Theory and Decision

, Volume 48, Issue 4, pp 359-381

First online:

Global Robustness with Respect to the Loss Function and the Prior

  • Christophe AbrahamAffiliated withUnité de Biométrie, ENSA.M INRA
  • , Jean-Pierre DauresAffiliated withUnité de Biométrie, ENSA.M INRA

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We propose a class [I,S] of loss functions for modeling the imprecise preferences of the decision maker in Bayesian Decision Theory. This class is built upon two extreme loss functions I and S which reflect the limited information about the loss function. We give an approximation of the set of Bayes actions for every loss function in [I,S] and every prior in a mixture class; if the decision space is a subset of ℝ, we obtain the exact set.

Bayesian Decision Theory Global robustness Loss function Mixture class