Statistical Methods for Spatially Correlated Hierarchical Functional Data

本研究项目旨在为层次功能数据的分析创造新的统计模型和方法。特别是，研究者提出了一种新的方法框架，用于快速和健壮的推理工具，当真实的数据生成过程考虑到模拟和代表真实生物结构的复杂相关机制时。该项目有以下目标。(一)。开发一种新的方法框架，用于分析最低层次上的函数相互关联时的分层单变量函数数据。理解和量化这些功能之间的依赖结构具有重要的科学意义。(b)。将已开发的方法扩展到多变量函数数据的分析。(c)。在功能数据具有自然层次结构和空间结构的情况下，提出新的组均值和组均值差异的推理方法。现代研究数据变得越来越复杂，提出了非传统的建模和推理挑战。特别是，技术和计算的进步使功能数据的记录和处理成为可能。越来越多的科学实验记录了具有复杂依赖结构的分层功能数据。虽然提出的研究的动机是来自结肠癌实验研究的数据，但相关的功能数据出现在许多研究领域。本提案中开发的统计方法是及时和重要的，并且将与许多新数据集相关，其中推断的对象是函数或图像，即使在对其测量的主题进行条件反射后仍然依赖。这些数据是在工程和气候模型等方面收集的。与其他已发表的方法相比，本文提出的方法计算效率高，并且可以很好地扩展到中等和大型数据集。

This research project is to create new statistical models and methods for the analysis of hierarchical functional data. In particular the investigator proposes a novel methodological framework for fast and robust inferential tools when the true data generating process accounts for complex correlation mechanisms that mimic and represent true biological structures. The project has the following aims. (a). To develop a new methodological framework for the analysis of hierarchical univariate functional data when the functions at the lowest level of hierarchy are correlated. Understanding and quantifying the dependence structure between these functions is of scientific importance. (b). To extend the developed methodology to the analysis of multivariate functional data. (c). To propose new inferential methods for group means and differences between group means when functional data have a natural hierarchical and spatial structure.Modern research data have become increasingly complex, raising non-traditional modeling and inferential challenges. In particular, advancements in technology and computation have made recording and processing of functional data possible. An increasing number of scientific experiments record hierarchical functional data with complex dependence structures. Although the proposed research was motivated by data from a colon cancer experimental study, correlated functional data arise in many areas of research. The statistical methods developed in this proposal are timely and important and will be relevant to many new data sets, where the object of inference are functions or images that remain dependent even after conditioning on the subject on which they are measured. Such data are collected in engineering and climate modeling among others. In contrast with other published methods, the methodology proposed here is computationally efficient and it scales well to moderate and large data sets.