Pinto Helder, Lazic Ivan, Antonacci Yuri, Pernice Riccardo, Gu Danlei, Barà Chiara, Faes Luca, Rocha Ana Paula
Departamento de Matemática, Faculdade de Ciências, Universidade do Porto, Porto, Portugal.
Centro de Matemática da Universidade do Porto (CMUP), Porto, Portugal.
Front Netw Physiol. 2024 May 21;4:1385421. doi: 10.3389/fnetp.2024.1385421. eCollection 2024.
The increasing availability of time series data depicting the evolution of physical system properties has prompted the development of methods focused on extracting insights into the system behavior over time, discerning whether it stems from deterministic or stochastic dynamical systems. Surrogate data testing plays a crucial role in this process by facilitating robust statistical assessments. This ensures that the observed results are not mere occurrences by chance, but genuinely reflect the inherent characteristics of the underlying system. The initial process involves formulating a null hypothesis, which is tested using surrogate data in cases where assumptions about the underlying distributions are absent. A discriminating statistic is then computed for both the original data and each surrogate data set. Significantly deviating values between the original data and the surrogate data ensemble lead to the rejection of the null hypothesis. In this work, we present various surrogate methods designed to assess specific statistical properties in random processes. Specifically, we introduce methods for evaluating the presence of autodependencies and nonlinear dynamics within individual processes, using Information Storage as a discriminating statistic. Additionally, methods are introduced for detecting coupling and nonlinearities in bivariate processes, employing the Mutual Information Rate for this purpose. The surrogate methods introduced are first tested through simulations involving univariate and bivariate processes exhibiting both linear and nonlinear dynamics. Then, they are applied to physiological time series of Heart Period (RR intervals) and respiratory flow (RESP) variability measured during spontaneous and paced breathing. Simulations demonstrated that the proposed methods effectively identify essential dynamical features of stochastic systems. The real data application showed that paced breathing, at low breathing rate, increases the predictability of the individual dynamics of RR and RESP and dampens nonlinearity in their coupled dynamics.
随着描绘物理系统属性演变的时间序列数据越来越容易获取，促使人们开发了一些方法，旨在深入了解系统随时间的行为，辨别其是源于确定性动力系统还是随机动力系统。替代数据测试在这一过程中起着关键作用，它有助于进行可靠的统计评估。这确保了观察到的结果并非偶然发生，而是真正反映了底层系统的固有特征。初始过程包括提出一个零假设，在缺乏关于底层分布假设的情况下，使用替代数据对其进行检验。然后为原始数据和每个替代数据集计算一个判别统计量。原始数据与替代数据集合之间显著偏离的值会导致零假设被拒绝。在这项工作中，我们提出了各种替代方法，旨在评估随机过程中的特定统计属性。具体而言，我们介绍了使用信息存储作为判别统计量来评估单个过程中自相关性和非线性动力学存在情况的方法。此外，还介绍了为此目的采用互信息率来检测双变量过程中的耦合和非线性的方法。所介绍的替代方法首先通过涉及具有线性和非线性动力学的单变量和双变量过程的模拟进行测试。然后，将它们应用于在自主呼吸和起搏呼吸期间测量的心脏周期（RR 间期）和呼吸流量（RESP）变异性的生理时间序列。模拟表明，所提出的方法有效地识别了随机系统的基本动力学特征。实际数据应用表明，在低呼吸频率下的起搏呼吸增加了 RR 和 RESP 个体动力学的可预测性，并减弱了它们耦合动力学中的非线性。
