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Error-rate and decision-theoretic methods of multiple testing: which genes have high objective probabilities of differential expression? (English) Zbl 1072.62106

Summary: Given a multiple testing situation, the null hypotheses that appears to have sufficiently low probabilities of truth may be rejected using a simple, nonparametric method based on decision theory. This applies not only to posterior levels of belief, but also to conditional probabilities in the sense of relative frequencies, as seen from their equality to local false discovery rates (dFDRs). This approach neither requires the estimation of probability densities, nor of their ratios. Decision theory can also inform the selection of false discovery rate weights. An application to gene expression microarrays is presented with a discussion of the applicability of the assumption of “clumpy dependence”.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62G10 Nonparametric hypothesis testing
62C99 Statistical decision theory
92D10 Genetics and epigenetics
62J15 Paired and multiple comparisons; multiple testing
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