A Bernstein–von-Mises theorem for the Calderón problem with piecewise constant conductivities

06/16/2022
by   Jan Bohr, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

12/11/2017

Asymptotically optimal empirical Bayes inference in a piecewise constant sequence model

Inference on high-dimensional parameters in structured linear models is ...
08/27/2016

Bayesian selection for the l2-Potts model regularization parameter: 1D piecewise constant signal denoising

Piecewise constant denoising can be solved either by deterministic optim...
11/23/2018

Note on universal algorithms for learning theory

We propose the general way of study the universal estimator for the regr...
09/05/2012

Learning Manifolds with K-Means and K-Flats

We study the problem of estimating a manifold from random samples. In pa...
08/03/2020

Convergence Rates for Bayesian Estimation and Testing in Monotone Regression

Shape restrictions such as monotonicity on functions often arise natural...
01/09/2018

A detailed treatment of Doob's theorem

Doob's theorem provides guarantees of consistent estimation and posterio...
06/07/2020

On forward invariance in Lyapunov stability theorem for local stability

Forward invariance of a basin of attraction is often overlooked when usi...