Variance of the number of false discoveries

In high throughput genomic work, a very large number d of hypotheses are tested based on n << d data samples. The large number of tests necessitates an adjustment for false discoveries in which a true null hypothesis was rejected. The expected number of false discoveries is easy to obtain. Dependences between the hypothesis tests greatly affect the variance of the number of false discoveries. Assuming that the tests are independent gives an inadequate variance formula. The paper presents a variance formula that takes account of the correlations between test statistics. That formula involves O(d(2)) correlations, and so a naive implementation has cost O(nd(2)). A method based on sampling pairs of tests allows the variance to be approximated at a cost that is independent of d.