Statistics and Computing

, Volume 6, Issue 3, pp 277–287 | Cite as

Bayesian analysis of contingency tables: a simulation and graphics-based approach

  • P. Vounatsou
  • A. F. M. Smith


In this paper we present a simulation and graphics-based model checking and model comparison methodology for the Bayesian analysis of contingency tables. We illustrate the approach by testing the hypotheses of independence and symmetry on complete and incomplete simulated tables.


Bayesian inference contingency tables Gibbs sampling graphical methods hypothesis testing independence intraclass tables model comparison predictive densities quasisymmetry simulation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Altham, P. M. E. (1975) Quasi-independent triangular contingency tables. Biometrics, 31, 233–8.Google Scholar
  2. Bhapkar, V. P. (1979) On tests of marginal symmetry and quasisymmetry in two and three-dimensional contingency tables. Biometrics, 35, 417–26.Google Scholar
  3. Bishop, Y. V. V., Fienberg, S. E. and Holland, P. W. (1975) Discrete Multivariate Analysis. Cambridge, MA: MIT Press.Google Scholar
  4. Box, G. E. P. (1980) Sampling and Bayes' inference in scientific modelling and robustness (with discussion). Journal of the Royal Statistical Society, Series A, 143, 383–430.Google Scholar
  5. Caussinus, H. (1965) Contribution à l'analyse statistque des tableaux de correlation. Annales de la Faculté des Sciences de l'Université de Toulouse, 29, 77–182.Google Scholar
  6. Chen, T. and Fienberg, S. E. (1976) The analysis of contingency tables with incompletely classified data. Biometrics, 32, 133–44.Google Scholar
  7. Cohen, J. J. (1976) The distribution of the chi-square statistic under clustered sampling from contingency tables. Journal of the American Statistical Association, 71, 665–70.Google Scholar
  8. Devroye, L. (1986) Non-Uniform Random Variate Generation. New York: Springer-Verlag.Google Scholar
  9. Forster, J. J. and Skene, A. M. (1994) Calculation of marginal densities for parameters of multinomial distributions. Statistics and Computing, 4, 279–86.Google Scholar
  10. Gelman, A., Meng, X. L. and Stern, H. S. (1992) Bayesian tests for goodness of fit using tail area probabilities. Technical Report. Department of Statistics, University of California.Google Scholar
  11. Haber, M. (1982) Testing for independence in intraclass contingency tables. Biometrics, 38, 93–103.Google Scholar
  12. Ishii, G. (1960) Intraclass contingency tables. Annals of the Institute of Statistical Mathematics, 12, 161–207.Google Scholar
  13. Leonard, T. and Hsu, J. S. J. (1994) The Bayesian analysis of categorical data: a selective review. In P. R. Freeman and A. F. M. Smith (eds), Aspects of Uncertainty: a Tribute to D. V. Lindley. Chichester: Wiley.Google Scholar
  14. Roberts, G. O. (1992) Convergence diagnostics of the Gibbs sampler. In J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith (eds), Bayesian Statistics 4. Oxford: University Press, 777–84.Google Scholar
  15. Rubin, D. B. (1984) Bayesianly justifiable and relevant frequency calculations for the applied statistician. Annals of Statistics, 12, 1151–72.Google Scholar
  16. Smith, A. F. M. and Roberts, G. O. (1993) Bayesian computation via Gibbs sampler and related Markov chain Monte Carlo methods (with discussion). Journal of the Royal Statistical Society, Series B, 55, 3–23.Google Scholar
  17. Tanner, M. A. (1991) Tools for Statistical Inference: Observed Data and Data Augmentation Methods. Berlin: Springer.Google Scholar
  18. Wakefield, J. C., Gelfand, A. E. and Smith, A. F. M. (1991) Efficient Computation of random variates via the ratio-of-uniforms method. Statistics and Computing, 1, 129–33.Google Scholar

Copyright information

© Chapman & Hall 1996

Authors and Affiliations

  • P. Vounatsou
    • 1
  • A. F. M. Smith
    • 2
  1. 1.Swiss Tropical InstituteBasleSwitzerland
  2. 2.Department of MathematicsImperial CollegeLondonUK

Personalised recommendations