This project consists of two components, each motivated by the inference problem for functional magnetic resonance imaging (fMRI) data. In the first part, within the framework of generalized functional linear model (GFLM), a flexible semi-parametric model for neural hemodynamic response in the form of slope functions is introduced. To accommodate the variation of brain activity across different regions, stimulus types, and subjects, the new approach assumes the slope functions share the same but unknown functional shape for a given region and stimulus, while having subject-specific height, time to peak, and width. Several fast algorithms based on B-spline smoothing are proposed to estimate the model parameters for whole-brain analysis. The second part of the research focuses on building a novel Bayesian variable selection framework to study the relationship between individual traits and brain activity. The spline estimates of the brain hemodynamic responses from the first part are taken as predictors in a regression model where the response is the individual traits. Two types of priors are introduced jointly to achieve simultaneous variable selection and clustering.
FMRI is one of the most effective neuroimaging technologies for understanding brain activity. In recent years, fMRI data collected from complex studies with multiple subjects have been widely used in psychological and medical research. This project will provide tools for modeling, analysis and computation for this type of fMRI data. Project findings will advance basic understanding of the inter-relations between nature and nurture in shaping individual differences in brain function and behavior, and suggest new directions for interdisciplinary research that combines statistics, neuroscience and psychology. The open source R/Matlab software developed from the research will provide valuable data analysis and educational tools for the scientific community.
