Bayesian Methods and Simulation-Based Computation for Contingency Tables

Abstract

This chapter describes the Bayesian methods and simulation-based computation for contingency tables. Bayesian methods allow a user to explicitly model the uncertainty among a class of possible models by means of a prior distribution on the class of models, such that the posterior estimates of association parameters explicitly account for uncertainty about the “true” model, on which estimates should ideally be based. Much of the early Bayesian methodology for contingency tables has been devoted to issues regarding computation due to the difficulties in computing integrals of several variables. However, by virtue of great advances in computing posterior distributions by simulation, it is now possible to fit sophisticated Bayesian models for high-dimensional contingency tables. This chapter illustrates the relative ease of using WinBUGS of simulating from posterior distributions of categorical data models and comparing models by Bayes factors. Finally, Bayesian advances may be expected, especially with respect to criticism of single loglinear models, and model selection among large classes of hierarchical and graphical models.