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Bayesian and robust Bayesian analysis in a general setting

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  • Ali Karimnezhad
  • Ahmad Parsian

Abstract

In this paper we introduce a broad family of loss functions based on the concept of Bregman divergence. We deal with both Bayesian estimation and prediction problems and show that all Bayes solutions associated with loss functions belonging to the introduced family of losses satisfy the same equation. We further concentrate on the concept of robust Bayesian analysis and provide one equation that explicitly leads to robust Bayes solutions. The results are model-free and include many existing results in Bayesian and robust Bayesian contexts in the literature.

Suggested Citation

  • Ali Karimnezhad & Ahmad Parsian, 2019. "Bayesian and robust Bayesian analysis in a general setting," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(15), pages 3899-3920, August.
    • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:15:p:3899-3920
    DOI: 10.1080/03610926.2018.1482344
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    Cited by:

    1. Ali Karimnezhad & Mahmoud Zarepour, 2020. "A general guide in Bayesian and robust Bayesian estimation using Dirichlet processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(3), pages 321-346, April.

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