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Directed Spectral Methods

Encyclopedia of Computational Neuroscience

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Definition

Directed spectral measures quantify, in the frequency domain, directed statistical interactions between time-series variables. Most commonly, the various measures are computed based on a (linear) multivariate autoregressive (MVAR) model of the data. The various methods quantify in different ways the strength of interaction terms in the Fourier transform of the MVAR model. While these methods are sometimes referred to as capturing “causal” or “effective” connectivity, they are most properly described as reflecting “directed functional connectivity” (Friston et al. 2013).

Detailed Description

For a multivariate n-channel process X(t) = [X 1(t), X 2(t), …, X n (t)]T (with zero mean), the MVAR model is given by

$$ \boldsymbol{X}(t)={\displaystyle \sum_{k=1}^p{A}_k\cdot \boldsymbol{X}\left(t-k\right)+\boldsymbol{\epsilon} (t)}, $$
(1)

where A k are matrices of regression coefficients, p is the model order, and ϵ(t) are the residuals (Lütkepohl 2007). The coefficients of this...

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Authors and Affiliations

  1. Sackler Centre for Consciousness Science and Department of Informatics, University of Sussex, Brighton, UK

    Adam B. Barrett & Dr. Anil K. Seth

Authors
  1. Adam B. Barrett
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  2. Dr. Anil K. Seth
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Correspondence to Adam B. Barrett .

Editor information

Editors and Affiliations

  1. Atlanta, Georgia, USA

    Dieter Jaeger

  2. Department of Biomedical Engineering, Florida International University, Miami, Florida, USA

    Ranu Jung

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Barrett, A.B., Seth, A.K. (2014). Directed Spectral Methods. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_414-1

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  • DOI: https://doi.org/10.1007/978-1-4614-7320-6_414-1

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Chapter history

  1. Latest

    Directed Spectral Methods
    Published:
    28 July 2020

    DOI: https://doi.org/10.1007/978-1-4614-7320-6_414-2

  2. Original

    Directed Spectral Methods
    Published:
    01 April 2014

    DOI: https://doi.org/10.1007/978-1-4614-7320-6_414-1

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