AI RESEARCH
SPDE Methods for Nonparametric Bayesian Posterior Contraction and Laplace Approximation
arXiv CS.LG
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ArXi:2603.22468v1 Announce Type: cross 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 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.