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Hierarchical Bayesian level set inversion

Dunlop, Matthew M. and Iglesias, Marco A. and Stuart, Andrew M. (2017) Hierarchical Bayesian level set inversion. Statistics and Computing, 27 (6). pp. 1555-1584. ISSN 0960-3174. http://resolver.caltech.edu/CaltechAUTHORS:20161109-074003000

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Abstract

The level set approach has proven widely successful in the study of inverse problems for interfaces, since its systematic development in the 1990s. Recently it has been employed in the context of Bayesian inversion, allowing for the quantification of uncertainty within the reconstruction of interfaces. However, the Bayesian approach is very sensitive to the length and amplitude scales in the prior probabilistic model. This paper demonstrates how the scale-sensitivity can be circumvented by means of a hierarchical approach, using a single scalar parameter. Together with careful consideration of the development of algorithms which encode probability measure equivalences as the hierarchical parameter is varied, this leads to well-defined Gibbs-based MCMC methods found by alternating Metropolis–Hastings updates of the level set function and the hierarchical parameter. These methods demonstrably outperform non-hierarchical Bayesian level set methods.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s11222-016-9704-8DOIArticle
http://link.springer.com/article/10.1007%2Fs11222-016-9704-8PublisherArticle
https://arxiv.org/abs/1601.03605arXivDiscussion Paper
http://rdcu.be/tcdcPublisherFree ReadCube access
ORCID:
AuthorORCID
Dunlop, Matthew M.0000-0001-7718-3755
Additional Information:© 2016 Springer Science+Business Media New York. Received: 13 January 2016; Accepted: 09 September 2016; First Online: 21 September 2016. AMS is grateful to DARPA, EPSRC and ONR for financial support. MMD is supported by the EPSRC-funded MASDOC graduate training program. The authors are grateful to Dan Simpson for helpful discussions. The authors are also grateful for discussions with Omiros Papaspiliopoulos about links with probit. The authors would also like to the two anonymous referees for their comments that have helped improve the quality of the paper. This research utilized Queen Mary's MidPlus computational facilities, supported by QMUL Research-IT and funded by EPSRC grant EP/K000128/1.
Funders:
Funding AgencyGrant Number
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Engineering and Physical Sciences Research Council (EPSRC)EP/K000128/1
Office of Naval Research (ONR)UNSPECIFIED
Subject Keywords:Inverse problems for interfaces; Level set inversion; Hierarchical Bayesian methods
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartJ125
Record Number:CaltechAUTHORS:20161109-074003000
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20161109-074003000
Official Citation:Dunlop, M.M., Iglesias, M.A. & Stuart, A.M. Stat Comput (2017) 27: 1555. https://doi.org/10.1007/s11222-016-9704-8
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71856
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Nov 2016 18:04
Last Modified:07 Sep 2017 20:14

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