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.