New statistical methods for functional and array-valued brain imaging data: joint modelling and statistical machine learning perspectives

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This proposal develops novel statistical methodologies for flexible analysis of functional/array-valued brain imaging data, with the aim of providing a general framework for utilizing valuable information embedded in the brain imaging data to explain or predict a given outcome through Bayesian hierarchical modelling and its integration with statistical machine learning methods. In particular, the following specific aims are proposed:****In aim 1, a new class of Bayesian Growth Mixture Models for longitudinal outcome data that accommodate functional/array-valued brain imaging data as predictors is proposed. The main focus of this aim is to utilize mixture modelling to identify unobserved longitudinal trajectory pattern subgroups (i.e., latent classes), and develop a series of functional/tensor regression models to accommodate brain imaging data as covariates to predict the latent class memberships of longitudinal trajectories. ****In aim 2, a unified Bayesian modelling approach to joint analysis of functional/array-valued brain imaging data and cross-sectional outcome data is proposed. The focus is on flexible modelling of brain imaging data to capture informative latent data features, and simultaneous prediction of the outcome using the extracted latent features. ****In aim 3, the Bayesian hierarchical models in Aim 1 and 2 are extended by integrating with the Support Vector Machine (SVM) learning framework.****Although motivated by the problems of identifying highly informative/predictive features in the brain imaging data, the methodological innovations proposed are widely applicable to a number of different contexts that involve functional data and array-valued data with complex spatial correlation, for example, genetic studies. The proposed research will also advance training of highly qualified personnel (5 MSc students, 2 PhD students and 1 postdoc research fellow) to analyze high-dimensional complex data.**