On the Use of Linear Surrogate Models for Bayesian Inverse Problems

Explore the use of linear surrogate models in solving Bayesian inverse problems during this one-hour virtual seminar presented by the Society for Industrial and Applied Mathematics. Delve into high-dimensional problems arising from the discretization of partial differential equations across various applications. Learn about the Bayesian approach to account for model discrepancy and discover a surprising result regarding the invariance of approximate posteriors when using linear surrogates. Examine case studies in corrosion detection, scattering, and electrical impedance tomography. Gain insights from speaker Ru Nicholson of the University of Auckland as part of the 42nd Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series.

Introduction
Overview
Motivation
Bayesian Inverse Problems
Additive Error Model
Inference Problem
Bayesian approximation error approach
Corrosion detection
The likelihood
Examples
Scattering Case
EIT Samples
Conclusion