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

本提案开发了新的统计方法，用于灵活分析功能/数组值脑成像数据，目的是提供一个通用框架，利用嵌入在脑成像数据中的有价值信息，通过贝叶斯分层建模及其与统计机器学习方法的集成来解释或预测给定的结果。特别地，提出了以下具体目标：****在目标1中，提出了一类新的贝叶斯增长混合模型，用于纵向结果数据，以适应功能/数组值脑成像数据作为预测因子。该目标的主要重点是利用混合建模来识别未观察到的纵向轨迹模式亚组（即潜在类别），并开发一系列功能/张量回归模型，以容纳脑成像数据作为协变量来预测纵向轨迹的潜在类别隶属度。****在目标2中，提出了一种统一的贝叶斯建模方法来联合分析功能/阵列值脑成像数据和横截面结果数据。重点是对脑成像数据进行灵活建模，以捕获信息丰富的潜在数据特征，并使用提取的潜在特征同时预测结果。****在aim 3中，通过与支持向量机（SVM）学习框架集成，扩展了aim 1和aim 2中的贝叶斯层次模型。****虽然是由在脑成像数据中识别高信息量/预测性特征的问题所激发的，但所提出的方法创新广泛适用于涉及功能数据和具有复杂空间相关性的数组值数据的许多不同背景，例如，遗传研究。该研究还将促进高素质人才（5名硕士研究生，2名博士研究生和1名博士后）的培养，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.**