This project focuses on developing novel statistical methods for the analysis of dependent data arising in biomedical applications. Often, frequency patterns in such data contain interpretable scientific information. The main motivating applications in this project include epilepsy-related EEG (electroencephalogram), sleep, and DNA sequence data. In epilepsy research, advance warning of an epileptic seizure based on the analysis of intracranial EEG could minimize injury, and give patients a sense of control in their management of the disease. Simultaneous analysis of multiple channels may lead to more accurate estimates, compared to separate analyses of signals from individual channels. The proposed methodology will also be used to analyze data from the AgeWise study to help understand the connections between self-reported measures of sleep and electrophysiological signals.
This project is focused on adaptive spectral estimation for nonstationary multivariate time series using Bayesian modeling that relies on Markov chain Monte Carlo methods for the estimation. Methods are developed for estimating local spectra of qualitative or quantitative bivariate and trivariate nonstationary time series. The multivariate Whittle approximation is used for approximating local likelihoods corresponding to small segments of the time series. Each approximate local likelihood is a function of the discrete Fourier transform of the segment and the corresponding local spectral matrix. Spectral matrices are expressed as modified Cholesky decompositions, thus allowing estimation that guarantees Hermitian and positive definite matrices. Smoothing splines are used for estimating the elements of the spectral matrices as a function of frequency. Additionally, the proposal develops methodology for the analysis of time series collected along with covariates on multiple subjects, where the goal is to model spectral matrices as a function of both frequency and covariates. The proposed methods are applied to the analysis of intracranial EEG signals from two channels in the brain of an epileptic patient, sleep data on older adults from the AgeWise study, and DNA sequences.
