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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, October 2, 2001}
\centerline{Sequoia Hall Rm. 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl John David Storey}
\centerline{\sl Department of Statistics}
\centerline{\sl Stanford University}
\centerline{\sl Stanford,  CA 94305}
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\centerline{\bf The Positive False Discovery Rate}

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When testing multiple hypotheses it is important to assess the
number of false positives in some fashion. In order to accomplish this
task, we introduce the positive False Discovery Rate (pFDR), which is a
modified version of Benjamini and Hochberg's False Discovery Rate (FDR).
We show that the pFDR can be written in a very simple form and has a
Bayesian interpretation. We also suggest a more direct approach to
multiple hypothesis testing than what has traditionally been taken.
Instead of fixing the error rate and estimating the corresponding
rejection region, we take the opposite approach: we fix the rejection
region and estimate its corresponding error rate. We show how this
approach can be applied to the pFDR, resulting in substantial improvements
to power, interprebility, and applicability. This methodolgy works
particularly well for large numbers of hypothesis tests, and is also
immune to certain forms of dependence, both of which make it particularly
applicable to DNA microarrays.


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