Collaborative Research: Theory and Methods for Highly Multivariate Spatial Processes with Applications to Climate Data Science

地球物理、环境和生态数据集通常包括在一组不规则地理位置上观察到的许多变量。虽然空间数据集的规模越来越大，但它们的复杂性也在增加，因为许多变量同时被观察、记录、建模或导出。现有的空间统计方法无法处理这种高度多元的数据集；本研究解决了统计科学中的这一空白，旨在建立多元空间模型的新框架。新框架的试验台在气候数据科学领域。对地球系统的理解依赖于耦合的物理模型，这些模型代表了大气、海洋、土地利用、河流、冰川和其他过程的动态演变。这些模型导致了大量的气候模型数据，严重限制了存储资源。此外，统计仿真器越来越普遍，是直接运行复杂物理模型的理想替代方案。压缩和仿真算法的开发和验证需要理解和维护物理变量之间的复杂依赖关系，但当前的工具是单变量或基于成对的。本研究将为气候数据科学应用提供统计指导。本项目侧重于多尺度多变量空间过程的建模框架，并依赖于将图形模型纳入多尺度多变量空间过程表示的新理论。此外，许多多元数据集表现出非高斯行为。这项工作的一个伴随推力是在引入和探索大型多元空间过程的经验似然技术。最后，将提出的模型和估算框架应用于社区大气模型的气候数据集。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Geophysical, environmental and ecological datasets often include many variables observed over a set of irregular geographical locations. While spatial datasets are increasing in size, they are also increasing in complexity with many variables being simultaneously observed, recorded, modeled or derived. Current methods in spatial statistics are unable to cope with such highly multivariate datasets; this research addresses this gap in statistical science, aiming to establish a new framework for multivariate spatial models. The testbed for the new framework is in the field of climate data science. Understanding of the Earth system relies on coupled physical models that represent the dynamic evolution of the atmosphere, ocean, land use, rivers, glaciers and other processes. These models have led to vast amounts of climate model data that severely constrain storage resources. Moreover, statistical emulators are increasingly common and desirable alternatives to running complex physical models directly. Development and validation of compression and emulation algorithms require understanding and maintaining complex dependencies between physical variables, but current tools are univariate or pairwise-based. This research will provide statistical guidance for climate data science applications.This project focuses on a modeling framework for multivariate spatial processes, and relies on new theory incorporating graphical models in multiscale multivariate spatial process representations. Moreover, many multivariate datasets exhibit non-Gaussian behavior. A companion thrust of this work is in introducing and exploring empirical likelihood techniques for large multivariate spatial processes. Finally, the proposed models and estimation frameworks will be applied to a climate dataset from the Community Atmosphere Model.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.