[2603.22468] SPDE Methods for Nonparametric Bayesian Posterior Contraction and Laplace Approximation

Statistics > Machine Learning arXiv:2603.22468 (stat) [Submitted on 23 Mar 2026] Title:SPDE Methods for Nonparametric Bayesian Posterior Contraction and Laplace Approximation Authors:Enric Alberola-Boloix, Ioar Casado-Telletxea View a PDF of the paper titled SPDE Methods for Nonparametric Bayesian Posterior Contraction and Laplace Approximation, by Enric Alberola-Boloix and 1 other authors View PDF HTML (experimental) Abstract:We derive posterior contraction rates (PCRs) and finite-sample Bernstein von Mises (BvM) results for non-parametric Bayesian models by extending the diffusion-based framework of Mou et al. (2024) to the infinite-dimensional setting. The posterior is represented as the invariant measure of a Langevin stochastic partial differential equation (SPDE) on a separable Hilbert space, which allows us to control posterior moments and obtain non-asymptotic concentration rates in Hilbert norms under various likelihood curvature and regularity conditions. We also establish a quantitative Laplace approximation for the posterior. The theory is illustrated in a nonparametric linear Gaussian inverse problem. Comments: Subjects: Machine Learning (stat.ML); Machine Learning (cs.LG); Statistics Theory (math.ST) Cite as: arXiv:2603.22468 [stat.ML]   (or arXiv:2603.22468v1 [stat.ML] for this version)   https://doi.org/10.48550/arXiv.2603.22468 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Ioar Casado [view email] [v1] Mo...