Sampling Based Approach for Combining Results from Binomial Experiments

  • Cho, Jang-Sik (Department of Statistical Information Science, Kyungsung University) ;
  • Kim, Dal-Ho (Department of Statistics, Kyungpook National University) ;
  • Kang, Sang-Gil (Department of Statistics, Kyungpook National University)
  • Published : 2001.04.30

Abstract

In this paper, the problem of information related to I binomial experiments, each having a distinct probability of success ${\theta}_i$, i = 1,2, $\cdots$, I, is considered. Instead of using a standard exchangeable prior for ${\theta}\;=\;({\theta}_1,\;{\theta}_2,\;{\cdots},\;{\theta}_I)$, we con-sider a partition of the experiments and take the ${\theta}_i$'s belonging to the same partition subset to be exchangeable and the ${\theta}_i$'s belonging to distinct subsets to be independent. And we perform Gibbs sampler approach for Bayesian inference on $\theta$ conditional on a partition. Also we illustrate the methodology with a real data.

References

  1. The Analysis of Cross-Classified Categorical Data(2nd ed.) Fienberg, S.E.
  2. Journal of the American Statistical Association v.85 Sampling-Based Approaches to Calculating Marginal Densities Gelfand,A.E.;Smith,A.F.M.
  3. Journal of the American Statistical Association v.90 A Bayesian Method for Combining Results From Several Binomial Experiments Consonni,G.;Veronese,P.
  4. Biometrika v.79 Bayesian methodology for the results from different experiments when the specification for pooling are uncertain Malec,D.;Sedransk,J.
  5. Communication in Statatistics-Theory and Methods v.20 Gibbs Sampling for Marginal Posterior Expectations Gelfand,A.E.;Smith,A.F.M.
  6. Applied Statistics v.41 Adaptive Rejection Sampling for Gibbs Sampling Gilks, W.R.;Wild, P.
  7. W. G. Cochran's Impact on Statistics Variance components models for combining estimators Rao
  8. Bayesian Ststistics v.3 Modelling with Heavy Tails O'Hagan,A.
  9. Statistical Sciences v.7 Inference from Iterative Simulation Using Multiple Sequences Gelman,A.;Rubin,D.B.