Hierarchical models for Large Geostatistical Datasets with Application

这项建议为对大量地点提供的以点为基准的高维空间数据进行统计推断制定了一个全面的框架。该提案的重点是方法论，而不是纯粹的理论或纯粹的应用。因此，统计理论被用来开发数学形式但在计算上可行的方法，这些方法可以有广泛的应用范围。理论推导和新的结果，将加强当前的方法(包括PI在以前的NSF资助的研究中的发现)将被探索，但始终牢记执业的空间分析员。其基本框架是使用通过将原始过程投影到较低维子空间而获得的低等级空间过程。PI旨在探索低阶空间过程关于不同度量的逼近性质。PI的长期目标是开发一整套统计方法，在林业、生态学和更广泛的环境科学领域的各种实验中估计空间模型。所提出的方法与现有方法不同的一个反复出现的基本主题是，建模者不需要牺牲建模的丰富性来折衷大数据集。这解决了统计学上的讽刺，即大数据集正是可以有效检测复杂关系的地方。现代空间技术，如地理信息系统(GIS)和全球定位系统(GPS)，通常使用简单的手持设备来识别地理坐标。因此，今天不同学科的科学家和研究人员可以前所未有地访问地理编码数据。随着数据在观测地点的数量和每个地点的观测数量方面变得越来越高维，科学家们正在寻求假设复杂的关系。反过来，这些又会产生相当复杂的分层模型，即使对于中等大小的数据集，这些模型的计算成本也很高。该团队认识到对大型多变量空间数据进行统计建模的必要性，并提出了一种基于模型的设置来处理各种各样的大型地质统计数据集。虽然一些更严肃的统计建模将需要多处理器能力，但本项目的重点是使用中等功能的计算工具可实现的方法。因此，拟议的方法将为大量研究人员所用。通过将这项研究的结果与公认的地理信息系统对人类社会的影响联系起来，可以最好地评估拟议方法的更广泛影响。从识别健康标准的空间差异到更精确的天气预测，地理信息系统技术今天几乎应用于社会的每个领域，拟议的方法可以在潜在触及社会意外角落的环境研究中产生深远的有益影响。

This proposal lays down a comprehensive framework for carrying out statistical inference on point-referenced high-dimensional spatial data available from a large number of locations. The focus of the proposal is methodological rather than purely theoretical or purely applied. Thus, statistical theory is used to develop mathematically formal but computationally feasible methods that can have a broad range of applications. Theoretical derivations and new results that will enhance current methods (including findings by the PI in prior NSF-funded research) will be explored, but always keeping in mind the practicing spatial analyst. The basic framework is to use a low-rank spatial process obtained by projecting the original process onto a lower-dimensional subspace. The PI intends to explore approximation properties of the low rank spatial process with regard to different metrics. The long-term goal of the PI is to develop a full suite of statistical methods that estimate spatial models in a wide variety of experiments in forestry, ecology and the broader environmental sciences. A recurrent underlying theme of the proposed methods that makes it different from existing methods is that the modeler does not need to sacrifice richness in modeling as a compromise for the large datasets. This resolves the statistical irony that large datasets are precisely where complex relationships can be detected effectively.Modern spatial technologies such as Geographical Information Systems (GIS) and Global Positioning Systems (GPS) routinely identify geographical coordinates with a simple hand-held device. Consequently, scientists and researchers in a variety of disciplines today have access to geocoded data as never before. With data becoming increasingly high-dimensional both in terms of number of observed locations and the number of observations per location, scientists are seeking to hypothesize complex relationships. These, in turn, yield rather complex hierarchical models that are computationally expensive even for moderately sized datasets. This team recognises a need for statistical modeling of large multivariate spatial data and proposes a model-based setup to tackle a wide variety of large geostatistical datasets. Although some of the more serious statistical modeling will require multi-processor capabilities, the emphasis on this project is on methodology implementable with moderately powerful computing tools. The proposed methodologies would, therefore, be accessible to a large number of researchers. The broader impact of the proposed methods is best assessed by connecting the outcome of this research with the widely recognized impact of GIS on human society. From identifying spatial disparities in health standards to more precise weather predictions, GIS technology is used today in almost every sphere of society and the proposed methods can have far reaching beneficial effects in environmental research that potentially touch unexpected corners of society.