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Abstract : |
In this work we 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. We assume cell count vectors for each group to be conditionally independent, and 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 ff and with weight c. We also assume a prior distribution for c, as a way of obtaining a better control on the clustering structure induced by the Dirichlet process. We use this setting to assess homogeneity of classification probabilities, and a "Bayes factor " is proposed. We 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 (1996) when k is moderate or large. The methods are illustrated with several examples., |
