Collaborative Research: Models and Methods for Nonstationary Behavioral Time Series

行为和生理数据的研究往往是困难的，因为这样的数据通常包括大维度，高分辨率的非平稳时间序列。 因此，对于复杂时间序列数据的统计原则和计算效率的方法的需求越来越大。 该研究项目的重点是开发一套新颖的统计模型和相关方法，用于高维，高分辨率的多变量时间序列。 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（如功能性磁共振成像（fMRI））与行为和神经认知评估数据联系起来。 该项目将开发两种多维时间序列建模方法。 第一种方法将建模的非平稳时间序列的集合通过局部平稳表示，其特征在于在一个随时间变化的谱密度矩阵的过程中的谱动态。 第二种方法包括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评分之间的关系。 将被研究的数据包括来自大脑图像的测量以及来自功能磁共振成像的各个感兴趣区域的时间序列。 还将研究记录的用于监测认知疲劳和工作负荷的行为和生理信号。 尽管该项目的重点是生理和行为数据的分析，但该研究项目中开发的模型和方法非常通用，并且具有影响其他科学领域的潜力，因为高度结构化的多变量时间序列数据通常收集在计量经济学，计量经济学，地球科学和信号处理领域。

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.