摘要翻译：
我们提出了一种新的度量方法来估计来自复杂系统的多元时间序列中信息流的方向。这种基于相位谱斜率（相位斜率指数）的测度具有在实际物理或生物系统中应用的重要不变性：(a)它对任意独立源的混合严格不敏感；(b)即使相位谱不是线性的，它也能给出有意义的结果；(c)它适当地加权了不同频率的贡献。对一类耦合多变量随机数据的仿真表明，对于真正单向的信息流，在没有附加噪声污染的情况下，我们的测度可以检测到与标准Granger因果关系一样正确的方向。对于独立源的随机混合，Granger因果关系错误地产生高度显著的结果，而我们的测度正确地变成非显著的。将我们的新方法应用于脑电数据（88名闭眼的受试者），揭示了绝大多数受试者中明显清晰的前后信息流，从而有助于更好地理解大脑中的信息处理。
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英文标题：
《Robustly estimating the flow direction of information in complex
  physical systems》
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作者：
Guido Nolte, Andreas Ziehe, Vadim V. Nikulin, Alois Schl\"ogl, Nicole
  Kr\"amer, Tom Brismar, Klaus-Robert M\"uller
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最新提交年份：
2007
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Statistics        统计学
二级分类：Applications        应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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英文摘要：
  We propose a new measure to estimate the direction of information flux in multivariate time series from complex systems. This measure, based on the slope of the phase spectrum (Phase Slope Index) has invariance properties that are important for applications in real physical or biological systems: (a) it is strictly insensitive to mixtures of arbitrary independent sources, (b) it gives meaningful results even if the phase spectrum is not linear, and (c) it properly weights contributions from different frequencies. Simulations of a class of coupled multivariate random data show that for truly unidirectional information flow without additional noise contamination our measure detects the correct direction as good as the standard Granger causality. For random mixtures of independent sources Granger Causality erroneously yields highly significant results whereas our measure correctly becomes non-significant. An application of our novel method to EEG data (88 subjects in eyes-closed condition) reveals a strikingly clear front-to-back information flow in the vast majority of subjects and thus contributes to a better understanding of information processing in the brain.
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PDF链接：
https://arxiv.org/pdf/712.2352