Posterior predictive arguments in favor of the Bayes-Laplace prior as the consensus prior for binomial and multinomial parameters

Bayesian Analysis

Volumn 4, Issue 1, 2009, Pages 151-158

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

^a Hunter New England Population Health   (Australia)

^b UNIVERSITY OF SYDNEY   (Australia)

^c QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

Bayesian inference; Binomial distribution; Invariance; Jeffreys prior; Noninformative priors

Indexed keywords

EID: 76649143337     PISSN: 19360975     EISSN: 19316690     Source Type: Journal    
DOI: 10.1214/09-BA405     Document Type: Article

References (19)

1. Agresti, A. and Min, Y. (2005). " Frequentist performance of Bayesian confidence inter- vals for comparing proportions in 2×2 contingency tables." Biometrics, 61: 515-523.
2. Bayes, T. R. (1763). " An essay towards solving a problem in the doctrine of chances." Phil. Trans. Roy. Soc. London, 53: 370-418.
3. Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis. New York: Springer-Verlag.
4. Bernardo, J. M. (1979). " Reference posterior distributions for Bayesian inference." Journal of the Royal Statistical Society, Series B, 41: 113-147 (with discussion).
5. Bernardo, J. M. (2005). " Reference analysis." In Dey, D. K. and Rao, C. R. (eds.), Bayesian thinking: modeling and computation, 17-90. Amsterdam: Elsevier.
6. 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.
7. Bernardo, J. M. and Smith, A. F. M. (1994). Bayesian Theory. New York: Wiley.
8. Box, G. E. P. and Tiao, G. C. (1973). Bayesian Inference in Statistical Analysis. New York: Wiley Classics.
9. Edwards, A. W. F. (1978). " Commentary on the arguments of Thomas Bayes." The Scandinavian Journal of Statistics, 5: 116-118.
10. Fisher, R. A. (1973). Statistical Methods and Scientific Inference. New York: Hafner Press.
11. Geisser, S. (1984). " On prior distributions for binary trials." The American Statistician, 38(4): 244-251.
12. Geisser, S. (1993). Predictive Inference: An Introduction. London: Chapman and Hall.
13. Hashemi, L., Nandram, B., and Goldberg, R. (1997). " Bayesian analysis for a single 2 × 2 table." Statistics in Medicine, 16: 1311-1328.
14. Huzurbazar, V. S. (1976). Sufficient Statistics. New York: Marcel Dekker.
15. Jaynes, E. T. (2003). Probability Theory - The Logic of Science. Cambridge: University Press.
16. Phillips, P. C. B. (1991). " To criticize the critics: an objective Bayesian analysis of stochastic trends." Journal of Applied Econometrics, 6(4): 333-364.
17. Stigler, S. M. (1982). " Thomas Bayes's Bayesian inference." Journal of the Royal Statistical Society, Series A, 145(2): 250-258.
18. Thatcher, A. R. (1964). " Relationships between Bayesian and confidence limits for prediction." Journal of the Royal Statistical Society, Series B, 26: 126-210.
19. Welsh, A. H. (1996). Aspects of Statistical Inference. New York: John Wiley and Sons Ltd.