Chapter 14 - Causality

Abstract

An important question often posed in the analysis of multiple channel records, concerns the causal structure between these channels or their components: that is, does one signal generate another? In neuroscience the underlying question is: does one area in the brain activate others? Ultimately, the answer to this question may help to unravel how neuronal networks function. A practical example of looking for a causal relationship is when an epileptologist examines multichannel recordings of brain electrical activity and attempts to find the seizure onset zone from where epileptic seizures originate. The strategy to find source signals that affect other brain areas is to find the lead or lag between signal pairs; the leading signals are then considered as causing the lagging ones. Cross-correlation, coherence, or their nonlinear equivalents (such as mutual information) can be used to formalize and quantify timing differences between signal pairs in multichannel data sets (Chapter 13). In this chapter we focus on two related techniques to investigate causal structure in multichannel data sets: Granger causality and the directed transfer function (DTF). Granger causality is based on the assumption that signal A causes signal B if the prediction of signal B improves by including knowledge of signal A. The DTF is the equivalent of the Granger causality in the frequency domain.