Richard Nickl - Statistical guarantees for the Bayesian approach to inverse problems
|Starts:||12:00 10 Mar 2020|
|Ends:||13:00 10 Mar 2020|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
|Who is it for:||University staff, External researchers, Current University students|
|Speaker:||Prof Richard Nickl|
- Postponed due to strike action*** The seminar should be rescheduled for the autumn.
Abstract: Bayes methods for inverse problems have become very popular in applied mathematics in the last decade after seminal work by Persi Diaconis and Andrew Stuart. They provide reconstruction algorithms as well as in-built “uncertainty quantification” via Bayesian credible sets, and particularly for Gaussian process priors can be efficiently implemented by MCMC methodology. For linear inverse problems, they are closely related to classical penalised least squares methods and thus not fundamentally new, but for non-linear and non-convex problems, they give genuinely distinct and computable algorithmic alternatives that cannot be studied by variational analysis or convex optimisation techniques. In this talk we will discuss recent progress in Bayesian non-parametric statistics that allows to give rigorous statistical guarantees for posterior consistency in such models, and illustrate the theory in a variety of concrete non-linear inverse problems arising with partial differential equations and X-ray transforms.
Prof Richard Nickl
Role: Professor of Mathematical Statistics
Organisation: Cambridge University
Travel and Contact Information
Frank Adams 1
Alan Turing Building