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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:301

Article

Guha, Nilabja¹  Wu, Xiaoqing²  Efendiev, Yalchin¹  Jin, Bangti³  Mallick, Bani K.² 

[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[2] Texas A&M Univ, Dept Stat, College Stn, TX 77843 USA

[3] UCL, Dept Comp Sci, London WC1E 6BT, England

关键词: Bayesian inverse problems;    Hierarchical Bayesian model;    Variational approximation;    Kullback-Leibler divergence;   

DOI  :  10.1016/j.jcp.2015.07.062

来源: Elsevier

【 摘 要 】

In this work, we develop a novel robust Bayesian approach to inverse problems with data errors following a skew-tdistribution. 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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free