TY - JOUR

T1 - A variational Bayesian approach for inverse problems with skew-t error distributions

AU - Guha, Nilabja

AU - Wu, Xiaoqing

AU - Efendiev, Yalchin

AU - Jin, Bangti

AU - Mallick, Bani K.

N1 - Funding Information:
The authors are grateful to the anonymous referees for their constructive comments, which have led to an improved presentation of the paper. The work of B. Jin is partially supported by EPSRC grant EP/M025160/1 . Y. Efendiev's work is partially supported by the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-FG02-13ER26165 and the DoD Army ARO Project.
Publisher Copyright:
© 2015 Elsevier Inc.

PY - 2015/11/15

Y1 - 2015/11/15

N2 - 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.

AB - 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.

KW - Bayesian inverse problems

KW - Hierarchical Bayesian model

KW - Kullback-Leibler divergence

KW - Variational approximation

UR - http://www.scopus.com/inward/record.url?scp=84941299719&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2015.07.062

DO - 10.1016/j.jcp.2015.07.062

M3 - Article

AN - SCOPUS:84941299719

VL - 301

SP - 377

EP - 393

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -