Institute of Mathematics

Talk

Modul:   MAT870  Zurich Colloquium in Applied and Computational Mathematics

On the Convergence of Laplace's Approximation and Its Implications for Bayesian Computation

Prof. Dr. Claudia Schillings talk

Date: 24.10.18  Time: 16.15 - 17.45  Room: ETH HG E 1.2

Inverse problems arise in various fields of sciences and engineering. Methods to efficiently incorporate data into models are needed to reduce the overall uncertainty and to ensure the reliability of the simulations under real world conditions. The Bayesian approach to inverse problems provides a rigorous framework for the incorporation and quantification of uncertainties in measurements, parameters and models. The concentration of the posterior is a highly desirable situation in practice, since it relates to informative or large data. However, sampling methods for Bayesian inference show numerical instabilities in the case of concentrated posterior distributions. In this talk, we will discuss convergence results of Laplace’s approximation and analyze the use of the approximation within sampling methods. This is joint work with Bjoern Sprungk (U Goettingen) and Philipp Wacker (FAU Erlangen).