Assessing mean and median filters in multiple testing for large-scale imaging data

A new multiple testing procedure, called the FDRL procedure, was proposed by Zhang et al. (Ann Stat 39:613–642, 2011) for detecting the presence of spatial signals for large-scale 2D and 3D imaging data. In contrast to the conventional multiple testing procedure, the FDRL procedure substitutes each p-value by a locally aggregated median filter of p-values. This paper examines the performance of another commonly used filter, mean filter, in the FDRL procedure. It is demonstrated that when the p-values are independent and uniformly distributed under the true null hypotheses, (i) in view of estimating the resulting false discovery rate, the mean filter better alleviates the “lack of identification phenomenon” of the FDRL procedure than the median filter; (ii) in view of signal detection, the median filter enjoys the “edge-preserving property” and lends support to its better performance in detecting sparse signals than the mean filter.