Naro Daniel, Rummel Christian, Schindler Kaspar, Andrzejak Ralph G
Universitat Pompeu Fabra, Department of Information and Communication Technologies, Barcelona, Spain.
Support Center for Advanced Neuroimaging, University Institute for Diagnostic and Interventional Neuroradiology, Inselspital, Bern University Hospital, University of Bern, Bern, Switzerland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Sep;90(3):032913. doi: 10.1103/PhysRevE.90.032913. Epub 2014 Sep 12.
The rank-based nonlinear predictability score was recently introduced as a test for determinism in point processes. We here adapt this measure to time series sampled from time-continuous flows. We use noisy Lorenz signals to compare this approach against a classical amplitude-based nonlinear prediction error. Both measures show an almost identical robustness against Gaussian white noise. In contrast, when the amplitude distribution of the noise has a narrower central peak and heavier tails than the normal distribution, the rank-based nonlinear predictability score outperforms the amplitude-based nonlinear prediction error. For this type of noise, the nonlinear predictability score has a higher sensitivity for deterministic structure in noisy signals. It also yields a higher statistical power in a surrogate test of the null hypothesis of linear stochastic correlated signals. We show the high relevance of this improved performance in an application to electroencephalographic (EEG) recordings from epilepsy patients. Here the nonlinear predictability score again appears of higher sensitivity to nonrandomness. Importantly, it yields an improved contrast between signals recorded from brain areas where the first ictal EEG signal changes were detected (focal EEG signals) versus signals recorded from brain areas that were not involved at seizure onset (nonfocal EEG signals).
基于秩的非线性可预测性得分最近被引入，作为点过程中确定性的一种检验方法。我们在此将该度量方法应用于从时间连续流中采样得到的时间序列。我们使用有噪声的洛伦兹信号，将这种方法与经典的基于幅度的非线性预测误差进行比较。两种度量方法对高斯白噪声都表现出几乎相同的鲁棒性。相比之下，当噪声的幅度分布具有比正态分布更窄的中心峰值和更重的尾部时，基于秩的非线性可预测性得分优于基于幅度的非线性预测误差。对于这种类型的噪声，非线性可预测性得分对噪声信号中的确定性结构具有更高的灵敏度。在对线性随机相关信号的零假设进行替代检验时，它也具有更高的统计功效。我们在对癫痫患者的脑电图（EEG）记录的应用中展示了这种改进性能的高度相关性。在这里，非线性可预测性得分再次表现出对非随机性更高的灵敏度。重要的是，它在检测到首次发作性脑电图信号变化的脑区（局灶性脑电图信号）记录的信号与发作开始时未涉及的脑区（非局灶性脑电图信号）记录的信号之间产生了更好的对比度。
