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Paper No. 11-17

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JAD Aston and C Kirch

Estimation of the distribution of change-points with appliction to fMRI data

Date: May 2011

Abstract: 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 is 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 functional magnetic resonance imaging (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 non-stationarities present in their time courses. It is found that a sizeable pro-portion of the subjects studied contain a epidemic change. The change-point distribution for those subjects is empirically determined as well as its theoretical properties examined.

Keywords: At most one change; Epidemic change; Functional time series; multidimensional functional data; Resting state fMRI.