False discovery rate for scanning statistics

The false discovery rate is a criterion for controlling Type I error in simultaneous testing of multiple hypotheses. For scanning statistics, due to local dependence, clusters of neighbouring hypotheses are likely to be rejected together. In such situations, it is more intuitive and informative to group neighbouring rejections together and count them as a single discovery, with the false discovery rate defined as the proportion of clusters that are falsely declared among all declared clusters. Assuming that the number of false discoveries, under this broader definition of a discovery, is approximately Poisson and independent of the number of true discoveries, we examine approaches for estimating and controlling the false discovery rate, and provide examples from biological applications.