Abstract
Nonparametric methods based on spectral factorization offer well validated tools for estimating spectral measures of causality, called Granger–Geweke Causality (GGC). In Pagnotta et al. (2018) [1] we benchmarked nonparametric GGC methods using EEG data recorded during unilateral whisker stimulations in ten rats; here, we include detailed information about the benchmark dataset. In addition, we provide codes for estimating nonparametric GGC and a simulation framework to evaluate the effects on GGC analyses of potential problems, such as the common reference problem, signal-to-noise ratio (SNR) differences between channels, and the presence of additive noise. We focus on nonparametric methods here, but these issues also affect parametric methods, which can be tested in our framework as well. Our examples allow showing that time reversal testing for GGC (tr-GGC) mitigates the detrimental effects due to SNR imbalance and presence of mixed additive noise, and illustrate that, when using a common reference, tr-GGC unambiguously detects the causal influence׳s dominant spectral component, irrespective of the characteristics of the common reference signal. Finally, one of our simulations provides an example that nonparametric methods can overcome a pitfall associated with the implementation of conditional GGC in traditional parametric methods.
Highlights
Nonparametric methods based on spectral factorization offer well validated tools for estimating spectral measures of causality, called Granger–Geweke Causality (GGC)
In Pagnotta et al (2018) [1] we benchmarked nonparametric GGC methods using EEG data recorded during unilateral whisker stimulations in ten rats; here, we include detailed information about the benchmark dataset
We provide codes for estimating nonparametric GGC and a simulation framework to evaluate the effects on GGC analyses of potential problems, such as the common reference problem, signal-to-noise ratio (SNR) differences between channels, and the presence of additive noise
Summary
The multichannel epicranial SEPs have been previously obtained from ten p21 Wistar rats [2,3]. The field Fs is a scalar that reports the sampling rate in Hz. Whisker-evoked SEPs are characterized by highly dynamic cortical activation pattern, which is initially observable over contralateral primary sensory cortex (cS1), and propagate over known areas, following relatively well known structural pathways [5,6]. Whisker-evoked SEPs are characterized by highly dynamic cortical activation pattern, which is initially observable over contralateral primary sensory cortex (cS1), and propagate over known areas, following relatively well known structural pathways [5,6] The latencies of this propagation are known, thank to studies that employed single-unit responses in cS1, e.g. The initial driving from cS1 is expected at early latency after stimulus onset (5–20 ms), and it should be characterized by dominant spectral components in the gamma-band [8,9,10]
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