Richard Nickl
This 6th Kálmán Lecture with Richard Nickl is opener for the 2nd Potsdam DA Days. Title of his talk is
'On posterior consistency in non-linear Bayesian data assimilation problems'.
Abstract
Bayesian methods are widely used in statistical data assimilation tasks. They model infinite-dimensional aspects of possibly non-linear dynamical systems — such as initial conditions, or diffusivity parameters -- by Gaussian process (or similar) prior probability measures. The posterior distribution is obtained from updating the system from discrete and noisy measurements of the observed dynamics, and can often be approximately computed by filtering or MCMC methods. In non-linear settings, such posterior distributions are not themselves Gaussian any longer, and very little is known rigorously about the statistical behaviour of the updated non-linear systems. In this talk we will explain how recent developments in the theory of nonlinear Bayesian inverse problems can be used to prove the statistical large sample consistency of posterior inferences in two representative PDE models arising with a) discretely sampled multi-dimensional SDEs as well as b) Eulerian measurements of the (2D) Navier Stokes equations.
