Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 3, pp. 405-417

ISSUES IN BAYESIAN LOSS ROBUSTNESS

By

JACINTO MARTÍN, Universidad Politecnica de Madrid, Madrid
DAVID R\'IOS INSUA, Universidad Rey Juan Carlos, Madrid
and
FABRIZIO RUGGERI, CNR-IAMI, Milano

SUMMARY. Bayesian robustness has concentrated mainly on checking sensitivity of a Bayesian analysis with respect to changes in the prior or the model. We deal here with several issues concerning robust Bayesian analysis with respect to the loss function. Stemming from foundational results, we suggest that a main computational objective would be the obtainment of the set of nondominated alternatives. We then discuss a number of structure questions concerning the nondominated set, mainly its existence and relation with the set of Bayes alternatives and discuss procedures to compute the nondominated set. Since this set may be too big to reach a final decision, we mention some problems concerning gathering additional information.

AMS (1991) subject classification. Primary 62E10; secondary 60E05.

Key words and phrases. Robust Bayesian analysis, classes of loss functions, nondominated alternative, Bayes alternative, $\Ll$-minimax.

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