Models for Reflecting Prior Beliefs of Association in two-way Contingency Tables

Abstract

In this survey paper, general classes of prior distributions are developed for four sampling models which are designed to reflect prior beliefs about the association structure in a two-way contingency table.These classes, special mixtures of Diriehlet distributions, are used to develop posterior estimates for the cell probabilities.In examples, it is shown how these classes can be used to reflect the vague notion of similarity of a set of binomial probabilities or reflect prior beliefs about bias in a non response problem.

Keywords:

• discrete data
• estimation
• similarity
• multivariate mixtures
• Diriehlet distribution
• nonresponse
• posterior analysis