Abstract: This paper presents a Bayes method to estimate the expected proportions for high-way contingency tables appropriate when prior knowledge about the interaction effects can be described by a particular kind of exchangeability assumption.We give the expressions of estimates for four-way contingency tables based on general expressions equations.It extends the work of Leonard (1975) and Nazaret(1987) and useful algorithm also discussed.

Key words: Logits transformation, contingency tables, Bayes estimates, statistical computation