We present a strongly robust Bayesian test of the hypothesis of equality of distributions for populations consisting of data in finitely many categories. The Bayes factors are the same for infinite and finite populations. Under the hypothesis of inequality, one distribution can be viewed as an exponentially tilted or exponentially distorted version of another. We illustrate the method by calculating Bayes factors for a range of data values.
AMS Subject Classification. Primary
62F15 62F03 62F35 Secondary 62E15
Tests of hypotheses Multiple populations SRSWOR Finite population sampling Bayes-ian testing Bayes factor Bayesian robustness Robust testing Limit distribution Exponential tilting Exponential distortion
This is a preview of subscription content, log in to check access.
Albert, J.H., Gupta, A.K., 1983. Estimation in contingency tables using prior information. Journal of the Royal Statistical Society, Series B, Methodological, 45, 60–69.MathSciNetMATHGoogle Scholar
Albert, J.H., Gupta, A.K., 1985. Bayesian methods for binomial data with applications to a nonresponse problem. Journal of the American Statistical Association, 80, 167–174.MathSciNetCrossRefGoogle Scholar
Bose, S., 2004. On the robustness of the predictive distribution for sampling from finite populations. Statist. Probab. Lett., 69(1), 21–27.MathSciNetCrossRefGoogle Scholar
Bose, S., Kedem, B., 1996. Non-dependence of the predictive distribution on the population size. Statist. Probab. Lett., 27(1), 43–47.MathSciNetCrossRefGoogle Scholar
Bratcher, T.L., Schucany, W.R., Hunt, H.H., 1971. Bayesian prediction and population size assumptions. Technometrics, 13(3), 678–681.CrossRefGoogle Scholar
Fokianos, K., Kaimi, I., 2006. On the effect of misspecifying the density ratio model. Annals of the Institute of Statistical Mathematics, 58(3), 475–497.MathSciNetCrossRefGoogle Scholar