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

头皮上的脑电图（EEG）测量可以看作是一个多变量时间序列，不同的位置对应不同的序列。大脑连通性可以通过观察这些序列之间的连接来评估。我们希望确定精神分裂症患者是否与对照组（非患者）具有不同的连接模式。时间序列之间的连接可以以图形模型的形式显示，图形模型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”的多变量时间序列的频域分析来确定。本研究旨在解决部分相干分析中出现的主要技术问题：非平稳性、谱阵零、伪视相干、置信区间临界值等。由此产生的“最佳实践”方法将应用于大量可用的数据集，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.