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

这个项目由两个部分组成，每个部分的动机都是功能磁共振成像(FMRI)数据的推断问题。在第一部分中，在广义泛函线性模型的框架下，介绍了一种以斜率函数形式表示的神经血流动力学响应的半参数模型。为了适应大脑活动在不同区域、刺激类型和受试者之间的差异，新方法假设对于给定的区域和刺激，斜率函数共享相同但未知的功能形状，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-Spline平滑的全脑分析模型参数快速估计算法。研究的第二部分着重于构建一个新的贝叶斯变量选择框架，以研究个体特征与大脑活动之间的关系。第一部分的脑血流动力学响应的样条化估计被用作回归模型中的预测因子，其中响应是个体特征。为了实现变量的同时选择和聚类，我们联合引入了两种先验知识。FMRI是了解大脑活动的最有效的神经成像技术之一。近年来，从多个受试者的复杂研究中收集的功能磁共振数据被广泛应用于心理学和医学研究。该项目将为这种类型的功能磁共振数据提供建模、分析和计算工具。该项目的发现将促进对在塑造大脑功能和行为的个体差异方面先天和后天之间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。通过这项研究开发的开源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.