  This paper intends to develop tools for characterizing non-linear spectral
dependence between spontaneous brain signals. We use parametric copula models
(both bivariate and vine models) applied on the magnitude of Fourier
coefficients rather than using coherence. The motivation behind this work is an
experiment on rats that studied the impact of stroke on the connectivity
structure (dependence) between local field potentials recorded at various
channels. We address the following major questions. First, we ask whether one
can detect any changepoint in the regime of a brain channel for a given
frequency band based on a difference between the cumulative distribution
functions modeled for each epoch (small window of time). Our proposed approach
is an iterative algorithm which compares each successive bivariate copulas on
all the epochs range, using a bivariate Kolmogorov-Smirnov statistic. Second,
we ask whether stroke can alter the dependence structure of brain signals; and
examine whether changes in dependence are present only in some channels or
generalized across channels. These questions are addressed by comparing
Vine-copulas models fitted for each epoch. We provide the necessary framework
and show the effectiveness of our methods through the results for the local
field potential data analysis of a rat.
