Sascha Gaudlitz: Bayesian inference in semi-linear SPDEs using spatial information

Speaker
Sascha Gaudlitz, Humboldt University Berlin

Abstract
We consider the Bayesian non-parametric estimation of the reaction term in a semi-linear parabolic SPDE. Posterior contraction rates are proven by making use of the spatial ergodicity of the SPDE while the time horizon is fixed. We additionally prove a non-parametric Bernstein- von Mises Theorem for the posterior distribution. The analysis of the posterior requires new concentration results for spatial averages of transformation of the SPDE, which are based the combination of the Clark-Ocone formula with bounds on the marginal densities. This is joint work with Randolf Altmeyer.