Nonparametric Bayesian analysis for assessing homogeneity in k × l contingency tables with fixed right margin totals

Quintana, F. A.


"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 ? 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."

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Título de la Revista: Journal Of The American Statistical Association
Volumen: 93
Número: 443
Fecha de publicación: 1998
Página de inicio: 1140
Página final: 1149