##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability & Statistics Seminar

## Claudia Kirch

#### Karlsruhe Institute of Technology

## Evaluating Stationarity Via Change-Point Alternatives with Applications to fMRI Data

##### 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 non-stationarities 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. This is joint work with John Aston (Warwick University).

Dimitris Politis

### March 11, 2013

### 11:00 AM

### AP&M 7321

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