Bayes robustness via the Kolmogorov metric

Agata Boratyńska; Ryszard Zieliński

Applicationes Mathematicae (1993)

  • Volume: 22, Issue: 1, page 139-143
  • ISSN: 1233-7234

Abstract

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An upper bound for the Kolmogorov distance between the posterior distributions in terms of that between the prior distributions is given. For some likelihood functions the inequality is sharp. Applications to assessing Bayes robustness are presented.

How to cite

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Boratyńska, Agata, and Zieliński, Ryszard. "Bayes robustness via the Kolmogorov metric." Applicationes Mathematicae 22.1 (1993): 139-143. <http://eudml.org/doc/219078>.

@article{Boratyńska1993,
abstract = {An upper bound for the Kolmogorov distance between the posterior distributions in terms of that between the prior distributions is given. For some likelihood functions the inequality is sharp. Applications to assessing Bayes robustness are presented.},
author = {Boratyńska, Agata, Zieliński, Ryszard},
journal = {Applicationes Mathematicae},
keywords = {stability of Bayes procedures; Bayes robustness; Kolmogorov metric; upper bound; Kolmogorov distance; posterior distributions; prior distributions; likelihood functions; inequality},
language = {eng},
number = {1},
pages = {139-143},
title = {Bayes robustness via the Kolmogorov metric},
url = {http://eudml.org/doc/219078},
volume = {22},
year = {1993},
}

TY - JOUR
AU - Boratyńska, Agata
AU - Zieliński, Ryszard
TI - Bayes robustness via the Kolmogorov metric
JO - Applicationes Mathematicae
PY - 1993
VL - 22
IS - 1
SP - 139
EP - 143
AB - An upper bound for the Kolmogorov distance between the posterior distributions in terms of that between the prior distributions is given. For some likelihood functions the inequality is sharp. Applications to assessing Bayes robustness are presented.
LA - eng
KW - stability of Bayes procedures; Bayes robustness; Kolmogorov metric; upper bound; Kolmogorov distance; posterior distributions; prior distributions; likelihood functions; inequality
UR - http://eudml.org/doc/219078
ER -

References

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  1. J. O. Berger (1985), Statistical Decision Theory and Bayesian Analysis, Springer Zbl0572.62008
  2. J. O. Berger and L. M. Berliner (1986), Robust Bayes and empirical Bayes analysis with ε-contaminated priors, Ann. Statist. 14, 461-486 Zbl0602.62004
  3. A. E. Gelfand and D. K. Dey (1991), On Bayesian robustness of contaminated classes of priors, Statist. Decisions 9, 63-80 Zbl0749.62007
  4. M. Męczarski and R. Zieliński (1991), Stability of the Bayesian estimator of the Poisson mean under the inexactly specified gamma priors, Statist. Probab. Lett. 12, 329-333 
  5. S. T. Rachev (1991), Probability Metrics and the Stability of Stochastic Models, Wiley, Chichester Zbl0744.60004
  6. S. Sivaganesan (1988), Ranges of posterior measures for priors with arbitrary contamination, Comm. Statist. Theory Methods 17 (5), 1591-1612 Zbl0639.62021
  7. S. Sivaganesan and J. O. Berger (1989), Ranges of posterior measures for priors with unimodal contaminations, Ann. Statist. 17, 868-889 Zbl0724.62032
  8. V. M. Zolotarev (1986), Contemporary Theory of Summation of Independent Random Variables, Nauka, Moscow (in Russian) Zbl0649.60016

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