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SIAM Conference on Uncertainty Quantification (UQ20)

Wednesday – 25.03.2020

14:00

iCal
Björn Sprungk | TU Bergakademie Freiberg | Germany

Aretha Teckentrup | University of Edinburgh | United Kingdom

Matteo Giordano | University of Cambridge | United Kingdom

Masoumeh Dashti | University of Sussex | United Kingdom

MS431: Would Hadamard have used Bayes' rule? - On robustness and brittleness of statistical inversion

Room:
MW HS 0250

Topic:
Inverse problems

Form of presentation:
Mini-symposium

Duration:
120 Minutes

Organized in co-operation with

GAMM AG UQ

In many scientific disciplines, researchers encounter inverse problems where observational data shall be used to calibrate mathematical models. Hadamard considered the solvability of such problems in terms of their "well-posedness". He called a problem well-posed, if a solution exists, if the solution is unique, and if the solution depends continuously on the data. Inverse problems are typically not well-posed (i.e., ill-posed) and require some regularization. Today's availability of high-performance computing has raised the popularity of statistical approaches to inverse problems and probabilistic regularizations; like the Bayesian approach.

In this minisymposium, we consider the robustness and non-robustness (that is, the brittleness) of Bayesian inverse problems and related approaches. This includes the robustness with respect to perturbations in the data (that is, the well-posedness), but also with respect to perturbations in the prior measure or the likelihood. Perturbations in the

prior also include a potential ill-specification of the prior model whereas perturbations in the likelihood include the replacement of the mathematical model by a discretised version or a surrogate. Moreover, we are interested in the robustness of algorithms used for statistical inversion, such as MCMC, particle filters, variational Bayes, and approximate Bayesian computation.

14:00

On the Local Lipschitz Robustness of Bayesian Inverse Problems

14:30

Gaussian process emulators in Bayesian inverse problems

15:00

- NEW - Consistency of Bayesian inference with Gaussian priors in an elliptic nonlinear inverse problem

15:30

MAP estimators and posterior consistency for Bayesian inverse problems for functions