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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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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

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

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