arXiv subjects

Adel Magra

Publications and source records attributed to Adel Magra.

3 recordsLinked to original sources

arXiv2026

Semi-parametric Bernstein-von Mises Theorem in a Parabolic PDE Problem

We consider the heat equation with absorption in a bounded domain of $\mathbb{R}^d$, where both the scalar diffusivity and the absorption function are unknown. We investigate a Bayesian approach for recovering the diffusivity from a noisy observation of the solution to the PDE over the domain. Given a Gaussian process prior on the absorption function, we derive a Bernstein-von Mises theorem for the marginal posterior distribution of the diffusivity under assumptions on the prior and on smoothness properties of the absorption.

math.ST↗

arXiv2026

Efficient Bayesian Inference in Strictly Semi-parametric Linear Inverse Problems

We consider the efficient inference of finite dimensional parameters arising in the context of inverse problems. Our setup is the observation of a transformation of an unknown infinite dimensional signal $f$ corrupted by statistical noise, with the transformation $K_\theta$ being linear but unknown up to a scalar $\theta$. We adopt a Bayesian approach and put a prior on the pair $(\theta,f)$ and prove a Bernstein-von Mises theorem for the marginal posterior of $\theta$ under regularity conditions on the operators $K_\theta$ and on the prior. We apply our results to the recovery of location parameters in semi-blind deconvolution problems and to the recovery of attenuation constants in X-ray tomography.

math.ST↗

arXiv2023

Semi-parametric Bernstein-von Mises in Linear Inverse Problems

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.

math.ST↗