Multiple Testing via Fdr for Large Scale Imaging Data.

The multiple testing procedure plays an important role in detecting the presence of spatial signals for large scale imaging data. Typically, the spatial signals are sparse but clustered. This paper provides empirical evidence that for a range of commonly used control levels, the conventional FDR procedure can lack the ability to detect statistical significance, even if the p-values under the true null hypotheses are independent and uniformly distributed; more generally, ignoring the neighboring information of spatially structured data will tend to diminish the detection effectiveness of the FDR procedure. This paper first introduces a scalar quantity to characterize the extent to which the "lack of identification phenomenon" (LIP) of the FDR procedure occurs. Second, we propose a new multiple comparison procedure, called FDR(L), to accommodate the spatial information of neighboring p-values, via a local aggregation of p-values. Theoretical properties of the FDR(L) procedure are investigated under weak dependence of p-values. It is shown that the FDR(L) procedure alleviates the LIP of the FDR procedure, thus substantially facilitating the selection of more stringent control levels. Simulation evaluations indicate that the FDR(L) procedure improves the detection sensitivity of the FDR procedure with little loss in detection specificity. The computational simplicity and detection effectiveness of the FDR(L) procedure are illustrated through a real brain fMRI dataset.