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epsilon-Contaminated priors in contingency tables

Gómez Villegas, Miguel Ángel and González Pérez, Beatriz (2008) epsilon-Contaminated priors in contingency tables. Test , 17 (1). pp. 163-178. ISSN 1133-0686

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Official URL: http://www.springerlink.com/content/120411/

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Abstract

An r x s table is used for different approaches to statistical inference. We develop a Bayesian procedure to test simple null hypotheses versus bilateral alternatives in contingency tables. We consider testing equality of proportions of independent multinomial distributions when the common proportions are known. A lower bound of the posterior probabilities of the null hypothesis is calculated with respect to a mixture of a point prior on the null and an epsilon-contaminated prior on the proportions under the alternative. The resulting Bayes tests are compared numerically to Pearson's chi(2) in a number of examples. For the examined examples the lower bound and the p-value can be made close. The obtained results are generalized when the common proportions vector under the null is unknown or has a known functional form.

Item Type:Article
Uncontrolled Keywords:Contingency tables; Epsilon-contaminated priors; Test statistic; Critical region; P-values; Posterior probabilities; Reconciliation
Subjects:Sciences > Mathematics > Mathematical statistics
ID Code:11168
Deposited On:16 Sep 2010 08:42
Last Modified:06 Feb 2014 08:58

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