Evaluating stationarity via change-point alternatives with applications to fMRI data. (English) Zbl 1257.62072

Summary: 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 applications 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.


62H35 Image analysis in multivariate analysis
92C55 Biomedical imaging and signal processing
92C20 Neural biology
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)


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