Hierarchical Bayesian level set inversion

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

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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.

Item Type: Article
RIS ID: https://nottingham-repository.worktribe.com/output/809927
Keywords: Inverse problems for interfaces, Level set inversion, Hierarchical Bayesian methods
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1007/s11222-016-9704-8
Depositing User: Iglesias Hernandez, Marco
Date Deposited: 01 Mar 2017 15:49
Last Modified: 04 May 2020 18:10
URI: https://eprints.nottingham.ac.uk/id/eprint/40915

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