Signal Identification for Rare and Weak Features: Higher Criticism or False Discovery Rates?

Statistics – Methodology

Scientific paper

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20 pages, 6 figures, 4 tables

Scientific paper

Signal identification in large-dimensional settings is a challenging problem in biostatistics. Recently, the method of higher criticism (HC) was shown to be an effective means for determining appropriate decision thresholds. Here, we study HC from a false discovery rate (FDR) perspective. We show that the HC threshold is best viewed as an approximation to a natural Bayesian decision threshold which in turn is expressible as a specific FDR threshold. We demonstrate that in a rare-weak setting in the region of the phase space where signal identification is possible at all both thresholds are practicably indistinguishable. The relationship of the HC and Bayesian thresholds and their properties are investigated further both analytically and by simulations. Finally, the investigated methods are compared by application to four cancer gene expression data sets.

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