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.

中文翻译：

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超越成对相互作用：双谱的完全反对称部分作为至少三个相互作用源的耦合测度

在本文中，我们对使用 CFC 技术分析大脑振荡做出了两个贡献。首先，我们引入了一种新的双谱 CFC 测量，它对三个或更多脑源之间的耦合具有选择性。通过对它们执行完全反对称化操作，可以从普通的交叉双谱推导出该度量。然后可以将显着的耦合值归因于至少三个相互作用的信号。这种对来源数量的选择性有助于检验有关产生常见大脑振荡（例如阿尔法节律）的大脑来源数量的假设。在第二步中，我们提出了耦合度量的正确经验分布，这对于正确评估耦合结果的重要性是必要的。然而更重要的是，这个校正后的统计量不限于我们的特定度量，而是适用于所有复值耦合估计量。我们说明了这种估计量的经验正态性的非常常见的错误假设如何导致 p 值的系统性低估、多重比较控制程序的崩溃以及假阳性数量的急剧膨胀。