Collaborative Research: Statistical Modeling and Inference for High-dimensional Multi-Subject Neuroimaging Data

该项目由两个部分组成，每个部分的动机是功能性磁共振成像（fMRI）数据的推理问题。第一部分在广义泛函线性模型（GFLM）的框架下，提出了一种以斜率函数形式表示的神经血流动力学反应的半参数模型。为了适应不同区域、刺激类型和受试者之间大脑活动的变化，新方法假设斜率函数对于给定区域和刺激具有相同但未知的函数形状，同时具有受试者特定的高度、达到峰值的时间和宽度。 提出了几种基于B样条平滑的全脑分析模型参数快速估计算法。研究的第二部分主要是建立一个新的贝叶斯变量选择框架来研究个体特征与大脑活动之间的关系。从第一部分的脑血流动力学响应的样条估计被视为回归模型中的预测因子，其中响应是个体特征。通过联合引入两种先验信息，实现了变量选择和聚类的同时进行。近年来，从多个受试者的复杂研究中收集的fMRI数据已被广泛应用于心理学和医学研究。本计画将提供这类功能性磁振造影资料的建模、分析与计算工具。项目研究结果将促进对先天和后天之间在塑造大脑功能和行为的个体差异方面的相互关系的基本理解，并为结合统计学，神经科学和心理学的跨学科研究提出新的方向。从研究中开发的开源R/Matlab软件将为科学界提供有价值的数据分析和教育工具。

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.