Theory and Decision

, Volume 48, Issue 4, pp 359–381 | Cite as

Global Robustness with Respect to the Loss Function and the Prior

  • Christophe Abraham
  • Jean-Pierre Daures
Article

Abstract

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 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. Abraham, C. (1998), Robustesse par rapport à la fonction de coût en théorie de la décision bayésienne. Ph.D. thesis, Université de Montpellier, France.Google Scholar
  2. Berger, J.O. (1984), The robust Bayesian viewpoint (with discussion). In J. Kadane (ed.) Robustness in Bayesian Statistics, pp. 63–144. North-Holland, Amsterdam.Google Scholar
  3. Berger, J.O. (1985), Statistical Decision Theory and Bayesian Analysis, 2nd ed. Springer, New York.Google Scholar
  4. Berger, J.O. (1990), Robust Bayesian analysis: Sensitivity to the prior. J. Statist. Planning and Inference 25: 303–328.Google Scholar
  5. Berger, J.O. (1994), An overview of robust Bayesian analysis (with discussion). Test 3: 5–124.Google Scholar
  6. Kadane, J.B. and Chuang, D.T. (1978), Stable decisions problems. Ann. Statist. 6: 1095–1110.Google Scholar
  7. Ríos Insua, D. and Martín, J. (1994), Robustness issue under imprecise beliefs and preferences. J. Statist. Planning and Inference 48: 383–389.Google Scholar
  8. Ríos Insua, D. and Martín, J. (1995), A general model for incomplete beliefs and preferences. Tech. Rep. Decision Analysis group, Madrid Technical University. Robert, C.P. and Goutis, C. (1994), in discussion of Berger (1994).Google Scholar
  9. Sivaganesan, S. and Berger, J.O. (1989), Ranges of posterior measures for priors with unimodal contaminations. Ann. Statist. 17: 868–889.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Christophe Abraham
    • 1
  • Jean-Pierre Daures
    • 1
  1. 1.Unité de BiométrieENSA.M INRAMontpellier cedex 1France

Personalised recommendations