The Annals of Applied Statistics

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

John A. D. Aston and Claudia Kirch

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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.

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Ann. Appl. Stat., Volume 6, Number 4 (2012), 1906-1948.

First available in Project Euclid: 27 December 2012

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Epidemic change functional time series high-dimensional data resting state fMRI separable covariance structure stationarity


Aston, John A. D.; Kirch, Claudia. Evaluating stationarity via change-point alternatives with applications to fMRI data. Ann. Appl. Stat. 6 (2012), no. 4, 1906--1948. doi:10.1214/12-AOAS565.

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Supplemental materials

  • Supplementary material: Supplementary material for evaluating stationarity via change-point alternatives with applications to fMRI data. The supplementary material provides added technical details along with the proofs of the results in the paper.