Robust Bayesian inference via γ-divergence

Tomoyuki Nakagawa and Shintaro Hashimoto

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 2, 343-360

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.

Date: 2020
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DOI: 10.1080/03610926.2018.1543765

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