Collaborative Research: Theory and Methods for Massive Nonstationary and Multivariate Spatial Processes

合作研究：大规模非平稳和多元空间过程的理论与方法

• 批准号: 1406622
• 负责人: Soutir Bandyopadhyay
• 金额: $ 16.6万
• 依托单位: Lehigh University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-01 至 2018-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1406622&HistoricalAwards=false
• 关键词: Collaborative; Research; Theory; Methods; Massive

The field of spatial statistics is an expanding subset of statistical science with numerous applications in a wide variety of specialties such as geophysical, environmental, ecological and economic sciences. Modern datasets in these sciences often involve multiple variables observed at thousands to millions of irregularly spaced geographical locations. Associated scientific goals include surface estimation, stochastic simulation and statistical modeling to gain insight of underlying phenomena. Statistical analyses require flexible nonstationary and multivariate constructions, which have heretofore been hampered by a lack of models adequate for datasets of large magnitude. This project addresses this gap in statistical science, developing a unifying framework for nonstationary and multivariate spatial models capable of modeling complex spatial dependencies. Additionally, the justification for the use of nonstationary models is generally relegated to empirical results with data and simulation experiments; this research will develop a companion theory for exploring the relative benefit of these more complex spatial models. Using the tools introduced in this project, the final major goal is to develop a gridded data product for the historical climate of the United States based on large, irregularly spaced observational networks with transparent statistical methodology and formal quantification of the uncertainty in such an analysis. Historical data products such as this are of crucial importance in the fields of atmospheric and climate sciences.Modern spatial statistics has increased focus on developing methods for massive spatial datasets that involve multiple variables with complex dependency structures. This research aims to foster a common framework via multiresolution processes for modeling nonstationary and multivariate spatial structures that does not break down in the face of large sample sizes. Multiresolution processes lend themselves to fast estimation and computation, and also to the linked theoretical questions of asymptotic behavior of spatial estimators. For example, there is a lack of rigorous theoretical treatment of nonstationary approaches, with current understanding limited to experimental results. The companion large sample theory of this research is aimed at identifying situations in which nonstationary models provide tangible benefits over simpler stationary cousins. A linked goal is approximation theory for existing spatial constructions; special multiresolution constructions can approximate existing covariances such as the Matern, allowing for a theoretical treatment of spatial smoothing under these common classes of covariances. Additionally, the project will generalize the notion of a multiresolution process to the multivariate setting, allowing for feasible and flexible inference-based modeling of massive multivariate spatial datasets.

空间统计的领域是统计科学的扩展子集，并在各种专业（例如地球物理，环境，生态和经济科学）中进行了许多应用。 这些科学中的现代数据集通常涉及数千至数百万不规律的地理位置的多个变量。 相关的科学目标包括表面估计，随机模拟和统计建模，以洞悉潜在现象。 统计分析需要灵活的非组织和多元构造，这些构造因缺乏足够大量数据集的模型而受到阻碍。 该项目解决了统计科学中的这一差距，为非机构和多元空间模型开发了一个统一的框架，能够对复杂的空间依赖性进行建模。 此外，使用数据和仿真实验的经验结果通常降级为实证结果。这项研究将开发一种伴随理论，用于探索这些更复杂的空间模型的相对好处。使用该项目中介绍的工具，最终的主要目标是基于具有透明的统计方法论和对这种分析中不确定性的正式量化的大型，不规则间隔的观察网络开发用于美国历史氛围的网格数据产品。 在大气和气候科学领域，诸如此类的历史数据产品至关重要。现代的空间统计量增加了关注开发大量空间数据集的方法，这些数据集涉及具有复杂依赖性结构的多个变量。 这项研究旨在通过多分辨率的过程来促进一个共同的框架，以建模非平稳和多元空间结构，这些空间结构不会在大型样本量面前分解。 多分辨率的过程将自己用于快速估计和计算，还涉及空间估计器的渐近行为的链接理论问题。 例如，缺乏对非组织方法的严格理论处理，而当前的理解仅限于实验结果。 这项研究的大型样本理论旨在确定非组织模型对简单固定堂兄提供切实益处的情况。 链接的目标是现有空间结构的近似理论。特殊的多分辨率结构可以近似现有的协方差，例如母校，从而在这些共同类别的协方差下对空间平滑进行了理论处理。 此外，该项目将将多分辨率过程的概念推广到多元设置，从而可以对大型多元空间数据集的可行且灵活的推理建模。