Quantile regression in brain imaging data analysis

这项建议有两个目的。从统计学的角度来看，新的分位数回归方法在功能变系数模型（FVCM）和空间变系数模型（SVCM），其中系数效应允许随位置而变化，将被开发用于科普具有遗传异方差性的预处理的成像数据，例如，扩散张量图像（DTI），磁共振图像（MRI）和其他图像。从应用的角度来看，所提出的分位数回归方法在FVCM和SVCM将使神经科学家了解人类大脑（在扩散纤维束，灰质和白色物质方面）是如何受到一些感兴趣的协变量的影响，如性别，年龄和精神障碍（例如自闭症）对角状态。虽然这些方法是由脑成像数据激发的，但是它们也能够分析功能数据、2维（2D）表面和3维（3D）体积数据。特别是，该提案侧重于三个不同但相关的研究主题：（1）分位数回归的FVCM及其在DTI数据分析中的应用;（2）分位数回归的SVCM及其在MRI数据分析中的应用;（3）分位数回归的FVCM和SVCM与纵向响应及其在神经影像数据分析中的应用。这项研究将扩大目前的工作范围，并提供新的统计工具，解决实际问题，不仅从神经科学，但也其他各种学科，如流行病学，环境科学，社会学和生物学。因此，它对统计理论和应用都有潜在的影响。

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.