False discovery rate: setting the probability of false claim of detection

Abstract

When testing multiple hypothesis in a survey --e.g. many different source locations, template waveforms, and so on-- the final result consists in a set of confidence intervals, each one at a desired confidence level. But the probability that at least one of these intervals does not cover the true value increases with the number of trials. With a sufficiently large array of confidence intervals, one can be sure that at least one is missing the true value. In particular, the probability of false claim of detection becomes not negligible. In order to compensate for this, one should increase the confidence level, at the price of a reduced detection power. False discovery rate control is a relatively new statistical procedure that bounds the number of mistakes made when performing multiple hypothesis tests. We shall review this method, discussing exercise applications to the field of gravitational wave surveys.