A Statistical Framework for the Spectral Analysis of High-Dimensional Physiological Time Series Signals

摘要 许多研究人员记录了一段时间内的生理信号。这些信号包含动态信息 关于重要的生物过程，更深入地了解这些过程对于推进预防至关重要， 疾病的诊断和治疗。生理时间序列信号的复杂性，这是内在的- 非平稳的，生物学的兴趣往往在于振荡模式，提出了挑战，他们的 分析.这些挑战在现代研究中加剧，研究人员经常记录大量 信号同时。考虑到交叉信号关系的这种数据的同时分析是 这对于全面了解复杂的生物学途径至关重要。研究人员的能力， 由于缺乏正式的统计方法，充分利用这些数据中的信息目前受到阻碍 用于现代研究设计下高维非平稳时间序列的谱分析。广大 本研究的目标是开发一个框架的可扩展方法的自适应频谱分析的非， 平稳高维时间序列该框架将引入一种新的谱域因子结构 以克服数据的高维性，并将在贝叶斯框架中制定， 适应数据的动态变化。具体目标将在这个框架内建立三个方面：（1）估计 和推断的高维时变功率谱，（2）分析之间的关联， 多维时变功率谱和生物协变量，以及（3）使用高维时变 光谱来预测未来的事件对于每个方面，我们将制定一个新的模型，并探索其属性， 使用高级蒙特卡罗技术创建用于估计和推断的抽样方案，开发用户 友好的软件，并比较经验的性能，现有的方法在模拟和验证 问题研究该框架将用于分析来自三项研究的数据：一项关于信号的观察性研究， 在重症监护患者的全身生理系统中选择，一项夜间高密度EEG研究， 对调节运动的生理系统的研究。

Abstract A wide range of researchers record physiological signals over time. These signals contain dynamic information about important biological processes, a deeper understanding of which is essential for advancing preventions, diagnoses and treatments of disease. The complex nature of physiological time series signals, which are inher- ently nonstationary and where biological interest often lies in oscillatory patterns, presents challenges for their analysis. These challenges are exacerbated in modern studies, where researchers often record a large number of signals simultaneously. Simultaneous analyses of such data that take into account cross-signal relations is essential to obtaining a comprehensive understanding of complex biological pathways. Researchers' ability to fully utilize the information contained in these data is currently hindered by a dearth of formal statistical methods for the spectral analysis of high-dimensional nonstationary time series under modern study designs. The broad goal of this research is to develop a framework of scalable methods for the adaptive spectral analysis of non- stationary high-dimensional time series. The framework will introduce a novel spectral domain factor structure to overcome the high-dimensionality of the data and will be formulated in a Bayesian framework that can flexibly adapt to the dynamics of the data. Specific aims will establish three aspects within this framework: (1) estimation and inference for a high-dimensional time-varying power spectrum, (2) analysis of associations between high- dimensional time-varying power spectra and biological covariates, and (3) using high-dimensional time-varying spectra to predict future events. For each aspect, we will formulate a novel model and explore its properties, create a sampling scheme for estimation and inference using advanced Monte Carlo techniques, develop user friendly software, and compare empirical performance to that of existing approaches in simulation and validation studies. The framework will be used to analyze data from three studies: an observational study of signals col- lected across systemic physiological systems in critical care patients, a study of nocturnal high-density EEG, and a study of physiological systems involved in regulating locomotion.