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

被引：36
作者：
Tuyl, Frank [1 ]
Gerlach, Richard [2 ]
Mengersen, Kerrie [3 ]
机构：
[1] Hunter New England Populat Hlth, Newcastle, NSW, Australia
[2] Univ Sydney, Fac Econ & Business, Sydney, NSW 2006, Australia
[3] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia
来源：
BAYESIAN ANALYSIS | 2009年 / 4卷 / 01期
关键词：
Bayesian inference; binomial distribution; invariance; noninformative priors; Jeffreys prior;
D O I：
10.1214/09-BA405
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is argued that the posterior predictive distribution for the binomial and mutlinomial distributions, when viewed via a hypergeometric-like representation, suggests the uniform prior on the parameters for these models. The argument is supported by studying variations on an example by Fisher, and complements Bayes' original argument for a uniform prior predictive distribution for the binomial. The fact that both arguments lead to invariance under transformation is also discussed.
引用
收藏
页码：151 / 158
页数：8
相关论文
共 20 条
[1]   Frequentist performance of Bayesian confidence intervals for comparing proportions in 2 x 2 contingency tables [J].
Agresti, A ;
Min, YY .
BIOMETRICS, 2005, 61 (02) :515-523
[2]  
Bayes T., 1763, Philos. Trans. R. Soc. Lond., V53, P370
[3]  
Berger J. O., 1985, Statistical decision theory and Bayesian analysis, V2nd
[4]  
Bernardo J. M., 1994, Bayesian theory, DOI 10.1002/9780470316870
[5]  
Bernardo JM, 2005, HANDB STAT, V25, P17, DOI 10.1016/S0169-7161(05)25002-2
[6]  
Bernardo JM, 1998, J ROY STAT SOC D-STA, V47, P101
[7]  
Bernoth K., 2004, INT FINANC, V7, P1
[8]  
Box G.E.P., 2011, Bayesian inference in statistical analysis
[9]  
EDWARDS AWF, 1978, SCAND J STAT, V5, P116
[10]  
Fisher R.A., 1973, Statistical Methods and Scientific Inference
12