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The exponential rates of convergence of posterior distributions

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Abstract

After the observations were observed, the posterior distribution under mild conditions becomes more concentrated in the neighbourhood of the mode of the posterior distribution as sample size n increase. In this paper, the exponential rate of convergence of posterior distribution around the mode is established by using the generalized Laplace method. An example is also given.

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References

  • Brenner, D., Fraser, D. A. S. and McDunnough, P. (1983). On asymptotic normality of likelihood and conditional analysis,Canad. J. Statist., 10, 163–172.

    Article  MathSciNet  Google Scholar 

  • Chen, C. F. (1983). On asymptotic normality of limiting density functions with Bayesian implications. Technical Report B-83–18, Institute of Statistics, Academia Sinica, China.

    Google Scholar 

  • Freedman, D. A. (1963). On the asymptotic behaviour of Bayes estimates in discrete case, Ann. Math. Statist., 34, 1386–1403.

    Article  MathSciNet  Google Scholar 

  • Fu, J. C. and Kass, R. E. (1983). The rate at which posterior distributions become concentrated, Technical Report, Dept. of Statist., Univ. of Manitoba, Canada.

    Google Scholar 

  • Johnson, R. A. (1967). An asymptotic expansion for posterior distributions, Ann. Math. Statist., 38, 1899–1907.

    Article  MathSciNet  Google Scholar 

  • Johnson, R. A. (1970). Asymptotic expansions associated with posterior distributions, Ann. Math. Statist., 41, 851–864.

    Article  MathSciNet  Google Scholar 

  • LeCam, L. (1953). On some asymptotic properties of maximum likelihood estimates and related Bayes' estimates, Univ. California Publ. Statist., 1, 227–330.

    MathSciNet  Google Scholar 

  • Lindley, D. V. (1965). Introduction to Probability and Statistics from a Bayesian Viewpoint, University Press, Cambridge.

    Book  Google Scholar 

  • Parzen, E. (1953). On uniform convergence of families or sequences of random variables, Univ. California Publ. Statist., 1, 23–53.

    MathSciNet  Google Scholar 

  • Schwartz, L. (1965). On Bayes procedures, Z. Wahrsch. Verw. Gebiete, 4, 10–26.

    Article  MathSciNet  Google Scholar 

  • Walker, A. M. (1969). On the asymptotic behavior of posterior distributions, J. Roy. Statist. Soc. Ser. B, 31, 80–88.

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, University of Manitoba, Winnipeg, Manitoba, Canada

    James C. Fu

  2. Department of Statistics, Carnegie-Mellon University, 15213, Pittsburgh, PA, U.S.A.

    Robert E. Kass

Authors
  1. James C. Fu
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  2. Robert E. Kass
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Additional information

This work was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant NSERC A-9216.

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Fu, J.C., Kass, R.E. The exponential rates of convergence of posterior distributions. Ann Inst Stat Math 40, 683–691 (1988). https://doi.org/10.1007/BF00049426

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  • DOI: https://doi.org/10.1007/BF00049426

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