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Robust Bayesian inference via γ-divergence

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  • Tomoyuki Nakagawa
  • Shintaro Hashimoto

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.

Suggested Citation

  • Tomoyuki Nakagawa & Shintaro Hashimoto, 2020. "Robust Bayesian inference via γ-divergence," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(2), pages 343-360, January.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:2:p:343-360
    DOI: 10.1080/03610926.2018.1543765
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