Hu Meng, Liang Hualou
School of Biomedical Engineering, Science & Health Systems, Drexel University, Philadelphia, PA 19104, USA.
School of Biomedical Engineering, Science & Health Systems, Drexel University, Philadelphia, PA 19104, USA.
Neuroimage. 2014 Oct 15;100:125-34. doi: 10.1016/j.neuroimage.2014.06.013. Epub 2014 Jun 17.
In neuroscience, as in many other fields of science and engineering, it is crucial to assess the causal interactions among multivariate time series. Granger causality has been increasingly used to identify causal influence between time series based on multivariate autoregressive models. Such an approach is based on linear regression framework with implicit Gaussian assumption of model noise residuals having constant variance. As a consequence, this measure cannot detect the cause-effect relationship in high-order moments and nonlinear causality. Here, we propose an effective model-free, copula-based Granger causality measure that can be used to reveal nonlinear and high-order moment causality. We first formulate Granger causality as the log-likelihood ratio in terms of conditional distribution, and then derive an efficient estimation procedure using conditional copula. We use resampling techniques to build a baseline null-hypothesis distribution from which statistical significance can be derived. We perform a series of simulations to investigate the performance of our copula-based Granger causality, and compare its performance against other state-of-the-art techniques. Our method is finally applied to neural field potential time series recorded from visual cortex of a monkey while performing a visual illusion task.
在神经科学领域，与许多其他科学和工程领域一样，评估多元时间序列之间的因果相互作用至关重要。格兰杰因果关系已越来越多地用于基于多元自回归模型来识别时间序列之间的因果影响。这种方法基于线性回归框架，并隐含地假设模型噪声残差具有恒定方差的高斯分布。因此，这种度量无法检测高阶矩和非线性因果关系中的因果效应关系。在此，我们提出了一种有效的基于无模型、copula的格兰杰因果关系度量，可用于揭示非线性和高阶矩因果关系。我们首先将格兰杰因果关系表示为条件分布的对数似然比，然后使用条件copula推导高效的估计程序。我们使用重采样技术构建一个基线零假设分布，从中可以得出统计显著性。我们进行了一系列模拟，以研究基于copula的格兰杰因果关系的性能，并将其性能与其他先进技术进行比较。我们的方法最终应用于猴子视觉皮层在执行视觉错觉任务时记录的神经场电位时间序列。
