Skip to main content
  • 758 Accesses

Abstract

Abstract The sensitivity of Bayesian multivariate parameter estimation to changes in the prior is investigated. In particular, robustness with respect to the dependence structure of the prior is considered. Methods using maximal association copulas, parametric copulas, and a sampling based method are demonstrated.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Berger, J. O. (1984), The robust Bayesian viewpoint. In: Robustness of Bayesian analyses, Stud. Bayesian Econometrics, 4. Amsterdam: North-Holland, pp. 63–144. With comments and with a reply by the author.

    Google Scholar 

  • Berger, J. O. (1990), Robust Bayesian analysis: sensitivity to the prior. J. Statist. Plann. Inference 25(3), 303–328.

    Article  MathSciNet  MATH  Google Scholar 

  • Berger, J. O. (1994), An overview of robust Bayesian analysis. Test 3(1), 5–124. With comments and a rejoinder by the author.

    Article  MathSciNet  MATH  Google Scholar 

  • Berger, J. O., D. Rios Insua, and F. Ruggeri (2000), Bayesian Robustness. In: D. Rios Insua and F. Ruggeri (eds.): Robust Bayesian Analysis, No. 152 in Lecture Notes in Statistics. New York: Springer Verlag.

    Google Scholar 

  • De la Horra, J. and C. Fernandez (1995), Sensitivity to prior independence via Farlie-GumbelMorgenstern model. Comm. Statist. Theory Methods 24(4), 987–996.

    Article  MathSciNet  MATH  Google Scholar 

  • Frank, M. J. (1979), On the simultaneous associativity of F (x,y) and x + y — F (x,y). Aequationes Math. 19, 194–226.

    Article  MathSciNet  MATH  Google Scholar 

  • Joe, H. (1997), Multivariate models and dependence concepts. London: Chapman & Hall.

    Book  MATH  Google Scholar 

  • Lavine, M., L. Wasserman, and R. L. Wolpert (1991), Bayesian inference with specified prior marginals. J. Amer Statist. Assoc. 86(416), 964–971.

    Article  MathSciNet  MATH  Google Scholar 

  • Liseo, B., E. Moreno, and G. Salinetti (1996), Bayesian robustness for classes of bidimensional priors with given marginals. In: Bayesian robustness (Rimini, 1995). Hayward, CA: Inst. Math. Statist., pp. 101–118. With a discussion by Sandra Fortini and a rejoinder by the authors.

    Chapter  Google Scholar 

  • Mikusifiski, P., H. Sherwood, and M. D. Taylor (1991), The Fréchet bounds revisited. Real Anal. Exchange 17(2), 759–764.

    MathSciNet  Google Scholar 

  • Mikusiński, P., H. Sherwood, and M. D. Taylor (1992), Shuffles of Min. Stochastica 13(1), 61–74.

    MathSciNet  MATH  Google Scholar 

  • Murphy, T. B. (2000), Non-informative priors for the Farlie-Gumbel-Morgenstern family of bivariate distributions. Submitted.

    Google Scholar 

  • Nelsen, R. B. (1999), An introduction to copulas. New York: Springer-Verlag.

    Book  MATH  Google Scholar 

  • Sklar, A. (1959), Fonctions de répartition à n dimensions et leur marges. Publ. Inst. Statist. Univ. Paris 8, 229–231.

    MathSciNet  Google Scholar 

  • Ware, J. H. (1989), Investigating therapies of potentially great benefit: ECMO. Statist. Sci. 4(4), 298–340. With comments and a rejoinder by the author.

    Article  MathSciNet  MATH  Google Scholar 

  • Wasserman, L. (1992), Recent methodological advances in robust Bayesian inference. In: Bayesian statistics, 4. New York: Oxford Univ. Press, pp. 483–502.

    Google Scholar 

  • Wasserman, L. (1997), Bayesian Robustness. In: S. Kotz, C. B. Read, and D. L. Banks (eds.): Encyclopedia of statistical sciences. Update Vol. 1, A Wiley-Interscience Publication. New York: John Wiley & Sons Inc., pp. 45–51.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Murphy, T.B. (2002). Bayesian Robustness for Multivariate Problems. In: Cuadras, C.M., Fortiana, J., Rodriguez-Lallena, J.A. (eds) Distributions With Given Marginals and Statistical Modelling. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0061-0_17

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-0061-0_17

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6136-2

  • Online ISBN: 978-94-017-0061-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics