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测到的许多变量。虽然空间数据集的规模不断增加，但它们的复杂性也在增加，同时观察，记录，建模或导出许多变量。目前的空间统计方法无法科普这样的高度多元数据集，本研究解决了统计科学中的这一空白，旨在建立一个新的框架，多元空间模型。新框架的试验平台是气候数据科学领域。对地球系统的了解依赖于反映大气、海洋、土地利用、河流、冰川和其他过程动态演变的耦合物理模型。这些模型产生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，并直接运行复杂的物理模型的理想替代品。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，但目前的工具是基于单变量或成对的。该研究将为气候数据科学应用提供统计指导。该项目侧重于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，许多多变量数据集表现出非高斯行为。 这项工作的同伴推力是在介绍和探索经验似然技术的大型多元空间过程。 最后，建议的模型和估算框架将应用于社区大气模型的气候数据集。该奖项反映了NSF的法定使命，并被认为值得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。

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.