Statistical Modelling and Inference for Next-Generation Functional Data

随着现代技术的快速发展，已经或正在进行许多大规模的成像研究，以收集具有海量成像数据的海量数据集，从而推动了对下一代功能数据的研究。这些庞大的影像数据集合包含了有趣的信息和有价值的知识，这提高了对功能数据分析方法的进一步发展的需求。尽管功能数据分析(FDA)近年来得到了广泛的欢迎，但提高下一代FDA的能力仍然是一个长期存在的挑战。这项研究的目标是将最先进的统计建模设备与现代计算和推理技术相结合，开发一套灵活和智能的统计工具，以便能够从下一代功能数据中学习和发现。这项研究中开发的工具的有效性将通过神经成像研究进行测试。所提出的方法和理论也适用于需要对空间和/或时间上收集的图像和其他复杂数据类型进行建模和分析的更广泛的领域，例如地理、环境科学和遥感研究。研究生支助将用于日常研究活动，包括部分理论/方法发展和数据分析。这项研究将丰富从复杂数据对象(高维、相关图像或形状)观察到的功能数据的处理方法，这些数据对象通常出现在成像研究中，例如健康/医学成像或遥感成像。PI旨在解决下一代功能数据分析中的一些具有挑战性的研究问题：(1)创新统计可靠的框架，从大规模纵向成像研究中提取有用信息；(2)开发灵活和智能的统计模型，描述海量成像数据与感兴趣协变量之间的关联，并表征和可视化成像数据的空间变异性；以及(3)开发高效、可扩展的算法和高性能统计软件包，以应对动态成像研究带来的挑战。特别是，拟议的研究涉及四个项目。项目1提供了一种统一的方法来描述成像反应与一组解释变量之间的变化联系。项目2的重点是高维和下一代功能数据之间的接口，以解决大规模成像遗传学研究中的几个基本瓶颈。项目3和4涉及纵向/动态成像研究，将开发一个全面的功能回归框架来分析这些研究的重复功能反应。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

With the rapid growth of modern technology, many large-scale imaging studies have been or are being conducted to collect massive datasets with large volumes of imaging data, thus boosting the investigation of "next-generation functional data". These enormous collections of imaging data contain interesting information and valuable knowledge, which has raised the demand for further advancement in functional data analytic approaches. Although functional data analysis (FDA) has gained widespread popularity in recent years, enhancing the capability of next-generation FDA remains a long-standing challenge. This research targets integrating state-of-the-art statistical modeling devices with modern computational and inferential techniques to develop a set of flexible and intelligent statistical tools to enable learning and discovery from next-generation functional data. The efficacy of the tools developed in this research will be tested by neuroimaging studies. The proposed methods and theory are also applicable to a broader range of fields that require modeling and analysis of images and other complex data types collected over space and/or time, such as geography, environmental science and remote sensing studies. The graduate student support will be used for day-to-day research activities, including parts of the theory/methodology developments and data analysis. This research will enrich the methods for dealing with functional data observed from complex data objects (high-dimensional, correlated images or shapes), which commonly arise in imaging studies, such as, health/medical imaging or remote sensing imaging. The PI aims to address some challenging research problems in analyzing next-generation functional data by: (1) innovating a statistically sound framework to extract useful information from large-scale longitudinal imaging studies; (2) developing flexible and intelligent statistical models to delineate the association between massive imaging data and covariates of interest and to characterize and visualize the spatial variability of the imaging data; and (3) developing efficient, scalable algorithms with high-performance statistical software packages to meet the challenges posed by dynamic imaging studies. In particular, the proposed research involves four projects. Project 1 provides a unifying approach to characterize the varying association between imaging responses with a set of explanatory variables. Project 2 focuses on the interface between high-dimensional and next-generation functional data to address several fundamental bottlenecks in large-scale imaging genetics studies. Projects 3 and 4 deal with longitudinal/dynamic imaging studies, and a comprehensive functional regression framework to analyze repeated functional responses from these studies will be developed.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.