CAREER: New Directions in Spatial Statistics

职业：空间统计的新方向

• 批准号: 1254840
• 负责人: Debashis Mondal
• 金额: $ 40万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-07-01 至 2015-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1254840&HistoricalAwards=false
• 关键词: CAREER; New; Directions; Spatial; Statistics

The de Wijs process (also known as the Gaussian free field in statistical physics) is a fundamental spatial process that arises as the scaling limit of lattice based Gaussian Markov random fields and generalizes Brownian motion in two-dimensions. However, at present, there is a wide gap between the theory of Gaussian free field (including the subsequent theory of random fields) in statistical physics and modern probability, and the current practice of spatial statistics via lattice based Gaussian Markov random fields. Thus, there is great need to bridge this gap to develop a principled framework for statistics and inference of spatial models and to pursue novel computations that make such inferences feasible. This project will consider formulating appropriate functionals of the de Wijs process to construct useful random fields and novel matrix-free computations via conjugate gradient and other methods, and will focus on developing new areas of scientific applications. The proposed research will also shed new light on and allow deeper understanding of theoretical and computational issues discussed by many researchers in spatial statistics in the past decades. Novel matrix-free computations will provide further impetus to study parametric bootstrap methods and multi-scale modeling, and to construct a new class of non-Gaussian random fields. The project will contribute to obtaining enhanced scientific understanding in studies of environmental bioassays, arsenic contamination of groundwater and distributions of galaxies. Advances in the field of spatial statistics are important because new statistical methods can be applied to a wide range of scientific questions in fields such as astronomy, agriculture, biomedical imaging, computer vision, climate and environmental studies, epidemiology and geology. The de Wijs process is one fundamental spatial process that generalizes Brownian motion from time to space. Using the de Wijs process as a fundamental building block, this project will develop novel mathematics and derive fast, efficient and large-scale statistical computations so that various scientific questions can be answered in a practical way. This will lead to new developments for the analysis of continuum spatial data and spatial point patterns, and will allow us to obtain enhanced scientific understanding in studies of environmental bioassays, arsenic contamination of groundwater and distributions of galaxies. The statistics and the computations that will be developed in this project will also be particularly relevant for various research problems that arise in environmental or global change, and in health studies. Finally, this project will integrate research and educational activities through the development of new graduate and undergraduate courses and will also provide valuable training and learning opportunities for students at graduate and undergraduate levels.

de Wijs过程（也称为统计物理学中的高斯自由场）是一个基本的空间过程，它是基于晶格的高斯马尔可夫随机场的缩放限制，并在二维中概括了布朗尼运动。然而，目前，统计物理学和现代概率的高斯自由场理论（包括随后的随机场理论）与通过基于晶状体的高斯马尔可夫随机场的当前空间统计的实践之间存在很大差距。因此，迫切需要弥合这一差距，以开发一个原则上的统计框架，以实现空间模型的统计框架，并追求使推断可行的新颖计算。 该项目将考虑制定De Wijs过程的适当功能，以通过共轭梯度和其他方法构建有用的随机字段和新颖的无基质计算，并专注于开发科学应用的新领域。拟议的研究还将为过去几十年来许多研究人员在空间统计方面讨论的理论和计算问题提供新的启示，并更深入地了解理论和计算问题。 新颖的无基质计算将为研究参数引导方法和多尺度建模提供进一步的动力，并构建一类新的非高斯随机场。 该项目将有助于在环境生物测定，地下水的砷污染和星系分布的研究中获得增强的科学理解。空间统计领域的进步很重要，因为可以将新的统计方法应用于天文学，农业，生物医学成像，计算机视觉，气候和环境研究，流行病学和地质学等领域的广泛科学问题。 De Wijs过程是一个基本的空间过程，它可以从时间到太空概括布朗尼运动。 该项目将De Wijs流程作为基本构建块，将开发新颖的数学，并得出快速，高效和大规模的统计计算，以便可以以实用的方式回答各种科学问题。这将为分析连续空间数据和空间点模式的分析带来新的发展，并使我们能够在环境生物测定的研究，地下水的砷污染和星系分布中获得增强的科学理解。 该项目中将开发的统计数据和计算也将与环境或全球变化以及健康研究中出现的各种研究问题特别相关。最后，该项目将通过开发新的研究生和本科课程来整合研究和教育活动，还将为研究生和本科生的学生提供宝贵的培训和学习机会。