2pm-3,30

Speaker: Richard Nickl (University of Cambridge)

Title: ‘On Bayes solutions of some nonlinear inverse problems’

Abstract: Bayesian methodology has recently become popular in inverse problems as algorithmic advances have made approximate computation of the posterior distribution viable — see the work by Andrew Stuart, Gareth Roberts and co-authors. A natural question to ask is whether the Bayesian algorithm `works’ in the sense that posterior-based inference gives an optimal solution of the inverse problem that is `objective' (independent of the prior). Interesting inverse problems typically lead to infinite-dimensional parameter spaces and thus this question cannot be answered by classical parametric theory, but has to be tackled by tools from Bayesian Non-parametrics. We will discuss recent results that establish the frequentist optimality of Bayesian solutions of a certain class of nonlinear inverse problems that arise when one observes a continuous-time stochastic process, such as a diffusion of Levy process, at finitely many discrete times. We will address both contraction theorems as well as `limiting shape’ results such as Bernstein von Mises theorems for posterior distributions.’

3:30-4:30

Speaker: Michael Goldstein (Durham University)

Title: Bayes linear uncertainty analysis for complex physical systems modelled by computer simulators

Abstract: Most large and complex physical systems are studied by mathematical models, implemented as high dimensional computer simulators. While all such cases differ in physical description, each analysis of a physical system based on a computer simulator involves the same underlying sources of uncertainty. There is a growing field of study which aims to quantify and synthesise all of the uncertainties involved in relating models to physical systems, within the framework of Bayesian statistics, and to use the resultant uncertainty specification to address problems of forecasting and decision making. This talk will give an overview of aspects of this emerging methodology, with illustrations from current areas of application.