Robust Bayesian Regression with Synthetic Posterior

Abstract

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not necessarily straightforward. We here propose a Bayesian approach to robust inference on linear regression models using synthetic posterior distributions based on $\gamma$-divergence, which enables us to naturally assess the uncertainty of the estimation through the posterior distribution. We also consider the use of shrinkage priors for the regression coefficients to carry out robust Bayesian variable selection and estimation simultaneously. We develop an efficient posterior computation algorithm by adopting the Bayesian bootstrap within Gibbs sampling. The performance of the proposed method is illustrated through simulation studies and applications to famous datasets.

arXiv comment23 pages, 5 figures

References in corpus (15)

• Least Angle Regression
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Rejoinder to "Least angle regression" by Efron et al
• A General Framework for Updating Belief Distributions
• Principles of Bayesian Inference using General Divergence Criteria
• Robust and Sparse Regression via $\gamma$-divergence
• A New Bayesian Approach to Robustness Against Outliers in Linear Regression
• Robust and Sparse Regression in GLM by Stochastic Optimization

Cited by in corpus (1)

• On default priors for robust Bayesian estimation with divergences