New statistical methods for functional and array-valued brain imaging data: joint modelling and statistical machine learning perspectives

这一建议为灵活分析功能/数组价值的脑成像数据开发了新的统计方法，目的是提供一个通用框架，用于通过贝叶斯分层建模及其与统计机器学习方法的集成，利用嵌入在脑成像数据中的有价值信息来解释或预测给定结果。具体地说，提出了以下具体目标：*在目标1中，提出了一类新的用于纵向结果数据的贝叶斯增长混合模型，该模型将函数/数组值的脑成像数据作为预测因子。这一目标的主要目的是利用混合建模来识别未观察到的纵向轨迹模式子组(即潜在类)，并开发一系列函数/张量回归模型来将脑成像数据作为协变量来预测纵向轨迹的潜在类成员。*在AIM 2中，提出了一种统一的贝叶斯建模方法，用于联合分析功能/阵列值的脑成像数据和横断面结果数据。重点是脑成像数据的灵活建模以捕获信息性的潜在数据特征，以及使用提取的潜在特征同时预测结果。*在AIM 3中，AIM 1和AIM 2中的贝叶斯层次模型通过与支持向量机(SVM)学习框架相结合进行了扩展。*虽然所提出的方法创新的动机是在脑成像数据中识别高信息量/预测性特征，但所提出的方法创新广泛适用于许多涉及函数数据和具有复杂空间相关性的数组值数据的不同环境，例如，基因研究。拟议的研究还将促进高素质人员的培训(5名硕士学生、2名博士生和1名博士后研究员)，以分析高维复杂数据。**

This proposal develops novel statistical methodologies for flexible analysis of functional/array-valued brain imaging data, with the aim of providing a general framework for utilizing valuable information embedded in the brain imaging data to explain or predict a given outcome through Bayesian hierarchical modelling and its integration with statistical machine learning methods. In particular, the following specific aims are proposed:****In aim 1, a new class of Bayesian Growth Mixture Models for longitudinal outcome data that accommodate functional/array-valued brain imaging data as predictors is proposed. The main focus of this aim is to utilize mixture modelling to identify unobserved longitudinal trajectory pattern subgroups (i.e., latent classes), and develop a series of functional/tensor regression models to accommodate brain imaging data as covariates to predict the latent class memberships of longitudinal trajectories. ****In aim 2, a unified Bayesian modelling approach to joint analysis of functional/array-valued brain imaging data and cross-sectional outcome data is proposed. The focus is on flexible modelling of brain imaging data to capture informative latent data features, and simultaneous prediction of the outcome using the extracted latent features. ****In aim 3, the Bayesian hierarchical models in Aim 1 and 2 are extended by integrating with the Support Vector Machine (SVM) learning framework.****Although motivated by the problems of identifying highly informative/predictive features in the brain imaging data, the methodological innovations proposed are widely applicable to a number of different contexts that involve functional data and array-valued data with complex spatial correlation, for example, genetic studies. The proposed research will also advance training of highly qualified personnel (5 MSc students, 2 PhD students and 1 postdoc research fellow) to analyze high-dimensional complex data.**