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

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

doi:10.1016/j.jcp.2015.07.062

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

Journal Article · Sun Nov 01 00:00:00 EDT 2015 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2015.07.062· OSTI ID:1247052

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

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Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: FG02-13ER26165; SC0010713

OSTI ID:: 1247052

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 301 Journal Issue: C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 9 works

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References (15)

The Skew-normal Distribution and Related Multivariate Families* Azzalini, Adelchi Scandinavian Journal of Statistics, Vol. 32, Issue 2 https://doi.org/10.1111/j.1467-9469.2005.00426.x	journal	June 2005
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Gene selection using a two-level hierarchical Bayesian model Bae, K.; Mallick, B. K. Bioinformatics, Vol. 20, Issue 18 https://doi.org/10.1093/bioinformatics/bth419	journal	July 2004
Expectation propagation for nonlinear inverse problems – with an application to electrical impedance tomography Gehre, Matthias; Jin, Bangti Journal of Computational Physics, Vol. 259 https://doi.org/10.1016/j.jcp.2013.12.010	journal	February 2014
Graphical Models Jordan, Michael I. Statistical Science, Vol. 19, Issue 1 https://doi.org/10.1214/088342304000000026	journal	February 2004
The multivariate skew-normal distribution Azzalini, A. Biometrika, Vol. 83, Issue 4 https://doi.org/10.1093/biomet/83.4.715	journal	December 1996
The Bayesian Lasso Park, Trevor; Casella, George Journal of the American Statistical Association, Vol. 103, Issue 482 https://doi.org/10.1198/016214508000000337	journal	June 2008
Hierarchical Bayesian inference for Ill-posed problems via variational method Jin, Bangti; Zou, Jun Journal of Computational Physics, Vol. 229, Issue 19 https://doi.org/10.1016/j.jcp.2010.06.016	journal	September 2010
Statistical applications of the multivariate skew normal distribution Azzalini, A.; Capitanio, A. Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 61, Issue 3 https://doi.org/10.1111/1467-9868.00194	journal	August 1999
A note on Bayesian spatial prediction using the elliptical distribution Kim, Hyoung-Moon; Mallick, Bani K. Statistics & Probability Letters, Vol. 64, Issue 3 https://doi.org/10.1016/S0167-7152(03)00171-8	journal	September 2003
Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution Azzalini, Adelchi; Capitanio, Antonella Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 65, Issue 2 https://doi.org/10.1111/1467-9868.00391	journal	May 2003
A variational Bayesian method to inverse problems with impulsive noise Jin, Bangti Journal of Computational Physics, Vol. 231, Issue 2 https://doi.org/10.1016/j.jcp.2011.09.009	journal	January 2012
Variational inference for Student-t models: Robust Bayesian interpolation and generalised component analysis Tipping, Michael E.; Lawrence, Neil D. Neurocomputing, Vol. 69, Issue 1-3 https://doi.org/10.1016/j.neucom.2005.02.016	journal	December 2005
A General Class of Multivariate Skew-Elliptical Distributions Branco, Márcia D.; Dey, Dipak K. Journal of Multivariate Analysis, Vol. 79, Issue 1 https://doi.org/10.1006/jmva.2000.1960	journal	October 2001
Bayesian nonlinear regression models with scale mixtures of skew-normal distributions: Estimation and case influence diagnostics Cancho, Vicente G.; Dey, Dipak K.; Lachos, Victor H. Computational Statistics & Data Analysis, Vol. 55, Issue 1 https://doi.org/10.1016/j.csda.2010.05.032	journal	January 2011

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