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.
Preview |
Text
variational_jcp_rev.pdf Download (2MB) | Preview |
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 |
Archive Staff Only
 |
View Item |
