Brain connectivity reflects how different regions of the brain interact during performance of a cognitive task. In studying brain signals such as electroencephalograms (EEG), this may be explored via an information-theoretic causal measure, called transfer entropy (TE), which does not impose any distributional assumption on the variables and covers any form of relationship (beyond linear) between them. To improve utility of TE in brain signal analysis, we propose a novel methodology to capture cross-channel information transfer in the frequency domain. Specifically, we introduce a new causal measure, the spectral transfer entropy (STE), to quantify the magnitude and direction of information flow from a certain frequency-band oscillation of a channel to an oscillation of another channel. In contrast with previous works on TE in the frequency domain, we differentiate our work by considering an extreme value perspective that employs the maximum magnitude of filtered series within time blocks. The main advantages of our proposed approach is that it is robust to the inherent problems of linear filtering and allows adjustments for multiple comparisons to control family-wise error rate (FWER). Another novel contribution is a simple yet efficient estimation method based on the combination vine copulas and extreme value theory that enables estimates to capture zero (boundary point) without the need for bias adjustments. With the vine copula representation, a null copula model, which exhibits zero STE, is defined, making significance testing for STE straightforward through a standard resampling approach. Lastly, we illustrate the advantage of our proposed measure through some numerical experiments and provide interesting and novel findings on the analysis of EEG recordings linked to a visual task.

翻译：脑连接性反映了认知任务执行过程中不同脑区之间的交互方式。在研究脑电图等脑信号时，可通过一种不依赖变量分布假设且能涵盖变量间所有形式关系（包括非线性关系）的信息论因果度量——转移熵（TE）来探索这一特性。为提升TE在脑信号分析中的实用性，我们提出了一种新颖方法，用于捕获频域中的跨通道信息传递。具体而言，我们引入了一种新的因果度量——谱转移熵（STE），用于量化某通道特定频段振荡到另一通道振荡的信息流强度与方向。与以往频域TE研究不同，我们的创新之处在于采用极值视角，利用时间块内滤波序列的最大幅值进行分析。该方法的主要优势在于对线性滤波固有问题的鲁棒性，并能通过多重比较校正控制族系错误率（FWER）。另一项创新贡献是提出了一种结合藤蔓Copula与极值理论的简洁高效估计方法，使其在不需偏差校正的情况下即可捕获零值（边界点）。基于藤蔓Copula表示，我们定义了零STE的零Copula模型，从而通过标准重采样方法即可实现STE的显著性检验。最后，通过数值实验验证了所提度量的优势，并在与视觉任务相关的脑电图记录分析中获得了有趣且新颖的发现。