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Beyond Pairwise Interactions: The Totally Antisymmetric Part of the Bispectrum as Coupling Measure of at Least Three Interacting Sources

Bartz, Sarah; Andreou, Christina; Nolte, Guido

FG Maschinelles Lernen

In this paper we make two contributions to the analysis of brain oscillations with CFC techniques. First, we introduce a new bispectral CFC measure which is selective to couplings between three or more brain sources. This measure can be derived from ordinary cross-bispectra by performing a total-antisymmetrization operation on them. Significant coupling values can then be attributed to at least three interacting signals. This selectivity to the number of sources can be helpful to test hypotheses on the number of brain sources involved in the generation of commonly observed brain oscillations, such as the alpha rhythm. In a second step we present the correct empirical distribution for the coupling measure, which is necessary to properly assess the significance of coupling results. More importantly however, this corrected statistic is not limited to our particular measure, but holds for all complex-valued coupling estimators. We illustrate how the very common misassumption of empirical normality of such estimators can lead to a systematic underestimation of p-values, the breakdown of multiple comparison control procedures and in consequence a drastic inflation of the number of false positives.