Wang Xue, Chen Yonghong, Bressler Steven L, Ding Mingzhou
J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, 121 BME Building, Gainesville, FL 32611, USA.
Int J Neural Syst. 2007 Apr;17(2):71-8. doi: 10.1142/S0129065707000944.
Granger causality is becoming an important tool for determining causal relations between neurobiological time series. For multivariate data, there is often the need to examine causal relations between two blocks of time series, where each block could represent a brain region of interest. Two alternative methods are available. In the pairwise method, bivariate autoregressive models are fit to all pairwise combinations involving one time series from the first block and one from the second. The total Granger causality between the two blocks is then derived by summing pairwise causality values from each of these models. This approach is intuitive but computationally cumbersome. Theoretically, a more concise method can be derived, which we term the blockwise Granger causality method. In this method, a single multivariate model is fit to all the time series, and the causality between the two blocks is then computed from this model. We compare these two methods by applying them to cortical local field potential recordings from monkeys performing a sensorimotor task. The obtained results demonstrate consistency between the two methods and point to the significance potential of utilizing Granger causality analysis in understanding coupled neural systems.
格兰杰因果关系正在成为确定神经生物学时间序列之间因果关系的重要工具。对于多变量数据，通常需要检验两个时间序列块之间的因果关系，其中每个块可以代表一个感兴趣的脑区。有两种替代方法。在成对方法中，将双变量自回归模型拟合到所有涉及第一个块中的一个时间序列和第二个块中的一个时间序列的成对组合。然后通过对这些模型中的每一个的成对因果关系值求和来得出两个块之间的总格兰杰因果关系。这种方法直观但计算繁琐。从理论上讲，可以推导出一种更简洁的方法，我们称之为逐块格兰杰因果关系方法。在这种方法中，将单个多变量模型拟合到所有时间序列，然后从该模型计算两个块之间的因果关系。我们通过将这两种方法应用于执行感觉运动任务的猴子的皮质局部场电位记录来比较它们。获得的结果表明这两种方法之间具有一致性，并指出了利用格兰杰因果关系分析理解耦合神经系统的潜在重要性。
