减少因果关系测量的偏差
Reducing the Bias of Causality Measures
摘要：
两个时间序列之间的相互依赖的方向和强度的措施进行评估和修改，以减少在估计的措施的偏差，使他们给零值时，没有因果关系的影响。为此，采用如在替代数据的帧中所使用的点重排。这种校正并不特定于特定的测量，并且在此基于状态空间重构和信息测量来实现。的因果关系的措施和它们的修改的性能进行评估，对模拟的非耦合和耦合的动力系统，并为不同的设置嵌入维数，时间序列长度和噪声水平。修正后的措施，特别是建议的修正传递熵，原来稳定在零水平的因果关系的情况下，并正确地检测信息流的方向时，它是存在的。这些措施也评估脑电图（EEG）的癫痫患者的大脑中的信息流的检测。EEG的措施的性能进行解释，鉴于从模拟研究的结果。
英文摘要：
Measures of the direction and strength of the interdependence between two time series are evaluated and modified in order to reduce the bias in the estimation of the measures, so that they give zero values when there is no causal effect. For this, point shuffling is employed as used in the frame of surrogate data. This correction is not specific to a particular measure and it is implemented here on measures based on state space reconstruction and information measures. The performance of the causality measures and their modifications is evaluated on simulated uncoupled and coupled dynamical systems and for different settings of embedding dimension, time series length and noise level. The corrected measures, and particularly the suggested corrected transfer entropy, turn out to stabilize at the zero level in the absence of causal effect and detect correctly the direction of information flow when it is present. The measures are also evaluated on electroencephalograms (EEG) for the detection of the information flow in the brain of an epileptic patient. The performance of the measures on EEG is interpreted, in view of the results from the simulation study.
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