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

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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.