Modeling Multivariate and Space-Time Processes: Foundations and Innovations

多元和时空过程建模：基础和创新

• 批准号: 2348154
• 负责人: Pulong Ma
• 金额: $ 19.56万
• 依托单位: Iowa State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-10-01 至 2026-09-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2348154&HistoricalAwards=false
• 关键词: Modeling; Multivariate; Space; Time; Processes

Geophysical processes for temperature and pressure are often highly correlated and are evolving in space over time with complex structures. For instance, many atmospheric processes such as turbulent processes can exhibit long-range dependence with correlation decays slowly as distance increases. While existing covariance models are successful in describing the smoothness behavior of these processes, the correlation in these models often decays exponentially fast and hence is inadequate. The data resulting from many geophysical processes are often continuously indexed and exhibit complicated dependence structures in many disciplines, including geophysics, ecology, environmental and climate sciences, engineering, public health, economics, political sciences, and business science. This project will develop new multivariate and space-time covariance functions with their theoretical properties to characterize complex behaviors such as long-range dependence and asymmetry and develop robust estimation procedures for estimating smoothness behaviors and long-range dependence. The project will also develop and distribute user-friendly open-source software, facilitate its broad adoption for complex data analytical problems, and provide training opportunities for next-generation statisticians and data scientists. This project is jointly funded by the Statistics Program and the Established Program to Stimulate Competitive Research (EPSCoR). This project will develop theoretical foundations and statistical models for inferring multivariate and space-time processes with long-range dependence using a model-based framework. This framework integrates and extends powerful techniques arising in the literature on scale-mixture modeling and objective Bayes. A scale-mixture technique is used to construct new multivariate and space-time covariance functions and offers flexible properties including arbitrary smoothness, long-range dependence, and asymmetry. Theoretical foundation will be provided to study the practical usefulness of the resultant covariances in a principled and unified manner in terms of several properties such as origin/tail behaviors and screening effect and offer theoretical insights on prediction accuracy in both interpolative and extrapolative settings. Objective Bayes inference is used to enable robust parameter estimation for Gaussian processes under the confluent hypergeometric covariance function with the reference prior in which the smoothness and tail-decay parameters are allowed to be estimated. The developed statistical theory and inferential tools will provide new foundations for modeling multivariate and space-time processes in spatial statistics and related areas that use covariance models.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.

温度和压力的地球物理过程通常高度相关，并且随着时间的推移在空间中以复杂的结构演变。例如，许多大气过程（例如湍流过程）可以表现出远程依赖性，相关性随着距离的增加而缓慢衰减。虽然现有的协方差模型成功地描述了这些过程的平滑行为，但这些模型中的相关性通常呈指数快速衰减，因此是不够的。许多地球物理过程产生的数据通常被连续索引，并在许多学科中表现出复杂的依赖结构，包括地球物理学、生态学、环境和气候科学、工程、公共卫生、经济学、政治科学和商业科学。该项目将开发新的多元和时空协方差函数及其理论特性，以表征复杂行为，例如远程依赖性和不对称性，并开发稳健的估计程序来估计平滑行为和远程依赖性。该项目还将开发和分发用户友好的开源软件，促进其在复杂数据分析问题上的广泛采用，并为下一代统计学家和数据科学家提供培训机会。该项目由统计计划和刺激竞争性研究既定计划（EPSCoR）共同资助。该项目将开发理论基础和统计模型，使用基于模型的框架推断具有远程依赖性的多元和时空过程。该框架集成并扩展了尺度混合建模和客观贝叶斯文献中出现的强大技术。尺度混合技术用于构造新的多元和时空协方差函数，并提供灵活的属性，包括任意平滑度、长程依赖性和不对称性。将为以原则性和统一的方式研究所得协方差在起源/尾部行为和筛选效应等几个属性方面的实际用途提供理论基础，并为内插和外推设置中的预测准确性提供理论见解。客观贝叶斯推理用于在具有参考先验的汇合超几何协方差函数下实现高斯过程的鲁棒参数估计，其中允许估计平滑度和尾部衰减参数。所开发的统计理论和推理工具将为使用协方差模型的空间统计和相关领域的多元和时空过程建模提供新的基础。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优势进行评估，被认为值得支持以及更广泛的影响审查标准。