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.

翻译：相位-振幅耦合是多种神经过程中观察到的现象，其中一个信号的相位调节另一个不同频率信号的振幅。调制指数（MI）是一种常用技术，通过评估均匀分布与观测信号相位相关振幅的经验条件分布之间的库尔贝克-莱布勒散度来量化这种相互作用。均匀分布是理想表征，预期在无耦合状态下出现，但它并不反映由随机因素导致的耦合值的统计特性。本文提出一种统计框架，用于评估观测MI值的显著性，其基于零假设：MI值完全可由偶然因素解释。通过将MI值与在信号间独立性（即无耦合）零假设下推导的参考分布进行比较，获得显著性水平。我们推导出该零模型的闭式分布，得到缩放贝塔分布。为验证所提框架的有效性，我们开展了全面的蒙特卡洛模拟，评估了多种实验场景（包括振幅调制、尖峰序列和高频振荡序列）下MI值的显著性。此外，通过将统计显著性阈值与其他研究在不同实验条件下报告的结果进行比较，验证了模型的可靠性。我们的方法无需通过采样过程生成替代数据即可提供p值和显著性水平，具有元分析可靠性、简单性和计算效率高等优势。