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

Nilabja Guha*, Xiaoqing Wu, Yalchin Efendiev, Bangti Jin, Bani K. Mallick

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)377-393
Number of pages17
JournalJournal of Computational Physics
Volume301
DOIs
StatePublished - Nov 15 2015

Keywords

  • Bayesian inverse problems
  • Hierarchical Bayesian model
  • Kullback-Leibler divergence
  • Variational approximation

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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