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November, 1976 On the Application of Symmetric Dirichlet Distributions and their Mixtures to Contingency Tables
I. J. Good
Ann. Statist. 4(6): 1159-1189 (November, 1976). DOI: 10.1214/aos/1176343649

Abstract

Bayes factors against various hypotheses of independence are proposed for contingency tables and for multidimensional contingency tables. The priors assumed for the nonnull hypothesis are linear combinations of symmetric Dirichlet distributions as in some work of 1965 and later. The results can be used also for probability estimation. The evidence concerning independence, provided by the marginal totals alone, is evaluated, and preliminary numerical calculations suggest it is small. The possibility of applying the Bayes/non-Bayes synthesis is proposed because it was found useful for an analogous problem for multinomial distributions. As a spinoff, approximate formulae are suggested for enumerating "arrays" in two and more dimensions.

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I. J. Good. "On the Application of Symmetric Dirichlet Distributions and their Mixtures to Contingency Tables." Ann. Statist. 4 (6) 1159 - 1189, November, 1976. https://doi.org/10.1214/aos/1176343649

Information

Published: November, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0348.62018
MathSciNet: MR428568
Digital Object Identifier: 10.1214/aos/1176343649

Subjects:
Primary: 62F15
Secondary: 05A15 , 62G10

Keywords: Bayes factor , Bayes/non-Bayes synthesis , combinations of Dirichlet distributions , Contingency tables , enumeration of arrays , independence , multidimensional asymptotic expansions , multidimensional contingency tables

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 6 • November, 1976
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