Assuming a multinomial sampling model, prior distributions are developed which can accept prior information about symmetry and independence in a two-way contingency table. Bayesian estimates for the cell probabilities are obtained from the posterior distributions which are attractive alternatives to the usual classical estimates when vague prior information about symmetry or independence is available.
"Mixtures of Dirichlet Distributions and Estimation in Contingency Tables." Ann. Statist. 10 (4) 1261 - 1268, December, 1982. https://doi.org/10.1214/aos/1176345991