Department of Mathematics & Statistics

Hernando Ombao
Department of Statistics
UC Irvine

Modeling Dependence in Multivariate Time Series with Applications to Brain Signals


In this talk, we shall discuss methods for characterizing dependence between components of a multivariate time series (e.g., between brain regions). My own interest in this area stems from a growing body of evidence suggesting that various neurological disorders, including Alzheimer’s disease, depression, and Parkinson’s disease may be associated with altered brain connectivity.

Dependence may be portrayed in a number of ways. This talk will be focused on measures that depict interactions in oscillations between brain regions. First, we shall discuss partial coherence which essentially identifies the frequency bands that drive direct linear association between regions. However, there are computational challenges to estimating this measure under high dimensionality. To overcome this problem, we developed a generalized shrinkage procedure which is a weighted average of a highly structured parametric estimator and a non-parametric estimator (based on mildly smoothed periodograms). Theoretical analysis and simulation studies demonstrate that the generalized shrinkage method has a lower mean-squared error than the standard approaches (Welch’s and multi-taper).

Second, we develop more comprehensive measures of coherence that capture complex dependence structures in brain signals. The classical notion of coherence pertains only to contemporaneous single-frequency interactions between signals. To generalize this notion, we introduce the time-lagged dual-frequency coherence which measures, as a specific example, oscillatory interactions between alpha activity on a current time block at one channel and beta activity on a future time block at another channel. We develop formal methods for statistical inference under the framework of harmonizable processes. This new approach will be applied to analyze an electroencephalographic data set to investigate dependence between the visual, parietal and pre-motor cortices under the context of a visual-motor task.

This is joint work with Mark Fiecas (UCSD) and Cristina Gorrostieta (Brown) and Sofia Olhede (Univ College London).