Bayesian Inference Regarding Independence in Two-Way Contingency Tables Having Intrinsic Priors

Estimating a Bayes factor is provided. Table dimensions of a contingency table are determined. A statistical model type to apply to the contingency table is determined. Fixed marginal totals are specified for either rows or columns when a Multinomial sampling model is applied. A table total is computed when a Poisson sampling model is applied or fixed marginal totals are computed when the Multinomial sampling model is applied to a two by two contingency table. The table total is compared to a first threshold when the Poisson sampling model is applied or fixed marginal totals are compared to a second threshold when the Multinomial sampling model is applied to a two by two contingency table. An estimation method is selected to apply to the contingency table to compute the Bayes factor based on table dimensions, sampling model applied, and fixed marginal totals of the contingency table.