A comparison of bayes-laplace, jeffreys, and other priors: the case of zero events

American Statistician

Volumn 62, Issue 1, 2008, Pages 40-44

  Tuyl, Frank ^a,b,c   Gerlach, Richard ^a,b,c   Mengersen, Kerrie ^a,d  

^a UNIVERSITY OF NEWCASTLE   (Australia)

^b HUNTER NEW ENGLAND POPULATION HEALTH   (Australia)

^c UNIVERSITY OF SYDNEY   (Australia)

^d QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

Bayesian inference; Binomial distribution; Noninformative priors; Prior families

Indexed keywords

EID: 39049108737     PISSN: 00031305     EISSN: None     Source Type: Journal    
DOI: 10.1198/000313008X267839     Document Type: Article

References (28)

1. Bayes, T. R. (1763), "An Essay Towards Solving a Problem in the Doctrine of Chances," Philosophical Transactions of the Royal Societv of London, 53, 370-418.
2. Berger, J. O., Liseo, B., and Wolpert, R. L. ( 1999), "Integrated Likelihood Methods for Eliminating Nuisance Parameters," Statistical Science, 14, 1-22.
3. Berger, J. O. (1985), Statistical Decision Theory and Bayesian Analysis, New York: Springer-Verlag.
4. (2006), "The Case for Objective Bayesian Analysis," Bayesian Statistics, 1, 385-402.
5. Bernardo, J. M. (1979), "Reference Posterior Distributions for Bayesian Inference" (with discussion), Journal of the Royal Statistical Society, Series B, 41, 113-147.
6. (2005), "Reference Analysis," in Bayesian Thinking: Modeling and Computation, eds. D. K. Dey and C. R. Rao, Amsterdam: Elsevier, pp. 17-90.
7. Bernardo, J. M., and Ramon, J. M. (1998), "An Introduction to Bayesian Reference Analysis: Inference on the Ratio of Multinomial Parameters," The Statistician, 47, 101-135.
8. Berry, D. A. (1996), Statistics - A Bayesian Perspective, Belmont, CA: Duxbury.
9. Blyth, C. R. (1986), "Approximate Binomial Confidence Limits," Journal of the American Statistical Association, 81, 843-855.
10. Box, G. E. P., and Tiao, G. C. (1973), Bayesian Inference in Statistical Analysis, New York: Wiley Classics.
11. Chen, J. J., and Novick, M. R. (1984), "Bayesian Analysis for Binomial Models with Generalized Beta Prior Distributions," Journal of Educational Statistics, 9, 2, 163-175.
12. Clopper, C. J., and Pearson, E. S. (1934), "The Use of Confidence or Fiducial Limits Illustrated in the Case of the Binomial," Biometrika, 26, 404-416.
13. Congdon, P. (2001), Bayesian Statistical Modeling, Chichester: Wiley.
14. Diaconis, P., and Ylvisaker, D. (1985), "Quantifying Prior Opinion," in Bayesian Statistics (vol. 2), eds. J. M. Bernardo, M. H. DeGroot, D. V. Lindley, and A. F. M. Smith, Amsterdam: North-Holland, pp. 163-175.
15. Edwards, A. W. F. (1978), "Commentary on the Arguments of Thomas Bayes," The Scandinavian Journal of Statistics, 5, 116-118.
16. Geisser, S. (1984), "On Prior Distributions for Binary Trials," The American Statistician, 38, 244-251.
17. Hanley, J. A., and Lippman-Hand, A. (1983), "If Nothing Goes Wrong, is Everything All Right?," Journal of the American Medical Association, 249, 1743-1745.
18. Henderson, M., and Meyer, M. C. (2001), "Exploring the Confidence Interval for a Binomial Parameter in a First Course in Statistical Computing," The American Statistician, 55, 337-344.
19. Hora, S. C., and Kelley, G. D. ( 1983), "Bayesian Inference on the Odds and Risk Ratios," Communications in Statistics - Theory and Methods, 12, 725-738.
20. Jeffreys, H. (1946), "An Invariant Form for the Prior Probability in Estimation Problems," Proceedings of the Royal Society of London, Series A, 186, 453-461.
21. Jovanovic, B. D., and Levy, P. S. (1997), "A Look at the Rule of Three," The American Statistician, 51, 137-139.
22. Leemis, L. M., and Trivedi, K. S. (1996), "A Comparison of Approximate Interval Estimators for the Bernoulli Parameter," The American Statistician, 50, 63-68.
23. Lindley, D. V. (1965), Introduction to Probability and Statistics from a Bayesian Viewpoint, New York: Cambridge University Press.
24. Louis, T. A. (1981), "Confidence Intervals for a Binomial Parameter After Observing No Successes," The American Statistician, 35, 154-154.
25. Robert, C. P. (1994), The Bayesian Choice (2nd ed.), New York: Springer-Verlag.
26. Tebbs, J. M., Bilder, R. B., and Moser, B. K. (2001), "An Empirical Bayes Group-Testing Approach to Estimating Small Proportions," Communications in Statistics - Theory and Methods, 32, 983-995.
27. Winkler, R. L., Smith, J. E., and Fryback, D. G. (2002), "The Role of Informative Priors in Zero-Numerator Problems: Being Conservative Versus Being Candid," The American Statistician, 56, 1-4.
28. Zellner, A. (1977), "Maximal Data Information Prior Distributions," in New Developments in the Applications of Bayesian Methods, eds. A. Aykac and C. Brumat, Amsterdam: North-Holland, pp. 211-232.