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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.

MSC:

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)

Software:

FLIRT; fda (R); FMRISTAT
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Full Text: DOI arXiv Euclid

References:

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