Collaborative Research: Hierarchical Sparsity-Inducing Gaussian Process Models for Bayesian Inference on Large Spatiotemporal Datasets

随着地理参考和遥感技术(如地理信息系统和全球定位系统)的能力日益增强，可以通过简单的手持设备识别地理坐标，今天各种学科的科学家和研究人员可以前所未有地获得空间参考数据。从识别健康标准的空间差异到更精确的天气预报，地理信息系统技术今天几乎应用于人类生活的各个领域，其有益影响可能是深远的。空间数据的统计建模和分析是利用地理信息系统和相关技术的科学潜力的关键要素。随着科学界进入数据丰富的时代，有前所未有的机会来理解环境生态系统如何运作，以及它们将如何应对不断变化的环境条件。这项研究项目将推进林业、生态学、公共和环境健康、气象学、工程学和地学等多个学科的数据建模。它将有助于发现复杂的科学关系，这反过来将导致更好地分析和理解我们的环境以及我们的生态系统是如何演变的。使用地理信息系统技术的分析人员和研究人员越来越多地面临分析海量空间数据的问题。随着空间和时空数据变得越来越高维--无论是在观测地点的数量方面，还是在每个地点的观测数量方面--科学家们正在寻求假设极其复杂的关系。在过去的十年里，考虑空间关联的统计模型已经成为一个非常活跃的研究领域，尤其是在多个尺度上捕捉变化的分层模型在空间建模中变得非常流行，这并不令人惊讶。这些反过来又导致了相当复杂的模型，即使对于中等大小的数据集，这些模型在计算上也是昂贵的，并且不可行。该项目认识到在大型高维空间和时空数据的统计建模方面增加的计算需求，并提供了一种基于模型的设置，以解决各种数据分析问题。该项目的重点是可在标准计算平台上实施的严格和有原则的统计方法，从而确保非常广泛的研究人员能够使用。该项目概述了一套空间模型，这些模型可以轻松扩展到大规模数据库，并具有广泛的应用范围。将介绍改进现有方法的理论和方法创新，并将使用作为该项目一部分开发的免费分发的开放源码统计软件产品说明其实际影响。

With the increasing capabilities of geographical referencing and remote-sensing technologies such as Geographical Information Systems (GIS) and Global Positioning Systems (GPS) that can identify geographical coordinates with a simple hand-held device, scientists and researchers in a variety of disciplines today have unprecedented access to spatially-referenced data. From identifying spatial disparities in health standards to more precise weather predictions, GIS technology is used today in almost every sphere of human life with beneficial effects that can be far-reaching. Statistical modeling and analysis for spatial data constitute a key element in harnessing the scientific potential of GIS and related technologies. As the scientific community moves into a data-rich era, there is unprecedented opportunity to build an understanding about how environmental ecosystems function and how they will respond to changing environmental conditions. This research project will advance data modeling in disciplines as diverse as forestry, ecology, public and environmental health, meteorology, engineering, and the geosciences. It will help discover complex scientific relationships, which, in turn, will lead to better analysis and understanding of our environment and how our ecosystem is evolving.Analysts and researchers using GIS technology are increasingly faced with analyzing massive amounts of spatial data. With spatial and spatial-temporal 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 extremely complex relationships. Not surprisingly, statistical models accounting for spatial associations have become an enormously active area of research over the last decade and, in particular, hierarchical models capturing variation at multiple scales have become extremely popular for spatial modeling. These, in turn, lead to rather complex models that are computationally expensive and unfeasible even for moderately sized data sets. This project recognizes the increased computational demands in statistical modeling of large high-dimensional spatial and spatial-temporal data and offers a model-based setup to tackle a wide variety of data analytic problems. The emphasis of this project is on rigorous and principled statistical methodology that can be implemented on standard computing platforms, thereby ensuring accessibility for a very wide group of researchers. The project outlines a suite of spatial models that easily scale to massive databases and have a broad range of applications. Theoretical and methodological innovations that enhance current methods will be presented, and their practical implications will be illustrated using freely distributed open-source statistical software products developed as a part of this project.