Marco Antonio Pinto-Orellana

arXiv2023

Statistical Inference for Modulation Index in Phase-Amplitude Coupling

Phase-amplitude coupling is a phenomenon observed in several neurological processes, where the phase of one signal modulates the amplitude of another signal with a distinct frequency. The modulation index (MI) is a common technique used to quantify this interaction by assessing the Kullback-Leibler divergence between a uniform distribution and the empirical conditional distribution of amplitudes with respect to the phases of the observed signals. The uniform distribution is an ideal representation that is expected to appear under the absence of coupling. However, it does not reflect the statistical properties of coupling values caused by random chance. In this paper, we propose a statistical framework for evaluating the significance of an observed MI value based on a null hypothesis that a MI value can be entirely explained by chance. Significance is obtained by comparing the value with a reference distribution derived under the null hypothesis of independence (i.e., no coupling) between signals. We derived a closed-form distribution of this null model, resulting in a scaled beta distribution. To validate the efficacy of our proposed framework, we conducted comprehensive Monte Carlo simulations, assessing the significance of MI values under various experimental scenarios, including amplitude modulation, trains of spikes, and sequences of high-frequency oscillations. Furthermore, we corroborated the reliability of our model by comparing its statistical significance thresholds with reported values from other research studies conducted under different experimental settings. Our method offers several advantages such as meta-analysis reliability, simplicity and computational efficiency, as it provides p-values and significance levels without resorting to generating surrogate data through sampling procedures.

stat.ME↗

arXiv2021

SCAU: Modeling spectral causality for multivariate time series with applications to electroencephalograms

Electroencephalograms (EEG) are noninvasive measurement signals of electrical neuronal activity in the brain. One of the current major statistical challenges is formally measuring functional dependency between those complex signals. This paper, proposes the spectral causality model (SCAU), a robust linear model, under a causality paradigm, to reflect inter- and intra-frequency modulation effects that cannot be identifiable using other methods. SCAU inference is conducted with three main steps: (a) signal decomposition into frequency bins, (b) intermediate spectral band mapping, and (c) dependency modeling through frequency-specific autoregressive models (VAR). We apply SCAU to study complex dependencies during visual and lexical fluency tasks (word generation and visual fixation) in 26 participants' EEGs. We compared the connectivity networks estimated using SCAU with respect to a VAR model. SCAU networks show a clear contrast for both stimuli while the magnitude links also denoted a low variance in comparison with the VAR networks. Furthermore, SCAU dependency connections not only were consistent with findings in the neuroscience literature, but it also provided further evidence on the directionality of the spatio-spectral dependencies such as the delta-originated and theta-induced links in the fronto-temporal brain network.

stat.ME↗