Neuroimaging time series, such as those which arise from functional magnetic resonance imaging (fMRI), are both high dimensional and contain complex dependencies in both time and space. In particular, in resting state fMRI, the analyses of these dependencies are used to try to infer neural connections. However, it can be fairly easily shown that if there are change points present in the time series, either in mean or covariance structure, then these can very much distort conclusions if they are not taken into account. In this presentation we will examine tests for stationarity of both the mean and the covariance of fMRI time series where each brain scan is treated as a three dimensional function. We will describe various methods to make the problem computationally tractable, and then find both theoretical and empirical methods to determine whether change points are present. These will be used to then make further insights into the dynamic structure of brain connectivity.
[Joint work with Andrew Davison, Claudia Kirch, Davide Pigoli, Christina Stoehr, Shahin Tavakoli, Wenda Zhou]