A Bayesian Approach to Some Multinomial Estimation and Pretesting Problems
- 1 December 1977
- journal article
- theory and-method
- Published by Taylor & Francis in Journal of the American Statistical Association
- Vol. 72 (360a) , 869-874
- https://doi.org/10.1080/01621459.1977.10479974
Abstract
New Bayesian estimates are proposed for multinomial probabilities, when the prior distribution is a mixture of Dirichlet distributions. They are based upon a distributional approximation for the χ2 statistic and may be contrasted with the frequentist approximations recommended by other authors. An alternative is also suggested to the χ2 goodness-of-fit test, when it is employed as a preliminary test of significance. The new procedure possesses remarkably different properties; it is used to reanalyze some data from Mendel's pea breeding experiment. The results suggest that the χ2 test may have no particular relevance in preliminary testing situations.Keywords
This publication has 8 references indexed in Scilit:
- On the Application of Symmetric Dirichlet Distributions and their Mixtures to Contingency TablesThe Annals of Statistics, 1976
- Some alternative approaches to multiparameter estimationBiometrika, 1976
- Reduced Mean Square Error Estimation in Contingency TablesJournal of the American Statistical Association, 1976
- Cross-validation and multinomial predictionBiometrika, 1974
- The Bayes/Non-Bayes Compromise and the Multinomial DistributionJournal of the American Statistical Association, 1974
- Simultaneous Estimation of Multinomial Cell ProbabilitiesJournal of the American Statistical Association, 1973
- A bayesian hypothesis-decision procedureAnnals of the Institute of Statistical Mathematics, 1967
- Has Mendel's work been rediscovered?Annals of Science, 1936