Robust Bayesian inference via γ-divergence

Abstract

This paper presents the robust Bayesian inference based on the γ-divergence which is the same divergence as “type 0 divergence” in Jones et al. (2001) on the basis of Windham (1995). It is known that the minimum γ-divergence estimator works well to estimate the probability density for heavily contaminated data, and to estimate the variance parameters. In this paper, we propose a robust posterior distribution against outliers based on the γ-divergence and show the asymptotic properties of the proposed estimator. We also discuss some robustness properties of the proposed estimator and illustrate its performances in some simulation studies.

Keywords:

• Bayes estimator
• density power divergence
• γ-divergence
• quasi-posterior
• robust estimation

Mathematics Subject Classification:

• Primary 62F15
• Secondary 62F35

Acknowledgements

The authors would like to thank the two anonymous referees for their valuable comments and suggestions to improve the quality of this article.

Additional information

Funding

The work of the second author was supported by Grant-in-Aid for Young Scientists (B), Japan Society for the Promotion of Science (JSPS), under Contract Number 17K14233.