Collaborative Research: Models and Methods for Nonstationary Behavioral Time Series

行为和生理数据的研究通常是困难的，因为这类数据通常由高维、高分辨率的非平稳时间序列组成。因此，对于复杂的时间序列数据，越来越需要具有统计原理和计算效率的方法。该研究项目致力于为高维、高分辨率的多变量时间序列开发一套连贯的新的统计模型和相关方法。将要开发的统计方法将用于将生理时间序列的非平稳特征，如功能磁共振图像(FMRI)，与行为和神经认知评估数据联系起来。该项目将开发两种建模多维时间序列的方法。第一种方法将通过局部平稳表示来对非平稳时间序列集进行建模，该局部平稳表示将根据时变谱密度矩阵来表征过程的谱动态。第二种方法是通过贝叶斯状态空间模型捕获数据中的动态依赖关系，该模型将能够估计时间序列随时间的一致性。本研究项目中开发的统计模型和方法将用于研究健康个体的生理时间序列与神经认知得分之间的关系。将研究的数据包括从大脑图像得出的测量数据，以及从功能磁共振成像得出的不同感兴趣区域的时间序列。还将研究为监测认知疲劳和工作量而记录的行为和生理信号。尽管这个项目的重点是生理和行为数据的分析，但这个研究项目中开发的模型和方法是非常通用的，并且有可能影响其他科学领域，因为高度结构化的多变量时间序列数据通常是在计量经济学、环境计量学、地球科学和信号处理领域收集的。

The study of behavioral and physiological data often is difficult because such data typically consist of large-dimensional, high-resolution nonstationary time series. Consequently, there is an increasing need for statistically principled and computationally efficient approaches for complex time series data. This research project focuses on the development of a coherent suite of novel statistical models and related methodology for large-dimensional, high-resolution multivariate time series. The statistical methods to be developed will be used to link nonstationary features of physiological time series, such as functional magnetic resonance image (fMRI), to behavioral and neurocognitive assessment data. The project will develop two types of approaches for modeling multi-dimensional time series. The first approach will model the set of nonstationary time series via the locally stationary representation that characterizes the spectral dynamics of the process in terms of a time-varying spectral density matrix. The second approach consists of capturing dynamical dependencies in the data via Bayesian state-space models that will be able to estimate the coherency across the time series over time.The statistical models and methods developed in this research project will be used to study how physiological time series in healthy individuals are related to neurocognitive scores. Data that will be studied include measures derived from brain images as well as time series of various regions of interest derived from fMRI. Behavioral and physiological signals recorded to monitor cognitive fatigue and workload also will be studied. Even though the focus of this project is on the analysis of physiological and behavioral data, the models and methods that will be developed in this research project are very general and have the potential of impacting other scientific fields given that highly structured multivariate time series data often are collected in the areas of econometrics, environmetrics, geosciences, and signal processing.