Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
권호 표지

Development of Matching Priors for P(X < Y) in Exprnential dlstributions

  • Lee, Gunhee (College of Business Administration, Sogang University)
  • Published : 1998.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, matching priors for P(X < Y) are investigated when both distributions are exponential distributions. Two recent approaches for finding noninformative priors are introduced. The first one is the verger and Bernardo's forward and backward reference priors that maximizes the expected Kullback-Liebler Divergence between posterior and prior density. The second one is the matching prior identified by matching the one sided posterior credible interval with the frequentist's desired confidence level. The general forms of the second- order matching prior are presented so that the one sided posterior credible intervals agree with the frequentist's desired confidence levels up to O(n$^{-1}$ ). The frequentist coverage probabilities of confidence sets based on several noninformative priors are compared for small sample sizes via the Monte-Carlo simulation.

Keywords

References

  1. Bayesian Statistics 4 Non-informative priors(with discus-sion) Ghosh, J. K.;Mukerjee, R.;J. M. Bernardo(ed.);J. O. Berger(ed.);A. P. Dawid(ed.);A. F. M. Smith(ed.)
  2. Frontiers in Reliability, Indian Association for Productivity Quality and Relability(IAPQR) Recent develpments of Bayesian inference for stress-strength models Ghosh, M.;Sun, D.
  3. Theory of Probability Jeffreys, H.
  4. Biometrika v.80 Frequetist validity of posterior quan-tiles in the presence of a nuisance prarameter: higher order asymptotics Mukerjee, R.;K. D. Dey
  5. Journal of Royal Statistical Society, Werices B v.27 On confidence sets and Bayesian probability points in the case of several parameters Peers, H. W.
  6. Annals of Statististics v.22 Integrable expansions for posterior distributions for a two-parameter exponential family Sun, D.
  7. Journal of Statistical Planning and Infernce v.61 A note on noninformative priors for Weibull distributions Sun, D.
  8. Journal of the American Statistical Association v.90 Refernce prior Bayesian analysis for normal mean products Sun, D.;Ye, K.
  9. Biometrika v.83 Frequentist validity of posterior quantiles for a two parameter exponential family Sun, D.;Ye, K.
  10. Advances in Reliability Bayesian reliability of stress-strength system Thompson, R. D.;Basu, A. P.;Basu, A.(ed.)
  11. Biometrika v.76 Noninformative priors for one parameter of many Tibshirani, R.
  12. Journal of Royal Statistical Society, Werices B v.35 On formulae for confidence points based on integrals of weighted likelihoods Welch, B. N.;B. Peers