Quantile regression in brain imaging data analysis

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The objectives of this proposal are twofold. From the statistical perspective, new quantile regression methodologies in functional varying coefficient models (FVCM) and spatial varying coefficient models (SVCM), where coefficient effects are allowed to change with location, will be developed to cope with preprocessed imaging data with inherited heteroscedasticity, such as, diffusional tensor image (DTI), magnetic resonance image (MRI) and other images. From the application perspective, the proposed quantile regression methods in FVCM and SVCM will enable neuroscientists to understand how human brains (in terms of diffusion fiber tracts, gray matter and white matter) are affected by some covariates of interest, such as gender, age and mental disorder (e.g. autism) diagonal status. Although the methods are motivated by brain imaging data, they are also capable of analyzing functional data, 2-dimensional (2D) surface and 3-dimensional (3D) volume data. In particular, the proposal focuses on three different but related research topics: (1) quantile regression in FVCM and its applications in DTI data analysis; (2) quantile regression in SVCM and its applications in MRI data analysis; (3) quantile regression in FVCM and SVCM with longitudinal responses and its applications in neuroimaging data analysis. This research will broaden the scope of current work and provide new statistical tools for solving practical problems arising from not only neuroscience but also other various disciplines such as epidemiology, environmental science, sociology, and biology. Therefore, it has potential impact on both statistical theory and applications.