Special CMX Lunch Seminar

We will discuss recent progress in our understanding of Bayesian inference methods for parameters or states of time evolution phenomena modelled by non-linear partial differential equations (PDEs) such as Navier-Stokes, McKean-Vlasov, and reaction-diffusion systems. We will show that posteriors can deliver consistent solutions in the `informative' large data/small noise limit, discuss probabilistic approximations to the fluctuations of such posterior measures in infinite dimensions, and how such results can be used to show that the non-convex problem of computation of the associated `filtering' distributions are polynomial time problems.