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Inverse problems : a Bayesian perspective
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Stuart, A. M. (2010) Inverse problems : a Bayesian perspective. Acta Numerica, Vol.19 . pp. 451-559. doi:10.1017/S0962492910000061 ISSN 0962-4929.
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Official URL: http://webcat.warwick.ac.uk:80/record=b2341209
Abstract
The subject of inverse problems in differential equations is of enormous practical importance, and has also generated substantial mathematical and computational innovation. Typically some form of regularization is required to ameliorate ill-posed behaviour. In this article we review the Bayesian approach to regularization, developing a function space viewpoint on the subject. This approach allows for a full characterization of all possible solutions, and their relative probabilities, whilst simultaneously forcing significant modelling issues to be addressed in a clear and precise fashion. Although expensive to implement, this approach is starting to lie within the range of the available computational resources in many application areas. It also allows for the quantification of uncertainty and risk, something which is increasingly demanded by these applications. Furthermore, the approach is conceptually important for the understanding of simpler, computationally expedient approaches to inverse problems.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Series Name: | Acta Numerica | ||||
Journal or Publication Title: | Acta Numerica | ||||
Publisher: | Cambridge University Press | ||||
Place of Publication: | Cambridge | ||||
ISBN: | 9780521192842 | ||||
ISSN: | 0962-4929 | ||||
Book Title: | Acta Numerica 19 | ||||
Editor: | Iserles, Arieh | ||||
Official Date: | May 2010 | ||||
Dates: |
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Volume: | Vol.19 | ||||
Number of Pages: | 110 | ||||
Page Range: | pp. 451-559 | ||||
DOI: | 10.1017/S0962492910000061 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
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