Objective priors for discrete parameter spaces

Journal of the American Statistical Association

Volumn 107, Issue 498, 2012, Pages 636-648

  Berger, James O ^a   Bernardo, Jose M ^b   Sun, Dongchu ^c,d  

^a Duke University   (United States)

^b UNIVERSITY OF VALENCIA   (Spain)

^c EAST CHINA NORMAL UNIVERSITY   (China)

^d UNIVERSITY OF MISSOURI   (United States)

Author keywords

Binomial; Discrete parameter space; Hypergeometric; Jeffreys rule priors; Parameter based asymptotics; Prior model probabilities; Reference priors

Indexed keywords

EID: 84864391190     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1080/01621459.2012.682538     Document Type: Article

References (27)

1. Barger, K., and Bunge, J. (2008), "Bayesian Estimation of the Number of Species Using Non informative Priors," Biometrical Journal, 50, 1064-1076. [636,637,644]
2. Basu, S., and Ebrahimi, N. (2001), "Bayesian Capture-Recapture Methods for Error Detection and Estimation of Population Size: Heterogeneity and Dependence," Biometrika, 88, 269-279. [638,643]
3. Berger, J. O., and Bernardo, J. M. (1992), "On the Development of Reference Priors" (with discussion), in Bayesian Statistics 4, eds. J. M. Bernardo, J. O. Berger, D. V. Lindley, and A. F. M. Smith, London: Oxford University Press, pp. 35-60. [636,637,641]
4. Berger, J. O., Bernardo, J. M., and Sun, D. (2009a), "The Formal Definition of Reference Priors," The Annals of Statistics, 37, 905-938. [636]
5. Berger, J. O. (2009b), "Natural Induction: An Objective Bayesian Approach," Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas, 103, 125-135. [641]
6. Berger, J. O., Liseo, B., and Wolpert, R. L. (1999), "Integrated Likelihood Methods for EliminatingNuisance Parameters" (with discussion), Statistical Science, 14, 1-28. [643,646]
7. Bernardo, J. M. (1979), "Reference Posterior Distributions for Bayesian Inference" (with discussion), Journal of the Royal Statistical Society, Series B, 41, 113-147; Reprinted in Bayesian Inference (1995, Vol. 1), eds. G. C. Tiao and N. G. Polson, Oxford: Edward Elgar, pp. 229-263. [636]
8. Bernardo, J. M. (2005), "Reference Analysis," in Handbook of Statistics (Vol. 25), eds. D. K. Dey and C. R. Rao, Amsterdam: Elsevier, pp. 17-90. [636]
9. Bernardo, J. M., and Smith, A. F. M. (1994), Bayesian Theory, New York: Wiley. [636]
10. Broad, C. D. (1918), "On the Relation Between Induction and Probability," Mind, 27, 389-404. [641]
11. DasGupta, A., and Rubin, H. (2005), "Estimation of Binomial Parameters When Both n, p Are Unknown," Journal of Statistical Planning and Inference, 130, 391-404. [643]
12. Goudie, I. B. J., and Goldie, C. M. (1981), "Initial Size Estimation for the Pure Death Process," Biometrika, 68, 543-550. [638,639]
13. Haldane, J. B. S. (1941), "The Fitting of Binomial Distributions," The Annals of Eugenics, London, 11, 179-181. [643]
14. He, C. Z. (2011), "Bayesian Analysis for the Multinomial Data Under Noninformative Priors," Technical Report, University of Missouri. [647]
15. Jeffreys, H. (1961), Theory of Probability, London: Oxford University Press. [636]
16. Jeffreys, H. (1946), "An Invariant from for the Prior Probability in Estimation Problems," Proceedings of the Royal Society of London A, 186, 453-461. [637]
17. Kahn, W. D. (1987), "A Cautionary Note for Bayesian Estimation of the Binomial Parameter n," The American Statistician, 41, 38-39. [636]
18. Kramer, M., and Starr, N. (1990), "Optimal Stopping in a Size Dependent Search," Sequential Analysis, 9, 59-80. [638]
19. Laplace, P. S. (1774), "Mémoire sur la Probabilité des Causes par les Événements," in Oeuvres Complètes (Vol. 8), Paris: Gauthier-Villars, pp. 27-68. [641]
20. Lawless, J. (1982), Statistical Models and Methods for Lifetime Data, New York: Wiley. [638]
21. Lindsay, B. G., and Roeder, K. (1987), "A Unified Treatment of Integer Parameter Models," Journal of the American Statistical Association, 82, 758-764. [636,637]
22. Moreno, E., and Giron, J. (1998), "Estimating With Incomplete Count Data: A Bayesian Approach," Journal of Statistical Planning and Inference, 66, 147-159. [644]
23. Raftery, A. E. (1988a), "Inference for the Binomial n Parameter: A Hierarchical Bayes Approach," Biometrika, 75, 223-228. [644,646]
24. Raftery, A. E. (1988b), "Analysis of a Simple Debugging Model," Applied Statistics, 37, 12-22. [639]
25. Rissanen, J. (1983), "AUniversal Prior for Integers and Estimation by Minimum Description Length," The Annals of Statistics, 11, 416-431. [636]
26. Starr, N. (1974), "Optimal and Adaptive Stopping Based on Capture Times," Journal of Applied Probability, 11, 294-301. [638]
27. Sweeting, T. J. (1992), "Parameter-Based Asymptotics," Biometrika, 79, 219-232. [637]