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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| Format: | Article |
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Springer
2016
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| Online Access: | https://eprints.nottingham.ac.uk/40915/ |
| _version_ | 1848796161728577536 |
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| author | Dunlop, Matthew M. Iglesias, Marco Stuart, Andrew M. |
| author_facet | Dunlop, Matthew M. Iglesias, Marco Stuart, Andrew M. |
| author_sort | Dunlop, Matthew M. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-14T19:43:35Z |
| format | Article |
| id | nottingham-40915 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:35Z |
| publishDate | 2016 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-409152020-05-04T18:10:12Z https://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 Dunlop, Matthew M., Iglesias, Marco and Stuart, Andrew M. (2016) Hierarchical Bayesian level set inversion. Statistics and Computing, 27 (6). pp. 1555-1584. ISSN 1573-1375 Inverse problems for interfaces Level set inversion Hierarchical Bayesian methods 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 |
| spellingShingle | Inverse problems for interfaces Level set inversion Hierarchical Bayesian methods Dunlop, Matthew M. Iglesias, Marco Stuart, Andrew M. Hierarchical Bayesian level set inversion |
| title | 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_short | Hierarchical Bayesian level set inversion |
| title_sort | hierarchical bayesian level set inversion |
| topic | Inverse problems for interfaces Level set inversion Hierarchical Bayesian methods |
| url | https://eprints.nottingham.ac.uk/40915/ https://eprints.nottingham.ac.uk/40915/ https://eprints.nottingham.ac.uk/40915/ |