AI Chat AI Image Generator AI Video Text to Speech

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

06/16/2022

∙

by Jan Bohr, et al.

∙

∙

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.

page 1

page 2

page 3

page 4

research

∙ 12/11/2017

Asymptotically optimal empirical Bayes inference in a piecewise constant sequence model

Inference on high-dimensional parameters in structured linear models is ...

0 Ryan Martin, et al. ∙

research

∙ 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...

0 Jordan Frecon, et al. ∙

research

∙ 09/05/2012

Learning Manifolds with K-Means and K-Flats

We study the problem of estimating a manifold from random samples. In pa...

0 Guillermo D. Canas, et al. ∙

research

∙ 11/23/2018

Note on universal algorithms for learning theory

We propose the general way of study the universal estimator for the regr...

0 Karol Dziedziul, et al. ∙

research

∙ 05/12/2023

Nonparametric Bayesian inference for stochastic processes with piecewise constant priors

We present a survey of some of our recent results on Bayesian nonparamet...

0 Denis Belomestny, et al. ∙

research

∙ 01/09/2018

A detailed treatment of Doob's theorem

Doob's theorem provides guarantees of consistent estimation and posterio...

0 Jeffrey W. Miller, et al. ∙

research

∙ 09/22/2018

A convex program for bilinear inversion of sparse vectors

We consider the bilinear inverse problem of recovering two vectors, x∈R^...

0 Alireza Aghasi, et al. ∙