The Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:15 pm
Date: 2nd of March 2020
Place: Room 3001.
Richard NICKL (University of Cambridge) – “On Bayesian solutions of some statistical inverse boundary value problems “

Abstract: We discuss Bayesian inference in a class of nonlinear statistical inverse problems arising with partial differential equations (PDEs): The main mathematical idea behind non-invasive tomography methods is related to the fact that observations of boundary values of the solutions of certain PDEs can in certain cases determine the parameters governing the dynamics of the PDE also in the interior of the domain in question. The parameter to data maps in such settings are typically non-linear, as with the Calderon problem (relevant in electric impedance tomography) or with non-Abelian X-ray transforms (relevant in neutron spin tomography). Real world discrete data in such settings carries statistical noise, and Bayesian inversion methodology has been extremely popular in computational and applied mathematics in the last decade after seminal contributions by Andrew Stuart (2010) and others. In this talk we will discuss recent progress which provides rigorous statistical guarantees for such inversion algorithms in the large sample/small noise limit.

 
Organizers:
Cristina BUTUCEA, Alexandre TSYBAKOV, Julie JOSSE, Eric MOULINES, Mathieu ROSENBAUM
Sponsors:
CREST-CMAP