The geometry of time-varying cross-correlation random fields

The goal of this paper is to assess the P-value of local maxima of time-varying cross-correlation random fields. The motivation for this comes from an electroencephalography (EEG) experiment, where one seeks connectivity between all pairs of voxels inside the brain at each time point of the recording window. In this way, we extend the results of [Cao, J., Worsley, K.J., 1999b. The geometry of correlation fields with an application to functional connectivity of the brain. The Annals of Applied Probability 9 (4), 1021-1057] by searching for high correlations not only over all pairs of voxels, but over all time points as well. We apply our results to an EEG data set of a face recognition paradigm. Our analysis determines those time instants for which there are significantly correlated regions involved in face recognition.