Title: Exact Inference of Causal Relations in Dynamical Systems,
Abstract: From philosophers of ancient times to modern economists, biologists and other
researchers are engaged in revealing causal relations. The most challenging
problem is inferring the type of the causal relationship: whether it is uni- or
bi-directional or only apparent - implied by a hidden common cause only. Modern
technology provides us tools to record data from complex systems such as the
ecosystem of our planet or the human brain, but understanding their functioning
needs detection and distinction of causal relationships of the system
components without interventions. Here we present a new method, which
distinguishes and assigns probabilities to the presence of all the possible
causal relations between two or more time series from dynamical systems. The
new method is validated on synthetic datasets and applied to EEG
(electroencephalographic) data recorded in epileptic patients. Given the
universality of our method, it may find application in many fields of science.