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The Multivariate Point Null Testing Problem: A Bayesian Discussion

Gomez-Villegas, Miguel Angel and Gonzalez-Perez, Beatriz (2008) The Multivariate Point Null Testing Problem: A Bayesian Discussion. Statistics & Probability Letters, 78 (17). pp. 3070-3074. ISSN 0167-7152

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Abstract

In this paper the problem of testing a multivariate point hypothesis is considered. Of interest is the relationship between the p-value and the posterior probability. A Bayesian test for simple H0 V � D �0 versus bilateral H0 V 6D 0, with a mixed prior distribution for the parameter , is developed. The methodology consists of fixing a sphere of radius around 0 and assigning a prior mass,0, to H0 by integrating the density ./ over this sphere and spreading the remainder, 1 0, over H1 according to ./. A theorem that
shows when the frequentist and Bayesian procedures can give rise to the same decision is proved. Then, some examples are revisited.


Item Type:Article
Uncontrolled Keywords: P-Values; Hypothesis; Probability; Frequentist;Statistics & Probability
Subjects:Sciences > Mathematics > Mathematical statistics
ID Code:15829
References:

Gómez-Villegas, M.A., González-Pérez, B., 2005. Bayesian analysis of contingency tables. Commun. Stat.-Theory Methods 34 (8), 17431754.

Gómez-Villegas, M.A., González-Pérez, B., 2006. A condition to obtain the same decision in the homogeneity testing problem from the frequentist and Bayesian point of view. Commun. Stat.-Theory Methods 35, 22112222.

Gómez-Villegas, M.A., Maín, P., Sanz, L., 2002. A suitable Bayesian approach in testing point null hypothesis: Some examples revisited. Commun. Stat.-Theory Methods 31 (2), 201217.

Gómez-Villegas, M.A., Maín, P., Sanz, L., 2007. Contraste de hipótesis nula puntual multivariante para variables normales correladas. Actas del XXX Congreso Nacional de Estadística e Investigación Operativa y IV Jornadas de Estadística Pública 2007.

Gómez-Villegas, M.A., Sanz, L., 2000. "-contaminated priors in testing point null hypothesis: A procedure to determine the prior probability. Statist. Probab. Lett. 47, 5360.

Lindley, D.V., 1957. A statistical paradox. Biometrika 44, 187192.Oh, H.S., Dasgupta, A., 1999. Comparison of the p-value and posterior probability. J. Stat. Plan. Inference 76, 93107.

Sellke, T., Bayarri, M.J., Berger, J.O., 2001. Calibration of p-values for testing point null hypotheses. Amer. Stat. 55, 6271.

Deposited On:05 Jul 2012 10:05
Last Modified:06 Feb 2014 10:32

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