On Default Priors for Robust Bayesian Estimation with Divergences |
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Authors: | Tomoyuki Nakagawa Shintaro Hashimoto |
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Affiliation: | 1.Department of Information Sciences, Tokyo University of Science, Chiba 278-8510, Japan;2.Department of Mathematics, Hiroshima University, Hiroshima 739-8521, Japan; |
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Abstract: | This paper presents objective priors for robust Bayesian estimation against outliers based on divergences. The minimum -divergence estimator is well-known to work well in estimation against heavy contamination. The robust Bayesian methods by using quasi-posterior distributions based on divergences have been also proposed in recent years. In the objective Bayesian framework, the selection of default prior distributions under such quasi-posterior distributions is an important problem. In this study, we provide some properties of reference and moment matching priors under the quasi-posterior distribution based on the -divergence. In particular, we show that the proposed priors are approximately robust under the condition on the contamination distribution without assuming any conditions on the contamination ratio. Some simulation studies are also presented. |
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Keywords: | divergence moment matching prior reference prior robust estimation |
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