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Bayesian approach to inverse problems
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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 In: LMS-EPSRC Short Course 2011, University of Oxford, 3–8 Apr 2011 (Unpublished)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) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Official Date: | April 2011 | ||||
Dates: |
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Status: | Not Peer Reviewed | ||||
Publication Status: | Unpublished | ||||
Description: | A series of 5 lectures delivered at the same event |
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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 |
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