Nonparametric Bayesian Analysis for Assessing Homogeneity ink×lContingency Tables with Fixed Right Margin Totals
Fernando Andrés Quintana · Journal of the American Statistical Association · 1998
In this work I postulate a nonparametric Bayesian model for data that can be accommodated in a contingency table with fixed right margin totals. This data structure usually arises when comparing different groups regarding classification probabilities for a number of categories. I assume that cell count vectors for each group are conditionally independent, with multinomial distribution given vectors of classification probabilities. In turn, these vectors of probabilities are assumed to be a sample from a distribution F, and the prior distribution of F is assumed to be a Dirichlet process, centered on a probability measure α and with weight c. I also assume a prior distribution for c, as a way of obtaining a better control on the clustering structure induced by the Dirichlet process. I use this setting to assess homogeneity of classification probabilities, and propose a “Bayes factor.” I derive exact expressions for the relevant quantities. These can be directly computed when the number of rows k is small, and through the sequential importance sampling algorithm proposed by MacEachern, Clyde, and Liu when k is moderate or large. The methods are illustrated with several examples.