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Hierarchical Bayesian level set inversion
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Dunlop, Matthew M., Iglesias, Marco A. and Stuart, A. M. (2017) Hierarchical Bayesian level set inversion. Statistics and Computing, 27 (6). pp. 1555-1584. doi:10.1007/s11222-016-9704-8
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Official URL: http://dx.doi.org/10.1007/s11222-016-9704-8
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: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Bayesian statistical decision theory, Inverse problems (Differential equations) , Monte Carlo method, Markov processes | ||||||||
| Journal or Publication Title: | Statistics and Computing | ||||||||
| Publisher: | Springer | ||||||||
| ISSN: | 0960-3174 | ||||||||
| Official Date: | November 2017 | ||||||||
| Dates: |
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| Date of first compliant deposit: | 3 March 2017 | ||||||||
| Volume: | 27 | ||||||||
| Number: | 6 | ||||||||
| Page Range: | pp. 1555-1584 | ||||||||
| DOI: | 10.1007/s11222-016-9704-8 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Funder: | United States. Defense Advanced Research Projects Agency (DARPA), Great Britain. Office for Nuclear Regulation (ONR), Engineering and Physical Sciences Research Council (EPSRC) | ||||||||
| Grant number: | EP/K000128/1 (EPSRC) |
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