Complete Inference of Causal Relations between Dynamical Systems

From ancient philosophers to modern economists, biologists, and other researchers, there has been a continuous effort to unveil causal relations. The most formidable challenge lies in deducing the nature of the causal relationship: whether it is unidirectional, bidirectional, or merely apparent - implied by an unobserved common cause. While modern technology equips us with tools to collect data from intricate systems such as the planet's ecosystem or the human brain, comprehending their functioning requires the identification and differentiation of causal relationships among the components, all without external interventions. In this context, we introduce a novel method capable of distinguishing and assigning probabilities to the presence of all potential causal relations between two or more time series within dynamical systems. The efficacy of this method is verified using synthetic datasets and applied to EEG (electroencephalographic) data recorded from epileptic patients. Given the universal applicability of our method, it holds promise for diverse scientific fields.