SPDE Methods for Nonparametric Bayesian Posterior Contraction and Laplace Approximation
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.
| Authors | Enric Alberola-Boloix, Ioar Casado-Telletxea |
|---|---|
| Primary category | stat.ML |
| Published | 23 March 2026 |
| Last updated at source | 23 March 2026 |
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