In this paper we explore partial coherence as a tool for evaluating causal influence of one signal sequence on another. In some cases the signal sequence is sampled from a time- or space-series. The key idea is to establish a connection between questions of causality and questions of partial coherence. Once this connection is established, then a scale-invariant partial coherence statistic is used to resolve the question of causality. This coherence statistic is shown to be a likelihood ratio, and its null distribution is shown to be a Wilks Lambda. It may be computed from a composite covariance matrix or from its inverse, the information matrix. Numerical experiments demonstrate the application of partial coherence to the resolution of causality. Importantly, the method is model-free, depending on no generative model for causality.
翻译:在本文中,我们探索部分一致性作为评价一个信号序列对另一个信号序列的因果影响的工具。 在某些情况下, 信号序列取自时间序列或空间序列样本。 关键的想法是建立因果关系问题与部分一致性问题之间的联系。 一旦建立了这种联系, 就会使用一个规模变化中部分一致性统计来解决因果关系问题。 这个一致性统计被证明是一个可能性比率, 其无效分布被显示为 Wilks Lambda 。 它可以从一个复合变量矩阵或从它的反面信息矩阵中计算出来。 数字实验表明对因果关系的解决应用了部分一致性。 重要的是, 这种方法是没有模型的, 取决于没有因果关系的遗传模型 。