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Multiple testing problems arising in modern scientific applications caninvolve simultaneously testing thousands or even millions of hypotheses, withrelatively few true signals. In this paper, we consider the multiple testingproblem where prior information is available (for instance, from an earlierstudy under different experimental conditions), that can allow us to test thehypotheses as a ranked list in order to increase the number of discoveries.Given an ordered list of n hypotheses, the aim is to select a data-dependentcutoff k and declare the first k hypotheses to be statistically significantwhile bounding the false discovery rate (FDR). Generalizing several existingmethods, we develop a family of "accumulation tests" to choose a cutoff k thatadapts to the amount of signal at the top of the ranked list. We introduce anew method in this family, the HingeExp method, which offers higher power todetect true signals compared to existing techniques. Our theoretical resultsprove that these methods control a modified FDR on finite samples, andcharacterize the power of the methods in the family. We apply the tests tosimulated data, including a high-dimensional model selection problem for linearregression. We also compare accumulation tests to existing methods for multipletesting on a real data problem of identifying differential gene expression overa dosage gradient.

Accumulation tests for FDR control in ordered hypothesis testing