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

该项目由两个部分组成，每个部分都由功能磁共振成像（fMRI）数据的推理问题驱动。第一部分，在广义泛函线性模型（GFLM）的框架下，以斜率函数的形式介绍了神经血流动力学响应的柔性半参数模型。为了适应不同区域、刺激类型和受试者的大脑活动变化，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功能形状，同时具有受试者特定的高度、峰值时间和宽度。提出了几种基于b样条平滑的快速全脑分析模型参数估计算法。第二部分的研究重点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。第一部分脑血流动力学反应的样条估计被作为回归模型的预测因子，其中反应是个体特征。同时引入两类先验，实现变量选择和聚类的同步进行。功能磁共振成像是了解大脑活动的最有效的神经成像技术之一。近年来，从多学科复杂研究中收集的功能磁共振成像数据已广泛应用于心理和医学研究。本项目将为这类fMRI数据的建模、分析和计算提供工具。该项目的研究成果将促进对先天和后天在形成个体大脑功能和行为差异方面的相互关系的基本理解，并为统计学、神经科学和心理学相结合的跨学科研究提出新的方向。该研究开发的开源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.