42nd Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series Talk
Date: Wednesday, April 13, 10:00am Eastern
Speaker: Ru Nicholson, University of Auckland

Abstract: In this talk we consider the use of surrogate (forward) models to efficiently solve Bayesian inverse problems. We particularly concern ourselves with the use of linear surrogates. The problems considered are from a range of applications but are all high dimensional problems resulting from the discretisation of partial differential equations. We adopt the Bayesian approach to account for the model discrepancy, which is treated as an additional stochastic error term. We prove a somewhat surprising result: under the assumption of a Gaussian prior and additive noise model the approximate posterior found by using a linear(-ised) surrogate is invariant to the choice of linear surrogate, so long as the model discrepancy is (approximately) taken into account. This is ongoing joint work with Noemi Petra, Umberto Villa, and Jari P. Kaipio.

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