Stuart, A. M. (2011) Bayesian approach to inverse problems. In: LMS-EPSRC Short Course 2011, University of Oxford, 3–8 Apr 2011 (Unpublished)

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Abstract

Inverse problems in differential equations are ubiquitous in applications and provide formidable mathematical challenges due to their ill-posedness. One approach to regularization of inverse problems is to adopt a Bayesian framework for the problem. I will develop this Bayesian approach in a Banach space setting, leading to an interesting class of problems for probability measures on function space, defined via their Radon-Nikodym derivative with respect to a reference (prior) measure. I will develop a stability theory for these measures, showing that they are Lipschitz in the data, with respect to the Hellinger metric. I will then use this theory as the basis to quantify approximations of the measure, using finite dimensional subspaces. I will also show that a wide range of problems fit into the general framework, including inverse problems for the di�ffusion coefficient in an elliptic PDE, the wavespeed in a wave equation and the initial condition for the heat equation and nonlinear generalizations.

Item Type:	Conference Item (Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Date:	April 2011
Status:	Not Peer Reviewed
Publication Status:	Unpublished
Description:	A series of 5 lectures delivered at the same event
Conference Paper Type:	Paper
Title of Event:	LMS-EPSRC Short Course 2011
Type of Event:	Conference
Location of Event:	University of Oxford
Date(s) of Event:	3–8 Apr 2011
URI:	http://wrap.warwick.ac.uk/id/eprint/48239

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