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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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Online
ISSN
1569-3945
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Volume 22, Issue 2

Issues

Convergence of posteriors for structurally non-identified problems using results from the theory of inverse problems

Nicole E. Radde / Jonas Offtermatt
Published Online: 2013-05-25 | DOI: https://doi.org/10.1515/jip-2012-0057

Abstract.

We consider convergence of the posterior distribution in a Bayesian parameter estimation framework in the large sample size limit for structurally non-identified problems. These belong to the class of ill-posed problems, and the large sample theory is not applicable here. In particular, the influence of the prior distribution does not vanish in the large sample size limit. We review recent results in this area and present ideas inspired from the theory of ill-posed inverse problems that can be used towards a more general concept of posterior convergence for non-identified problems.

Keywords: Bayesian regularization; Tikhonov regularization; ill-posed inverse problem; non-identifiability; convergence in probability

MSC: 62F15; 65J20

About the article

Received: 2012-08-14

Published Online: 2013-05-25

Published in Print: 2014-04-01


Funding Source: German Research Foundation (DFG)

Award identifier / Grant number: Cluster of Excellence in Simulation Technology (EXC 310)

Funding Source: Ministry of Science, Research and Arts (MWK) Baden-Württemberg

Award identifier / Grant number: program for junior professors


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 22, Issue 2, Pages 251–276, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jip-2012-0057.

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