Title: A Bernstein-von Mises theorem for stochastic PDEs
Authors: Randolf Altmeyer - Cambridge University (United Kingdom) [presenting]
Abstract: The Bayesian paradigm is considered in the context of statistics for SPDEs (stochastic partial differential equations). The goal is to perform nonparametric estimation of the diffusivity function in the stochastic heat equation, driven by space time white noise. Observations are given by local measurements, that is, the solution convoluted in a space with a compactly supported kernel function. Starting with a Gaussian process prior for the diffusivity, we discuss a Bernstein-von Mises theorem. This proves that the posterior distribution allows for asymptotically valid and optimal frequentist statistical inference on the diffusivity. As an important ingredient in the proof, we will also discuss the local asymptotic normality (LAN) property of the statistical model.