Hierarchical Bayesian level set inversion

Dunlop, Matthew M.; Iglesias, Marco; Stuart, Andrew M.

Abstract

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.

Citation

Dunlop, M. M., Iglesias, M., & Stuart, A. M. (in press). Hierarchical Bayesian level set inversion. Statistics and Computing, 27(6), https://doi.org/10.1007/s11222-016-9704-8

• Journal Article Type: Article
• Acceptance Date: Sep 9, 2016
• Online Publication Date: Sep 21, 2016
• Deposit Date: Mar 1, 2017
• Publicly Available Date: Mar 1, 2017
• Journal: Statistics and Computing
• Print ISSN: 0960-3174
• Electronic ISSN: 1573-1375
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 27
• Issue: 6
• DOI: https://doi.org/10.1007/s11222-016-9704-8
• Keywords: Inverse problems for interfaces, Level set inversion, Hierarchical Bayesian methods
• Public URL: https://nottingham-repository.worktribe.com/output/809927
• Publisher URL: https://link.springer.com/article/10.1007%2Fs11222-016-9704-8
• Contract Date: Mar 1, 2017