Statistical Methods for Spatially Correlated Hierarchical Functional Data

本研究计画旨在建立新的统计模式与方法，以分析阶层式功能资料。特别是研究人员提出了一种新的方法框架，快速和强大的推理工具时，真实的数据生成过程占复杂的相关机制，模仿和代表真实的生物结构。该项目的目标如下。（一）.建立一个新的方法框架，用于分析层次结构中最低层函数相关的单变量层次结构函数数据。理解和量化这些函数之间的依赖结构具有重要的科学意义。（B）。将所发展的方法学推广到多元函数数据的分析。（c）.当功能数据具有自然的层次和空间结构时，提出新的组均值和组均值之间差异的推断方法。现代研究数据变得越来越复杂，提出了非传统建模和推断的挑战。特别是，技术和计算的进步使得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层次函数数据。虽然这项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，将与许多新的数据集相关，其中推断的对象是即使在对测量对象进行调节后仍然依赖的函数或图像。这些数据是在工程和气候建模等方面收集的。与其他已发表的方法相比，这里提出的方法是计算效率高，它的规模以及中等和大的数据集。

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.