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An overview of robust Bayesian analysis. (With discussion). (English) Zbl 0827.62026
Summary: Robust Bayesian analysis is the study of the sensitivity of Bayesian answers to uncertain inputs. This paper seeks to provide an overview of the subject, one that is accessible to statisticians outside the field. Recent developments in the area are also reviewed, though with very uneven emphasis. The topics to be covered are as follows: 1. Introduction: 1.1 Motivation; 1.2 Preview; 1.3 Notation. 2. Development of inherently robust procedures: 2.1 Introduction; 2.2 Use of flat-tailed distributions; 2.3 Use of noninformative and partially informative priors; 2.4 Nonparametric Bayes procedures. 3. Diagnostics, influence, and sensitivity: 3.1 Diagnostics; 3.2 Influence and sensitivity. 4. Global robustness: 4.1 Introduction; 4.2 Parametric classes; 4.3 Nonparametric classes of priors: 4.3.1 Factors involved in choosing a class; 4.3.2 Common classes; 4.3.3 Application to hypothesis testing and Ockham’s razor; 4.4 Nonparametric classes of likelihoods; 4.5 Limitations of global robustness; 4.6 Optimal robust procedures. 5. Computing: 5.1 Computational issues; 5.2 Interactive elicitation. 6. Future directions.

MSC:
62F15Bayesian inference
62F35Robustness and adaptive procedures (parametric inference)
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References:
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