ε-Contaminated priors in contingency tables

• Autores: Miguel Ángel Gómez Villegas, Beatriz González Pérez
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 17, Nº. 1, 2008, págs. 163-178
• Idioma: inglés
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• Resumen

  • An r×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 ε-contaminated prior on the proportions under the alternative. The resulting Bayes tests are compared numerically to Pearson’s χ 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.