Assessing the strength of directed influences among neural signals: An approach to noisy data

Linda Sommerlade, Marco Thiel, Malenka Mader, Wolfgang Mader, Jens Timmer, Bettina Platt, Bjoern Schelter*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)
10 Downloads (Pure)


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. (C) 2014 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)47-64
Number of pages18
JournalJournal of Neuroscience Methods
Early online date23 Sept 2014
Publication statusPublished - 15 Jan 2015

Bibliographical note

This work was supported by the German Science Foundation (Ti315/4-2), the German Federal Ministry of Education and Research (BMBF grant 01GQ0420), and the Excellence Initiative of the German Federal and State Governments. B.S. is indebted to the Kosterlitz Centre for the financial support of this research project.


  • Granger-causality
  • Observational noise
  • Statistics
  • Expectation-maximisation algorithm
  • Kalman filter
  • Incomplete data likelihood
  • Analytical covariance matrix
  • Multivariate time-series
  • Granger causality
  • Maximum-likelihood
  • Linear-dependence
  • Information-flow
  • Coherence
  • EEG
  • Feedback
  • Interval
  • Algorithm


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