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Criteria for Causality: Bradford Hill Criteria - II01:28

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Conditional Granger causality and partitioned Granger causality: differences and similarities.

Sheida Malekpour1, William A Sethares2

  • 1Department of Electrical and Computer Engineering, University of Wisconsin-Madison, 2556 Engineering Hall, 1415 Engineering Dr., Madison, WI, 53706, USA. malekpour2@wisc.edu.

Biological Cybernetics
|October 18, 2015
PubMed
Summary
This summary is machine-generated.

This study clarifies the relationship between conditional Granger causality (cGC) and partitioned Granger causality (pGC) in neural signal analysis. We present matrix equalities simplifying pGC calculation, revealing key differences in parameter dependence and noise residual assumptions.

Keywords:
Conditional Granger causality (cGC)Multivariate autoregressive (MVAR) modelPartitioned Granger causality (pGC)

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Area of Science:

  • Neuroscience
  • Computational Neuroscience
  • Signal Processing

Background:

  • Neural information modeling requires measuring signal interdependencies.
  • Conditional Granger causality (cGC) is a common technique for time series influence analysis.
  • Existing methods like cGC can yield problematic negative values, leading to alternatives such as partitioned Granger causality (pGC).

Purpose of the Study:

  • To clarify the relationship between conditional Granger causality (cGC) and partitioned Granger causality (pGC).
  • To simplify the calculation of pGC using matrix equalities.
  • To highlight the distinct properties and assumptions of cGC and pGC.

Main Methods:

  • Derivation of matrix equalities to simplify pGC calculations.
  • Comparative analysis of cGC and pGC based on simplified expressions.
  • Illustration of mathematical findings with simulations.
  • Application of the measures to electroencephalography (EEG) data.

Main Results:

  • The simplified pGC expression clarifies its differences and similarities with cGC.
  • pGC is shown to depend on a subset of model estimation parameters.
  • Unlike cGC, pGC does not require uncorrelated noise residuals.

Conclusions:

  • The presented matrix equalities offer a clear understanding of pGC and its relationship to cGC.
  • pGC offers an alternative with different underlying assumptions, particularly regarding noise residuals.
  • The findings are validated through simulations and real-world EEG data application.