Bayesian Estimation in Multidimensional Contingency Tables

Abstract

This paper examines a new class of prior distributions for Bayesian estimation in contingency tables. It exploits both the conjugate Dirichlet prior when the data follow a multinomial distribution and the traditional loglinear parametrization by applying it to the means of the Dirichlet prior. The resulting prior distributions can reflect the user’s uncertainty about both the applicability of a loglinear structure and the values of the cell probabilities. Connections with the maximum likelihood approach permit the user to provide initial guesses at the cell probabilities either through various margins of the cell prior means or through the “effects” of a loglinear model. We apply our method to medical data concerning skin cancer.