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