Robust Bayesian inference via γ-divergence

Tomoyuki Nakagawa, Shintaro Hashimoto

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)343-360
Number of pages18
JournalCommunications in Statistics - Theory and Methods
Volume49
Issue number2
DOIs
Publication statusPublished - 17 Jan 2020

Fingerprint

Bayesian inference
Divergence
Estimator
Posterior distribution
Probability Density
Estimate
Asymptotic Properties
Outlier
Simulation Study
Robustness

Keywords

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

Cite this

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Robust Bayesian inference via γ-divergence. / Nakagawa, Tomoyuki; Hashimoto, Shintaro.

In: Communications in Statistics - Theory and Methods, Vol. 49, No. 2, 17.01.2020, p. 343-360.

Research output: Contribution to journalArticle

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