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On Bayesian Robustness: An Asymptotic Approach

  • Daniel Peña
  • Ruben H. Zamar
Part of the Lecture Notes in Statistics book series (LNS, volume 109)

Abstract

This paper presents a new asymptotic approach to study the robustness of Bayesian inference to changes on the prior distribution. We study the robustness of the posterior density score function when the uncertainty about the prior distribution has been restated as a problem of uncertainty about the model parametrization. Classical robustness tools, such as the influence function and the maximum bias function, are defined for uniparametric models and calculated for the location case. Possible extensions to other models are also briefly discussed.

Key words and phrases

gross error sensitivity influence function maximum bias curve prior robustness 

AMS 1980 subject classifications

Primary 62F15 secondary 62F35 

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References

  1. [1]
    Berger, J.O. (1984): The robust Bayesian viewpoint. In Robustness of Bayesian Analysis (J. Kadane ed.). North Holland, Amsterdam.Google Scholar
  2. [2]
    Berger, J.O. (1990): Robust Bayesian analysis: Sensitivity to the prior. J. Statist. Plann. Inference 25 303–328.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    Berger, J.O. and Berliner, L.M. (1986): Robust Bayes and empirical Bayes analysis with ε-contaminated priors. Ann. Statist. 14 461–486.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    Box, G.E.P. and Tiao, G.C. (1968): A Bayesian approach to some outlier problems. Biometrika 75 651–659.MathSciNetGoogle Scholar
  5. [5]
    Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J. and Stahel, W.A. (1986): Robust Statistics — The Approach Based on Inßuece Functions. Wiley, New York.Google Scholar
  6. [6]
    Huber, P.J. (1981): Robust Statistics. Wiley, New York.CrossRefzbMATHGoogle Scholar
  7. [7]
    Kadane, J.B. (1984): Robustness of Bayesian Analysis. North Holland, Amsterdam.Google Scholar
  8. [8]
    Marazzi, A. (1985): On constrained minimization of the Bayes risk for the linear model. Statist. Decisions 3 277–296.MathSciNetzbMATHGoogle Scholar
  9. [9]
    Mardia, K.V., Kent, J.T. and Bibby, J.M. (1979): Multivariate Analysis. Academic Press, New York.zbMATHGoogle Scholar
  10. [10]
    Martin, R.D., Yohai, V.J. and Zamar, R.H. (1989): Min-max bias robust regression. Ann. Statist. 17 1608–1630.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    Moreno, E. and Cano, J.A. (1991): Robust Bayesian analysis with ε-contamination partially known. J. Roy. Statist. Soc. B 53 143–155.MathSciNetzbMATHGoogle Scholar
  12. [12]
    Pericchi, L.R. and Walley, P. (1991): Robust Bayesian credible interval and prior ignorance. Internat. Statist. Rev. 58 1–23.CrossRefGoogle Scholar
  13. [13]
    Rieder, H. (1994): Robust Asymptotic Statistics. Springer, New York.zbMATHGoogle Scholar
  14. [14]
    Walley, P. (1990): Statistical Reasoning with Imprecise Probabilities. Chapman & Hall, London.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • Daniel Peña
    • 1
  • Ruben H. Zamar
    • 2
  1. 1.Universidad Carlos III de MadridSpain
  2. 2.University of British ColumbiaVancouverCanada

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