Related Experiment Video
Updated: May 11, 2026

New Framework for Understanding Cross-Brain Coherence in Functional Near-Infrared Spectroscopy (fNIRS) Hyperscanning Studies
Published on: October 6, 2023
Spurious causalities with transfer entropy
1Saratov Branch of V. A. Kotel'nikov Institute of Radio Engineering and Electronics of the Russian Academy of Sciences, 38 Zelyonaya St., Saratov 410019, Russia. smirnovda@yandex.ru
Abstract:
Transfer entropy (TE) seems currently to be the most widely used tool to characterize causal influences in ensembles of complex systems from observed time series. In particular, in an elemental case of two systems, nonzero TEs in both directions are usually interpreted as a sign of a bidirectional coupling. However, one often overlooks that both positive TEs may well be encountered for unidirectionally coupled systems so that a false detection of a causal influence on the basis of a nonzero TE is rather possible. This work highlights typical factors leading to such "spurious couplings": (i) unobserved state variables of the driving system, (ii) low temporal resolution, and (iii) observation errors. All are shown to be particular cases of a general problem: imperfect observations of states of the driving system. Importantly, exact values of TEs, rather than their statistical estimates, are computed here for selected benchmark systems. Conditions for a "spurious" TE to be large and even strongly exceed a "correct" TE are presented and discussed.
Related Concept Videos
Entropy
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
Entropy
Entropy Change in Reversible Processes
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The Entropy as a State Function
Causality in Epidemiology
Propagation of Uncertainty from Random Error