Bayesian approach to inverse problems
Stuart, A. M. (2011) Bayesian approach to inverse problems. In: LMS-EPSRC Short Course 2011, University of Oxford, 3–8 Apr 2011 (Unpublished)Full text not available from this repository.
Official URL: http://www.stats.ox.ac.uk/people/academic_staff/al...
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|
|Status:||Not Peer Reviewed|
|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|
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