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A variational Bayesian approach for inverse problems with skew-t error distributions

Guha, N; Wu, X; Efendiev, Y; Jin, B; Mallick, BK; (2015) A variational Bayesian approach for inverse problems with skew-t error distributions. Journal of Computational Physics , 301 pp. 377-393. 10.1016/j.jcp.2015.07.062. Green open access

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Abstract

In this work, we develop a novel robust Bayesian approach to inverse problems with data errors following a skew-t distribution. A hierarchical Bayesian model is developed in the inverse problem setup. The Bayesian approach contains a natural mechanism for regularization in the form of a prior distribution, and a LASSO type prior distribution is used to strongly induce sparseness. We propose a variational type algorithm by minimizing the Kullback-Leibler divergence between the true posterior distribution and a separable approximation. The proposed method is illustrated on several two-dimensional linear and nonlinear inverse problems, e.g. Cauchy problem and permeability estimation problem.

Type: Article
Title: A variational Bayesian approach for inverse problems with skew-t error distributions
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.jcp.2015.07.062
Publisher version: http://dx.doi.org/10.1016/j.jcp.2015.07.062
Language: English
Additional information: Copyright © 2015. This manuscript version is published under a Creative Commons Attribution Non-commercial Non-derivative 4.0 International licence (CC BY-NC-ND 4.0). This licence allows you to share, copy, distribute and transmit the work for personal and non-commercial use providing author and publisher attribution is clearly stated. Further details about CC BY licences are available at http://creativecommons.org/licenses/by/4.0. Access may be initially restricted by the publisher.
Keywords: Bayesian inverse problems, Hierarchical Bayesian model, Kullback-Leibler divergence, Variational approximation
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/1470596
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