Work

Semi-parametric Bernstein-von Mises theorem in linear inverse problems

Year: 2025

Type: article

Abstract: We consider a Bayesian approach for the recovery of scalar parameters arising in inverse problems. We consider a general signal-in white noise model where we have access to two independent noisy observations of a function, and of a linear transformation of the function. The linear operator is unknown up to a scalar parameter. We present a Bernstein-von Mises theorem for the marginal posterior of the scalar under regularity assumptions of the operator. We further derive Bernstein-von Mises results for different priors and apply them to two concrete examples: the recovery of the thermal diffusivity in a heat equation problem, and the recovery of a location parameter in a semi-blind deconvolution problem.

Source: Electronic Journal of Statistics

DOI: 10.1214/25-ejs2372

Authors: Adel Magra, Aad van der Vaart, Harry van Zanten

Institutions: Vrije Universiteit Amsterdam, Delft University of Technology

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $675

Funder: Nederlandse Organisatie voor Wetenschappelijk Onderzoek