Journal of Statistical Theory and Practice

, Volume 5, Issue 4, pp 675–682 | Cite as

When Population Size Does Not Matter: Robust Bayesian Testing for Categorical Populations

  • Sudip BoseEmail author
  • Mark Bauder


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 


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  1. 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.MathSciNetzbMATHGoogle Scholar
  2. 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
  3. Bose, S., 2004. On the robustness of the predictive distribution for sampling from finite populations. Statist. Probab. Lett., 69(1), 21–27.MathSciNetCrossRefGoogle Scholar
  4. Bose, S., Kedem, B., 1996. Non-dependence of the predictive distribution on the population size. Statist. Probab. Lett., 27(1), 43–47.MathSciNetCrossRefGoogle Scholar
  5. Bratcher, T.L., Schucany, W.R., Hunt, H.H., 1971. Bayesian prediction and population size assumptions. Technometrics, 13(3), 678–681.CrossRefGoogle Scholar
  6. 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
  7. Fokianos, K, Kedem, B, Qin, J, Short, D.A., 2001. A semiparametric approach to the one-way layout. Technometrics, 43(1), 56–65.MathSciNetCrossRefGoogle Scholar
  8. Johnson, N.L., Kotz, S., Balakrishnan, N. 1997. Discrete Multivariate Distributions. John Wiley and Sons, New York.zbMATHGoogle Scholar
  9. Kedem, B., Wolff, D.B., Fokianos, K., 2004. Statistical comparison of algorithms. IEEE Transactions on Instrumentation and Measurement, 53(3), 770–776.CrossRefGoogle Scholar
  10. Kiefer, N., 2010. Personal communication.Google Scholar
  11. Wright, T., 1992. A note on sampling to locate rare defectives with strong prior evidence. Biometrika, 79, 685–691.MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2011

Authors and Affiliations

  1. 1.Department of StatisticsThe George Washington UniversityWashington, D.C.USA

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