Markov Random Fields, Geostatistics and Matrix-Free Computation

马尔可夫随机场、地统计学和无矩阵计算

• 批准号: 1916448
• 负责人: Debashis Mondal
• 金额: $ 12万
• 依托单位: Oregon State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-09-01 至 2021-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1916448&HistoricalAwards=false
• 关键词: Markov; Random; Fields; Geostatistics; Matrix

In the past few decades, spatial statistics has become increasingly important in agriculture, epidemiology, geology, image analysis and environmental science. PI's prior research provided new perspectives in connecting two major branches of spatial statistics, namely the Markov random fields and geostatistics and in advancing fast statistical computations. At present, many important scientific applications demand use of complex spatial models and their multivariate and spatial-temporal versions. However, statistical computations of these complex spatial models have remained a challenge. The project derives new mathematical understanding on these complex spatial and spatial-temporal models, which then opens up the possibility of advancing various scalable statistical computations with minimal storage. The project will contribute to obtaining enhanced scientific understanding in studies such as arsenic and magnesium contamination and hydro-chemical analysis of groundwater and spatial and spatial temporal variations in opioid overdose cases in the United States.The project brings together mathematical and computational knowledge from different scientific fields to develop principled frameworks for spatial statistics and inference. The research aims to provide new understanding on (i) constructions of higher neighborhood order Gaussian Markov random fields, (ii) joint modeling of two or more spatial variables, and (iii) complex spatial-temporal models. Novel matrix-free computations are proposed to advance statistical inference. These computations include not just best linear unbiased predictions and residual maximum likelihood estimation, but also scalable Hamiltonian Monte Carlo methods. Applications will include mapping (1) heavy metal contamination in groundwater and (2) geographic variations in drug overdose cases across the United States. The project also aims to integrate research and educational activities through developing short courses and case studies on spatial statistics and scalable computation, and through providing valuable training and learning opportunities for graduate students.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

在过去的几十年中，空间统计在农业，流行病学，地质学，图像分析和环境科学方面变得越来越重要。 PI的先前研究提供了连接两个主要统计分支的新观点，即马尔可夫随机领域和地统计学以及进步快速统计计算。 目前，许多重要的科学应用都需要使用复杂的空间模型及其多元和时空版本。但是，这些复杂的空间模型的统计计算仍然是一个挑战。该项目对这些复杂的时空和时空模型产生了新的数学理解，然后开辟了以最小的存储来推进各种可扩展统计计算的可能性。 该项目将有助于在砷和镁污染以及对阿片类药物过量案例的地下水以及空间和空间的时间变化等研究中获得增强的科学理解。该项目在美国，来自不同科学领域的数学和计算知识从不同的科学领域汇总了从不同的科学领域来开发原则上的框架，以开发有原则的框架。该研究旨在对（i）较高邻居阶的高斯马尔可夫随机场的构建，（ii）两个或多个空间变量的联合建模以及（iii）复杂的时空模型。提出了新的无基质计算来提高统计推断。这些计算不仅包括最佳的线性无偏预测和剩余的最大似然估计，还包括可扩展的哈密顿蒙特卡洛方法。应用将包括（1）地下水中的重金属污染以及（2）美国药物过量病例的地理变化。该项目还旨在通过开发有关空间统计和可扩展计算的简短课程和案例研究，并为研究生提供宝贵的培训和学习机会来整合研究和教育活动。该奖项反映了NSF的法定任务，并被视为值得通过基金会的知识分子优点和更广泛影响的评估来审查审查的审查标准。