CAREER: New Statistical Methods for Massive Spatial, Temporal and Spatial-Temporal Processes

该奖项由2009年美国复苏和再投资法案(公法111-5)资助。降维在降低数据的复杂性方面发挥着至关重要的作用，以便能够成功地提取数据中最有用的信息。现有的降维方法大多是在假设数据相互独立的基础上发展起来的。因此，它们可能效率低下，有时甚至不适合分析通常是自然相关的空间/时间数据。为了填补这一空白，本研究针对三种不同类型的时空过程：空间点过程、重复事件过程和定量空间过程，提出了基于逆回归的降维方法。该项目的具体目标包括：1)开发对单变量和多变量空间点过程进行降维的一般框架和方法；2)将这些方法推广到重复事件过程和定量空间过程的情况。当反应的维度也很高时，将给予特别关注。随着现代数据收集技术的快速发展，特别是随着更准确的全球定位系统和地理信息系统的普及，近年来大规模的空间、时间和时空数据迅速可用。这些数据中有许多是海量和高度复杂的，给数据分析带来了前所未有的挑战。拟议的研究将开发可用于分析此类数据的有效统计工具。PI将与来自不同学科的现场科学家密切合作，应用这些工具来解决推动这项研究的现实问题。这些合作的具体目标包括但不限于：1)增进对热带森林多样性的了解；2)更好地评估空气污染对哮喘儿童的健康影响；3)提供对美国分水岭特征的更准确的空间预测，如流量和通量。该项目的主要教育组成部分包括为研究生和本科生提供跨学科的统计培训，特别是为少数民族学生提供培训，并帮助当地三所高中改进AP统计教学。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).Dimension reduction plays an essential role in reducing the complexity of data so that the most useful information in data can be successfully extracted. Most existing dimension reduction methods are developed under the assumption that the data are independent. Consequently, they may be inefficient and sometimes even inappropriate for analyzing spatial/temporal data which are often naturally correlated. The proposed research intends to fill in this gap by developing inverse regression based dimension reduction methods for data arising from three different types of spatial/temporal processes: spatial point processes, recurrent event processes and quantitative spatial processes. Specific goals of the project include 1) developing general frameworks and methods for conducting dimension reduction for both univariate and multivariate spatial point processes and 2) generalizing these methods to the cases of recurrent event processes and quantitative spatial processes. Special attentions will be given when the dimension of the response is also high. In addition, the PI will also develop computationally efficient analytical tools such as second-order analysis for the modeling of massive recurrent event process data.With the fast development of modern data collection technologies, especially with the increased availability of more accurate Global Positioning System and Geographical Information System, large-scale spatial, temporal and spatial-temporal data have become rapidly available in recent years. Many of these data are massive and highly complex in nature, posing unprecedented challenges to data analysis. The proposed research will develop efficient statistical tools that can be used to analyze such data. The PI will collaborate closely with field scientists from various disciplines to apply these tools to solve real-life problems that have motivated this research. Specific goals of these collaborations includes, but are not limited to, 1) improving the understanding of tropical forestry diversity, 2) better assessing the health effects of air pollution on asthmatic children and 3) providing more accurate spatial predictions of US watershed characteristics such as discharges and fluxes. Key educational components of the project include providing interdisciplinary statistical trainings to students especially minority students at both the graduate and undergraduate levels and helping three local high schools improve their AP Statistics teaching.