Estimation in Contingency Tables Using Prior Information

SUMMARY Prior beliefs of association and independence in a two-way contingency table are discussed, and estimators of the cell probabilities are proposed which can incorporate this prior information. In the 2 x 2 table where the cell counts are assumed to have a multinomial distribution, estimators are developed which can incorporate prior beliefs about the correlation coefficient and the cross-product ratio. In the I x 2 table in which one set of marginal totals is fixed, estimators are developed which reflect prior information about the similarity of a set of cell probabilities. Numerical examples are given to illustrate the use of these estimators.