https://doi.org/10.1088/1361-6420/ac9db8
https://doi.org/10.1088/1361-6420/ac9db8
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Funder: EPSRC Centre for Doctoral Training
Funder: Munro–Greaves Bursary (Queens’ College Cambridge)
This note considers a finite dimensional statistical model for the Calderón 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.
Funder: Munro–Greaves Bursary (Queens’ College Cambridge)
This note considers a finite dimensional statistical model for the Calderón 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.