Networks for multivariate time series

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This program focuses on the development of novel statistical methods for high dimensional time series data with a particular emphasis on the application of these methods to data from neuroimaging. The analysis of time series data has been of interest to statisticians for many decades. Traditionally, researchers examined problems relating to one time series and eventually to multiple time series. In this program, we concentrate on specific problems in high dimensional time series analysis. Firstly, we consider creating original statistical methodology for classes of processes that can experience changes in their generating mechanism over the time course of observation. These processes are important as they allow for the modelling of the evolution of an observable quantity, and enable the quantification of this evolution explicitly. Secondly, we propose new methods for testing networks between groups of subject specific time series and also for estimating and testing longitudinal networks from groups of subject specific time series. Thirdly, we introduce novel methods that classify networks from subject specific multivariate time series into groups that correspond to discrete events (such as presence of disease). Finally, we are interested in developing statistical methodology that evaluate how the network structure relate to a set of behaviors. ******The work proposed in this program is fundamental research in statistics, but it also directly impacts other areas such as engineering, economics and the natural sciences. Statistics also has an additional impact on society through collaborations and users of developed technologies, such as computer software. In short, statistics is how we make sense of information, and the world around us. The methods created in this program have a broad range of applicability due to the ubiquity of high dimensional time series in many applications. This increases the potential for impact. A number of the proposed collaborations in this project will ensure that the methodological developments will connect to end-users and that the results will be of direct practical utility and of importance to society. In particular, as the people of Canada and other countries across the world live longer lives, the number of brain disorders such as Alzheimer's disease is certain to rise dramatically. Resting state functional magnetic resonance imaging (fMRI) is a popular tool to study neurological disorders and the development of nonstationary statistical methods will significantly contribute to the understanding of these disorders and the possible identification of biomarkers. In addition, testing group differences in baseline networks and network aging effects for longitudinal data is very important in order to understand brain function and to identify possible biomarkers for disease. This research will eventually impact clinical practice through my collaborations.