Consistency of Bayesian inference for a parabolic inverse problem

Hanne Kekkonen (TU Delft)

May 18. 2022, 15:15 — 16:00

Bayesian methods for inverse problems have become increasingly popular in applied mathematics in the last decades but the theoretical understanding of the statistical performance of these methods for non-linear inverse problems is still developing. In this talk I'll consider the inverse problem of discovering the absorption term f>0 in a heat equation, with given boundary and initial value functions, from N discrete noisy point evaluations of the forward solution. I will show that for this non-linear parabolic inverse problem the optimal minimax rate can be achieved with truncated Gaussian priors.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Computational Uncertainty Quantification: Mathematical Foundations, Methodology & Data (Thematic Programme)
Clemens Heitzinger (TU Vienna)
Fabio Nobile (EPFL, Lausanne)
Robert Scheichl (U Heidelberg)
Christoph Schwab (ETH Zurich)
Sara van de Geer (ETH Zurich)
Karen Willcox (U of Texas, Austin)