Work

Multilevel Markov Chain Monte Carlo with Likelihood Scaling for Bayesian Inversion with High-resolution Observations

Year: 2025

Type: article

Abstract: . We propose a multilevel Markov chain Monte Carlo (MCMC) method for the Bayesian inference of random field parameters in PDEs using high-resolution data. Compared to existing multilevel MCMC methods, we additionally consider level-dependent data resolution and introduce a suitable likelihood scaling to enable consistent cross-level comparisons. We theoretically show that this approach attains the same convergence rates as when using level-independent treatment of data, but at significantly reduced computational cost. The convergence analysis focuses on Lipschitz continuous transformations of Gaussian random fields with Matérn covariance structure. These results are illustrated using numerical experiments for a two-dimensional plane stress problem, where Young’s modulus is estimated from discretizations of the displacement field.

Source: SIAM/ASA Journal on Uncertainty Quantification

DOI: 10.1137/24m1634333

Authors: P. Vanmechelen, G. Lombaert, G. Samaey

Institution: KU Leuven

Language: English

Topic: Markov Chains and Monte Carlo Methods

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Fonds Wetenschappelijk Onderzoek, KU Leuven, Vlaamse regering

Award: Multilevel Markov Chain Monte Carlo methods for Bayesian full-field data assimilation