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Bayesian Theory and Applications$
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Paul Damien, Petros Dellaportas, Nicholas G. Polson, and David A. Stephens

Print publication date: 2013

Print ISBN-13: 9780199695607

Published to Oxford Scholarship Online: May 2013

DOI: 10.1093/acprof:oso/9780199695607.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 22 April 2021

Inverse problems

Inverse problems

(p.619) 31 Inverse problems
Bayesian Theory and Applications

Fox Colin

Haario Heikki

Christen J Andrés

Oxford University Press

This chapter discusses the features that are characteristic for the problems most typically treated under the umbrella of inverse problems. It begins by listing representative examples of inverse problems followed by a discussion of the key mathematical property of ill-posedness. It then discusses deterministic and regularization methods, and presents some history of Bayesian analysis, as viewed from physics. Next, it provides the framework for current methodology and describes some of the recent advances in Markov chain Monte Carlo (MCMC) algorithms. The chapter concludes with a glimpse of future directions.

Keywords:   inverse problems, Bayesian analysis, Markov chain Monte Carlo algorithms

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