Multiscale Bayesian state-space model for Granger causality analysis of brain signal
Modelling time-varying and frequency-specific relationships between two brain signals is becoming an essential methodological tool to answer theoretical questions in experimental neuroscience. In this article, we propose to estimate a frequency Granger causality statistic that may vary
in time in order to evaluate the functional connections between two brain regions during a task. We use for that purpose an adaptive Kalman filter type of estimator of a linear Gaussian vector autoregressive model with coefficients evolving over time. The estimation procedure is achieved through
variational Bayesian approximation and is extended for multiple trials. This Bayesian State Space (BSS) model provides a dynamical Granger-causality statistic that is quite natural. We propose to extend the BSS model to include the à trous Haar decomposition. This wavelet-based
forecasting method is based on a multiscale resolution decomposition of the signal using the redundant à trous wavelet transform and allows us to capture short- and long-range dependencies between signals. Equally importantly it allows us to derive the desired dynamical and frequency-specific
Granger-causality statistic. The application of these models to intracranial local field potential data recorded during a psychological experimental task shows the complex frequency-based cross-talk between amygdala and medial orbito-frontal cortex.
Keywords: multiple trials; neuroscience data; nonstationarity; time–frequency; variational methods; À trous Haar wavelets
Document Type: Research Article
Affiliations: 1: Methodology and Data Analysis Group, Department of Psychology, University of Geneva, Geneva, Switzerland 2: Neuroscience of Emotion and Affective Dynamics Lab, Department of Psychology, University of Geneva, Geneva, Switzerland
Publication date: 02 January 2019
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