JSM 2004 - Toronto

Abstract #301565

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Activity Number: 423
Type: Topic Contributed
Date/Time: Thursday, August 12, 2004 : 10:30 AM to 12:20 PM
Sponsor: Biometrics Section
Abstract - #301565
Title: Multiple Testing in a Hierarchical Framework
Author(s): Aurelie Labbe*+
Companies: University of Waterloo
Address: Statistics and Actuarial Science, Waterloo, ON, N2L3G1, Canada
Keywords: microarray ; multiple testing
Abstract:

We study the problem of testing the equality of two sample means under a Bayesian framework, when the number of tests performed is large. We propose to use the posterior probability of the one-sided alternative as a measure of significance for each test. We show that under some conditions on a model associated with Jeffreys prior, this posterior probability can be seen as a conditional p value, given one of the two observed samples. When a model with an informative prior is used, the conjugate gamma model for example, we also show that it is approximately uniformly distributed under the null hypothesis. In both cases, this type of posterior probability can then be used in the spirit of a p value in some standard multiple testing procedures developed under a frequentist framework, with the advantage of working with a probability combining the prior and the observed information. The proposed methodology shows all its potential in a practical problem like microarray data analysis, where the number of hypotheses tested is large.

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