Fa. Quintana, NONPARAMETRIC BAYESIAN-ANALYSIS FOR ASSESSING HOMOGENEITY IN KXL CONTINGENCY-TABLES WITH FIXED RIGHT MARGIN TOTALS, Journal of the American Statistical Association, 93(443), 1998, pp. 1140-1149
In this work I postulate a nonparametric Bayesian model for data that
can be accommodated in a contingency table with fixed right margin tot
als. This data structure usually arises when comparing different group
s regarding classification probabilities for a number of categories. I
assume that cell count vectors for each group are conditionally indep
endent, 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 a
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 cla
ssification probabilities, and propose a ''Bayes factor.'' I derive ex
act expressions for the relevant quantities. These can be directly com
puted when the number of rows k is small. and through the sequential i
mportance sampling algorithm proposed by MacEachern. Clyde, and Liu wh
en k is moderate or large. The methods are illustrated with several ex
amples.