Hierarchical Bayesian level set inversion

The level set approach has proven widely successful in the study of inverse problems for inter- faces, since its systematic development in the 1990s. Re- cently it has been employed in the context of Bayesian inversion, allowing for the quantification of uncertainty within the reconstruction of inte...

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Main Authors:	Dunlop, Matthew M., Iglesias, Marco, Stuart, Andrew M.
Format:	Article
Language:	English
Published:	Springer 2016
Online Access:	http://eprints.nottingham.ac.uk/40915/ http://eprints.nottingham.ac.uk/40915/ http://eprints.nottingham.ac.uk/40915/ http://eprints.nottingham.ac.uk/40915/1/hierarchical_new2-3.pdf

id	nottingham-40915
recordtype	eprints
spelling	nottingham-409152017-10-13T01:41:05Z http://eprints.nottingham.ac.uk/40915/ Hierarchical Bayesian level set inversion Dunlop, Matthew M. Iglesias, Marco Stuart, Andrew M. The level set approach has proven widely successful in the study of inverse problems for inter- faces, since its systematic development in the 1990s. Re- cently 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 cir- cumvented by means of a hierarchical approach, using a single scalar parameter. Together with careful con- sideration of the development of algorithms which en- code probability measure equivalences as the hierar- chical 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 demon- strably outperform non-hierarchical Bayesian level set methods. Springer 2016-09-21 Article PeerReviewed application/pdf en http://eprints.nottingham.ac.uk/40915/1/hierarchical_new2-3.pdf Dunlop, Matthew M. and Iglesias, Marco and Stuart, Andrew M. (2016) Hierarchical Bayesian level set inversion. Statistics and Computing, 27 (6). pp. 1555-1584. ISSN 1573-1375 https://link.springer.com/article/10.1007%2Fs11222-016-9704-8 doi:10.1007/s11222-016-9704-8 doi:10.1007/s11222-016-9704-8
repository_type	Digital Repository
institution_category	Local University
institution	University of Nottingham Malaysia Campus
building	Nottingham Research Data Repository
collection	Online Access
language	English
description	The level set approach has proven widely successful in the study of inverse problems for inter- faces, since its systematic development in the 1990s. Re- cently 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 cir- cumvented by means of a hierarchical approach, using a single scalar parameter. Together with careful con- sideration of the development of algorithms which en- code probability measure equivalences as the hierar- chical 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 demon- strably outperform non-hierarchical Bayesian level set methods.
format	Article
author	Dunlop, Matthew M. Iglesias, Marco Stuart, Andrew M.
spellingShingle	Dunlop, Matthew M. Iglesias, Marco Stuart, Andrew M. Hierarchical Bayesian level set inversion
author_facet	Dunlop, Matthew M. Iglesias, Marco Stuart, Andrew M.
author_sort	Dunlop, Matthew M.
title	Hierarchical Bayesian level set inversion
title_short	Hierarchical Bayesian level set inversion
title_full	Hierarchical Bayesian level set inversion
title_fullStr	Hierarchical Bayesian level set inversion
title_full_unstemmed	Hierarchical Bayesian level set inversion
title_sort	hierarchical bayesian level set inversion
publisher	Springer
publishDate	2016
url	http://eprints.nottingham.ac.uk/40915/ http://eprints.nottingham.ac.uk/40915/ http://eprints.nottingham.ac.uk/40915/ http://eprints.nottingham.ac.uk/40915/1/hierarchical_new2-3.pdf
first_indexed	2018-09-06T13:09:37Z
last_indexed	2018-09-06T13:09:37Z
_version_	1610863741415456768

Hierarchical Bayesian level set inversion

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