Evaluating stationarity via change-point alternatives with applications to fMRI data

TL;DR

This paper develops change-point detection methods for functional data, specifically applied to resting state fMRI data, to assess stationarity and identify nonstationarities in brain activity over time.

Contribution

The paper introduces new statistical methods for detecting change-points in dependent functional data with tensor-structured covariance, applied to large-scale fMRI analysis.

Findings

A significant proportion of subjects show nonstationarity in their fMRI time courses.

Empirical and theoretical analysis of change-point distribution in fMRI data.

Methods enable efficient detection of level shifts in high-dimensional functional data.

Abstract

Functional magnetic resonance imaging (fMRI) is now a well-established technique for studying the brain. However, in many situations, such as when data are acquired in a resting state, it is difficult to know whether the data are truly stationary or if level shifts have occurred. To this end, change-point detection in sequences of functional data is examined where the functional observations are dependent and where the distributions of change-points from multiple subjects are required. Of particular interest is the case where the change-point is an epidemic change---a change occurs and then the observations return to baseline at a later time. The case where the covariance can be decomposed as a tensor product is considered with particular attention to the power analysis for detection. This is of interest in the application to fMRI, where the estimation of a full covariance structure for the three-dimensional image is not computationally feasible. Using the developed methods, a large study of resting state fMRI data is conducted to determine whether the subjects undertaking the resting scan have nonstationarities present in their time courses. It is found that a sizeable proportion of the subjects studied are not stationary. The change-point distribution for those subjects is empirically determined, as well as its theoretical properties examined.