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Modeling non-linear spectral domain dependence using copulas with applications to rat local field potentials

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  • Fontaine, Charles
  • Frostig, Ron D.
  • Ombao, Hernando

Abstract

Tools for characterizing non-linear spectral dependence between spontaneous brain signals are developed, based on the use of parametric copula models (both bivariate and vine models) applied on the magnitude of Fourier coefficients rather than using coherence. The motivation is an experiment on rats that studied the impact of stroke on the connectivity structure (dependence) between local field potentials recorded by various microelectrodes. The following major questions are addressed. The first is to determine changepoints in the regime within a microelectrode for a given frequency band based on a difference between the cumulative distribution functions modeled for each epoch (small window of time). The proposed approach is an iterative algorithm which compares each successive bivariate copulas on all the epochs range, using a bivariate Kolmogorov–Smirnov statistic. The second is to determine if such changes are present only in some microelectrodes versus generalized across the entire network. These issues are addressed by comparing Vine-copulas models fitted for each epoch. The necessary framework is provided and the effectiveness of the methods is shown through the results for the local field potential data analysis of a rat.

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  • Fontaine, Charles & Frostig, Ron D. & Ombao, Hernando, 2020. "Modeling non-linear spectral domain dependence using copulas with applications to rat local field potentials," Econometrics and Statistics, Elsevier, vol. 15(C), pages 85-103.
    • Handle: RePEc:eee:ecosta:v:15:y:2020:i:c:p:85-103
    DOI: 10.1016/j.ecosta.2019.06.003
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    1. Granados-Garcia, Guilllermo & Fiecas, Mark & Babak, Shahbaba & Fortin, Norbert J. & Ombao, Hernando, 2022. "Brain waves analysis via a non-parametric Bayesian mixture of autoregressive kernels," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).

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