Direct or Indirect? Graphical Models for Neural Oscillators

Up to now, time series analysis techniques like synchronization analysis or coherence analysis are mostly applied to bivariate data sets. If more than two signals are available, investigations based on pairwise combinations are still the most favored procedure. However, multivariate data contain more information than those inferable from multiple bivariate examinations. Direct as well as indirect influences may lead to significant inter-relations between signals. A methodology that is able to distinguish between spurious and non-spurious influences will yield deeper insights into underlying physiology. Furthermore, in many cases, detections of causal influences are hardly possible by, for example, coherence analysis. Graphical models are a rather general concept to graphically visualize multivariate systems. Graphical models applying partial coherence are a methodology to decide whether significantly coherent signals are directly linked or not. In multivariate data spurious links could thus be detected. Abilities as well as limitations will be discussed on the basis of neural oscillators. Recent extensions for graphical models in application to partial directed coherence allowing us to determine causal dependencies will be presented. In specific cases time lags can be estimated through this procedure.