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Bayesian Perturbation Diagnostics and Robustness

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Book cover Bayesian Analysis in Statistics and Econometrics

Part of the book series: Lecture Notes in Statistics ((LNS,volume 75))

Abstract

A Bayesian analysis may depend critically on the modeling assumptions which include prior, likelihood and loss function. A model that has been judged adequate in previous more or less similar situations may be assumed to be the standard. However one ought to consider the effect of perturbing the standard model in potentially conceivable directions especially if graphical procedures indicate the standard may only be marginally adequate. We discuss a variety of perturbation models and Bayesian diagnostics that can be helpful in a local or a more global analysis of the robustness of the sample.

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References

  • Box, G.E.P.(1980). Sampling and Bayes’ inference in scientific modelling and robustness. Jour. of the Royal Statistical Society A, 143, 383–430.

    Article  MathSciNet  MATH  Google Scholar 

  • Burbea, J. and Rao, C.R. (1982). Entropy differential metric, distance and divergence measures in probability spaces: a unified approach. Jour. of Multivariate Analysis, 12, 575–596.

    Article  MathSciNet  MATH  Google Scholar 

  • Cook, R.D.(1986). Assessment of local influence (with discussion). Jour. of the Royal Statistical Society B, 48, 2, 133–169.

    MATH  Google Scholar 

  • Devroye, L. (1987). A Course in Density Estimation. Birkhauser.

    Google Scholar 

  • Geisser, S. (1982) Aspects of predictive and estimative approaches in the determination of probabilities, Biometrics Supplement: Current Topics in Biostatistics and Epidemiology 38, 1, March, 75–85.

    Google Scholar 

  • Geisser, S. (1985) On the predicting of observables: a selective update, in: Bernardo, J.M. et al. (Ed.) Bayesian Statistics 2, (with discussion) 203–230. Amsterdam, North-Holland.

    Google Scholar 

  • Gnedenko, B.B., Belyayev, Y.K., and Solovyev, A.D. (1969). Mathematical Methods of Reliability Theory. New York and London: Academic Press.

    MATH  Google Scholar 

  • Johnson, W. and Geisser, S. (1982) Assessing the predictive influence of observations, in: G. Kallianpur, P.R. Krishnaiah & J.K. Ghosh (Eds) Statistics and Probability Essays in Honor of C.R. Rao, 343–358. Amsterdam, North-Holland.

    Google Scholar 

  • Johnson, W. and Geisser, S. (1983) A predictive view of the detection and characterization of influential observations in regression analysis, Journal of American Statistical Association 78, 137–144.

    Article  MathSciNet  MATH  Google Scholar 

  • Johnson, W. and Geisser, S. (1985) Estimative influence measures for the multivariate general linear model, Journal of Statistical Planning and Inference 11, 33–56.

    Article  MathSciNet  MATH  Google Scholar 

  • Kullback, S. (1959). Information Theory and Statistics. New York, John Wiley and Sons.

    MATH  Google Scholar 

  • Lavine, M. (1988). Prior influence in Bayesian Statistics. University of Minnesota Technical Report No. 504

    Google Scholar 

  • McCulloch, R. (1986). Local prior influence. University of Minnesota Technical Report No 477.

    Google Scholar 

  • Pitman, E.J.G. (1979). Some Basic Theory for Statistical Influence. London, Chapman and Hall.

    Google Scholar 

Additional References

  • Bayarri, S.J., M. H. DeGroot and Kadane, J.B. (1988), What is the Likelihood Function? (with discussion), in Proceedings of the Fourth Purdue Symposium on Decision Theory and Related Topics, S. Gupta and J. Berger, eds. Springer-Verlag, New York, 3–27.

    Google Scholar 

  • Berliner, L.M. and B. Hill (1988), Bayesian Nonparametric Survival Analysis, (with discussion), Journal of the American Statistical Association, 83, 772–784.

    Article  MathSciNet  MATH  Google Scholar 

  • Berger, J. (1988), The Robust Bayesian Viewpoint, in Robustness of Bayesian Analysis, J. Kadane, ed., North-Holland Publishing Company, Amsterdam, 63–144.

    Google Scholar 

  • Box, G.E.P. and Tiao, G. (1973), Bayesian Inference in Statistical Analysis, Addison-Wesley, MA.

    MATH  Google Scholar 

  • Edwards, W., Lindman, H. and Savage, L.J. (1963), Bayesian Statistical Inference, Psychological Research.

    Google Scholar 

  • Tierney, L.J., Kass, R. and Kadane, J.B. (1989), Approximate Methods for Assessing Influence and Sensitivity in Bayesian Analysis, Technical Report No. 430, Department of Statistics. Carnegie-Mellon University, Biometrika. To appear.

    Google Scholar 

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© 1992 Springer-Verlag New York, Inc.

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Geisser, S. (1992). Bayesian Perturbation Diagnostics and Robustness. In: Goel, P.K., Iyengar, N.S. (eds) Bayesian Analysis in Statistics and Econometrics. Lecture Notes in Statistics, vol 75. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2944-5_20

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  • DOI: https://doi.org/10.1007/978-1-4612-2944-5_20

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97863-5

  • Online ISBN: 978-1-4612-2944-5

  • eBook Packages: Springer Book Archive

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