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December 2012 Evaluating stationarity via change-point alternatives with applications to fMRI data
John A. D. Aston, Claudia Kirch
Ann. Appl. Stat. 6(4): 1906-1948 (December 2012). DOI: 10.1214/12-AOAS565

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.

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John A. D. Aston. Claudia Kirch. "Evaluating stationarity via change-point alternatives with applications to fMRI data." Ann. Appl. Stat. 6 (4) 1906 - 1948, December 2012. https://doi.org/10.1214/12-AOAS565

Information

Published: December 2012
First available in Project Euclid: 27 December 2012

zbMATH: 1257.62072
MathSciNet: MR3058688
Digital Object Identifier: 10.1214/12-AOAS565

Keywords: Epidemic change , functional time series , High-dimensional data , resting state fMRI , separable covariance structure , stationarity

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.6 • No. 4 • December 2012
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