Brain connectivity characterizes interactions between different regions of a brain network during resting-state or performance of a cognitive task. In studying brain signals such as electroencephalograms (EEG), one formal approach to investigating connectivity is through an information-theoretic causal measure called transfer entropy (TE). To enhance the functionality of TE in brain signal analysis, we propose a novel methodology that captures cross-channel information transfer in the frequency domain. Specifically, we introduce a new measure, the spectral transfer entropy (STE), to quantify the magnitude and direction of information flow from a band-specific oscillation of one channel to another band-specific oscillation of another channel. The main advantage of our proposed approach is that it formulates TE in a novel way to perform inference on band-specific oscillations while maintaining robustness to the inherent problems associated with filtering. In addition, an advantage of STE is that it allows adjustments for multiple comparisons to control false positive rates. Another novel contribution is a simple yet efficient method for estimating STE using vine copula theory. This method can produce an exact zero estimate of STE (which is the boundary point of the parameter space) without the need for bias adjustments. With the vine copula representation, a null copula model, which exhibits zero STE, is defined, thus enabling straightforward significance testing through standard resampling. Lastly, we demonstrate the advantage of the proposed STE measure through numerical experiments and provide interesting and novel findings on the analysis of EEG data in a visual-memory experiment.

翻译：脑连接性描述了静息态或执行认知任务期间脑网络中不同区域之间的相互作用。在研究脑电图（EEG）等脑信号时，研究连接性的一种形式化方法是通过一种称为转移熵（TE）的信息论因果度量。为增强TE在脑信号分析中的功能，我们提出了一种在频域捕获跨通道信息传递的新方法。具体而言，我们引入了一种新的度量——谱转移熵（STE），用于量化信息流从一个通道的特定频带振荡到另一个通道的特定频带振荡的幅度和方向。我们所提方法的主要优势在于，它以新颖的方式构建TE，从而对特定频带振荡进行推断，同时保持对滤波相关固有问题的鲁棒性。此外，STE的一个优点是允许进行多重比较校正以控制假阳性率。另一个新颖贡献是提出了一种利用藤Copula理论估计STE的简单而高效的方法。该方法能够产生STE的精确零估计（这是参数空间的边界点），而无需进行偏差调整。通过藤Copula表示，定义了一个呈现零STE的零Copula模型，从而可通过标准重采样进行直接的显著性检验。最后，我们通过数值实验证明了所提出的STE度量的优势，并在视觉记忆实验的EEG数据分析中提供了新颖且有趣的发现。