New procedures for false discovery control

Following Benjamini and Hochberg, the false discovery rate has emerged as a viable alternative to strong control of Type I error in multiple testing problems such as those which arise in functional neuroimaging. This paper reports on new methods for false discovery control that can usefully be applied to functional neuroimaging data, especially for thresholding statistical maps. The methods are based on controlling the unobserved false discovery proportion (FDP) the number of false rejections divided by the number of rejections simultaneously over all thresholds. From this, one can design thresholding procedures to control the false discovery rate and other features of the false discovery process, including the probability that FDP exceeds a specified level or the expected proportion of false regions. We give two variants on these procedures, one for unsmoothed data and one for smoothed data based on random field models. We illustrate the methods using data from a visual remapping study.