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Updated: Apr 23, 2026
Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms
Published on: November 1, 2019
Assessing the strength of directed influences among neural signals: an approach to noisy data
Linda Sommerlade1, Marco Thiel2, Malenka Mader3
1Institute for Complex Systems and Mathematical Biology, University of Aberdeen, King's College, Old Aberdeen AB24 3UE, United Kingdom; Institute for Pure and Applied Mathematics, University of Aberdeen, King's College, Old Aberdeen AB24 3UE, United Kingdom; Freiburg Center for Data Analysis and Modeling (FDM), University of Freiburg, Eckerstrasse 1, 79104 Freiburg, Germany; Institute for Physics, University of Freiburg, Hermann-Herder-Strasse 3a, 79104 Freiburg, Germany; Freiburg Institute for Advanced Studies (FRIAS), University of Freiburg, Albertstrasse 19, 79104 Freiburg, Germany.
Background:
Measurements in the neurosciences are afflicted with observational noise. Granger-causality inference typically does not take this effect into account. We demonstrate that this leads to false positives conclusions and spurious causalities.
New Method:
State space modelling provides a convenient framework to obtain reliable estimates for Granger-causality. Despite its previous application in several studies, the analytical derivation of the statistics for parameter estimation in the state space model was missing. This prevented a rigorous evaluation of the results.
Results:
In this manuscript we derive the statistics for parameter estimation in the state space model. We demonstrate in an extensive simulation study that our novel approach outperforms standard approaches and avoids false positive conclusions about Granger-causality.
Comparison With Existing Methods:
In comparison with the naive application of Granger-causality inference, we demonstrate the superiority of our novel approach. The wide-spread applicability of our procedure provides a statistical framework for future studies. The application to mice electroencephalogram data demonstrates the immediate applicability of our approach.
Conclusions:
The analytical derivation of the statistics presented in this manuscript enables a rigorous evaluation of the results of Granger causal network inference. It is noteworthy that the statistics can be readily applied to various measures for Granger causality and other approaches that are based on vector autoregressive models.
