Comparison of three random field sampling methods for high-resolution Bayesian inversion with application to a plane stress problem

Bayesian inversion aims to provide uncertainty quantification of posterior estimates conditional on observations. When the inferred parameter is a continuous spatial function, one common strategy is to model it as a random field. Several random field sampling strategies exist. In this article, we investigate three different approaches in terms of numerical efficiency and influence on the posterior distribution. These approaches are based on (i) Karhunen-Loeve and (ii) wavelet expansions, and (iii) local average subdivision. We use the multilevel Markov chain Monte Carlo algorithm to construct posterior estimates with all approaches. This enables a focus on high-dimensional problems discretised on high-resolution finite element grids. As an application, we consider the reconstruction of material parameters in a 2D plane stress model, conditional on static displacement observations. Through these numerical experiments, we deduce that the methods provide comparable posterior estimates and that the local average subdivision method attains slightly better numerical efficiency than the other two approaches.