Bayesian Estimation Methods for 2 × 2 Contingency Tables Using Mixtures of Dirichlet Distributions

Abstract

In the estimation of cell probabilities from a 2 × 2 table, a prior distribution is developed that can reflect prior beliefs about the cross-classification structure in the table. The posterior means using this prior shrink the classical estimates towards the association structure specified a priori by the user. Closed-form approximations to the posterior means and credible regions are developed in the special case where the two variables of the table are believed independent.

Key Words:

• Categorical data
• Mixtures of distributions
• Cross-product ratio
• Credible regions
• Shrinkage estimators