Collaborative Research: Models and Methods for Nonstationary Behavioral Time Series

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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.