A variational Bayesian approach for inverse problems with skew-t error distributions Academic Article uri icon

abstract

  • 2015 Elsevier Inc. 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.

published proceedings

  • JOURNAL OF COMPUTATIONAL PHYSICS

author list (cited authors)

  • Guha, N., Wu, X., Efendiev, Y., Jin, B., & Mallick, B. K.

complete list of authors

  • Guha, Nilabja||Wu, Xiaoqing||Efendiev, Yalchin||Jin, Bangti||Mallick, Bani K

publication date

  • January 1, 2015 11:11 AM