Bayesian Tests for Independence and Symmetry in Freund's Bivariate Exponential Model

  • Cho, Jang-Sik (Department of Statistical Information Science, Kyungsung University) ;
  • Kim, Dal-Ho (Department of Statistics, Kyungpook National University) ;
  • Kang, Sang-Gil (Department of Statistics, Kyungpook National University)
  • Published : 1999.04.30

Abstract

In this paper, we consider the Bayesian hypotheses testing for independence and symmetry in Freund's bivariate exponential model. In Bayesian testing problem, we use the noninformative priors for parameters which are improper and are defined only up to arbitrary constants. And we use the recently proposed hypotheses testing criterion called the intrinsic Bayes factor. Also we derive the arithmetic and median intrinsic Bayes factors and use these results to analyze some data sets.

Keywords

References

  1. Journal of the American Statistical Association v.84 Estimating a Product of means : Bayesian Analysis with Reference Priors Berger, J. O.;Bernardo, J. M.
  2. Bayesian Statistics Ⅳ On the Development of the Reference Prior method Berger, J. O.;Bernardo, J. M.;J. M. J. M. Bernardo(et al.)
  3. Bayesian Statistics Ⅴ The Intrinsic Bayes Factor for Linear Models (with discussion) Berger, J. O.;Pericchi, L. R.;J. M. Bernardo(et al.)
  4. Journal of the American Statistical Association v.91 The Intrinsic Bayes Factor for Model Selection and Prediction Berger, J. O.;Pericchi, L. R.
  5. Sankhya v.60 Accurate and Stable Bayesian Model Selection : the Median Intrinsic Bayes Factor Berger, J. O.;Pericchi, L. R.
  6. The Annals of Statistics v.18 Lower Bounds on the Bayes Factors for Multinomial Distribution Delampady, M.;Berger, J. O.
  7. Journal of American Statistical Association v.56 A Bivariate Extension of the Exponential Distribution Freund, J. E.
  8. Journal of the American Statistical Association v.74 A Predictive Aprroach to Model Selection Geisser, S.;Eddy, W. F.
  9. Theory of Probability Jeffreys, H.
  10. Communication in Statistics-Theory and Methods v.21 no.9 Estimation of System Reliability From Stress-Strength Relationship Hanagal
  11. Communication in Statistics-Theory and Methods v.21 no.9 Large Sample Tests for Testing Symmetry and Independence in Some Bivariate Exponential Model Hanagal, D. D.;Kale, B. K.
  12. Communication in Statistics-Theory and Methods v.23 no.11 Estimation of Reliability in Freund Model for Two Component System Kunchur, S. H.;Munoli, S. B.
  13. Statistical Models and Methods for Lifetime Data(2nd ed.) Lawless, J. F.
  14. Journal of Research of the National Bureau of Standards v.47 Statistical Investigation of the Fatigue Life of Deep-groove Ball Bearings Lieblein, J.;Zelen, M.
  15. Annals of the Institute of Statistical Mathematics v.49 Testing Hypotheses ablut the Power Law Process under Failure Truncation using the Intrinsic Bayes Factors Lingham, R. T.;Sivaganesan, S.
  16. Technical Report 71-C-011 Statistical Methods for Accelerated Lifetest Data-the Inverse Power Law Model Nelson, W. B.
  17. Journal of Royal Statistical Society v.56 Fractional Bayes Factors for Model Comparision (with discussion) O' Hagan, A.
  18. Journal of Royal Statistical Society v.46 A Predictive Model Selection Criterion San Martini, A.;Spezzaferri, F.
  19. Journal of Royal Statistical Society v.44 Bayes Factor for Linear and Log-linear Models with Vague Prior Information Spiegelhalter, D. J.;Smith, A. F. M.
  20. Bayesian Statistics Ⅴ Intrinsic Bayes Factors for Model Selection with Autoregressive Data Varshavsky, J. A.;J. M. Bernardo(et al.)
  21. Communication in Statistics-Theory and Methods v.10 no.14 Bayes Estimation for a Bivariate Survival Model Based on Exponential Distribution Weier, D. R.