On the application of symmetric Dirichlet distributions and their mixtures to contingency tables

Bayes factors against various hypotheses of independence are proposed for contingency tables and for multidimensional contingency tables. The priors assumed for the nonnull hypothesis are linear combinations of symmetric Dirichlet distributions as in some work of 1965 and later. The results can be used also for probability estimation. The evidence concerning independence, provided by the marginal totals alone, is evaluated, and preliminary numerical calculations suggest it is small. The possibility of applying the Bayes/non-Bayes synthesis is proposed because it was found useful for an analogous problem for multinomial distributions. As a spinoff, approximate formulae are suggested for enumerating "arrays" in two and more dimensions.