Multivariate time series graphical modelling for analysis of brain connectivity in schizophrenia sufferers

头皮上的脑电(EEG)测量可以看作是一个多变量的时间序列，不同的位置对应于不同的序列。通过观察这些序列之间的联系，可以评估大脑的连通性。我们希望确定精神分裂症患者与对照组(非患者)是否有不同的连接模式。时间序列之间的联系可以以图形模型的形式显示，该图形模型以图形方式显示链接的存在或不存在。这些模型的结构可以通过使用所谓的“部分相干性”对多变量时间序列进行频域分析来确定。这项研究试图解决部分相干分析中出现的主要技术问题：非平稳性、频谱矩阵中的零点、虚假的表观相干、可信区间的临界值等。随后，将对大量可用的数据集应用所产生的最佳实践方法，试图在更可靠的图形模型的基础上区分精神分裂症患者和对照组之间的大脑连接。

Electroencephalogram (EEG) measurements on the scalp can be considered as a multivariate time series, with different positions corresponding to different series. Brain connectivity can be assessed by looking at the connections between these series. We wish to determine whether schizophrenia sufferers have different patterns of connectivity to those for controls (non-sufferers). Connections between time series can be displayed in the form of graphical models which show the presence or absence of links graphically. The structure of these models may be determined by frequency domain analysis of the multivariate time series using so-called `partial coherence'. The research seeks to tackle the main technical problems which arise in partial coherence analysis: nonstationarity, zeros in the spectral matrix, spurious apparent coherence, critical values for confidence intervals etc. The resulting `best practice' approach will then be applied to substantial available data sets to try to differentiate brain connectivity between schizophrenia sufferers and controls on the basis of the more reliable graphical models.