In this technical note, we describe and validate a topological false discovery rate (FDR) procedure for statistical parametric mapping. This procedure is designed to deal with signal that is continuous and has, in principle, unbounded spatial support. We therefore infer on topological features of the signal, such as the existence of local maxima or peaks above some threshold. Using results from random field theory, we assign a p-value to each maximum in an SPM and identify an adaptive threshold that controls false discovery rate, using the Benjamini and Hochberg (BH) procedure (1995). This provides a natural complement to conventional family wise error (FWE) control on local maxima. We use simulations to contrast these procedures; both in terms of their relative number of discoveries and their spatial accuracy (via the distribution of the Euclidian distance between true and discovered activations). We also assessed two other procedures: cluster-wise and voxel-wise FDR procedures. Our results suggest that (a) FDR control of maxima or peaks is more sensitive than FWE control of peaks with minimal cost in terms of false-positives, (b) voxel-wise FDR is substantially less accurate than topological FWE or FDR control. Finally, we present an illustrative application using an fMRI study of visual attention.
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