Estimation, Modeling and Prediction of Nonseparable and Nonstationary Space-Time Processes

不可分离和非平稳时空过程的估计、建模和预测

• 批准号: 0353029
• 负责人: Montserrat Fuentes
• 金额: --
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0353029&HistoricalAwards=false
• 关键词: Estimation; Modeling; Prediction; Nonseparable; Nonstationary

M. FUENTES: DMS - 0353029 ABSTRACTClassical geostatistics and Fourier spectral methods are powerfultools to study the spatial temporal structure of stationary andseparable processes. However, it is widely recognized that in realapplications spatial temporal processes are rarely stationary andseparable. Thus an important extension of these spectral methods is toprocesses that are nonstationary and nonseparable. In this work, theinvestigator presents some new spectral approaches and tools toestimate, model, and test for nonstationarity and nonseparability.The investigator introduces nonparametric approaches and fittingalgorithms to estimate the spatial temporal structure of anonstationary and nonseparable spatial process defined on a continuousspace, and studies the asymptotic properties of these estimates. Themethods are based on a spectral approach, using spectral functionsthat are space-time dependent. The most important scientificcontributions of the research proposed here are: the parametric andnonparametric estimation of the complex spatial temporal dependence ofenvironmental processes in general situations (nonstationarity,anisotropy, nonseparability); the introduction of flexible models forspatial prediction of environmental processes using spectral methods;and new methodology for spatial prediction and estimation in thepresence of massive data.Spatial processes are an important modeling tool for manyenvironmental and scientific problems. Environmental scientists whowork with spatial temporal data, however, do not typically believethat real data satisfy the simple model assumptions such asseparability and stationarity that are currently used in practice.Therefore, it is is imperative for statisticians to develop methodswithout using those assumptions, especially for use with massivespatial-temporal (environmental) data sets. Through collaborationswith scientists, the new statistical models and methods proposed bythe investigator for estimation and prediction of space-timeprocesses, will enhance science by improving weather and air qualitymapping. The investigator will develop applications in collaborationwith atmospheric scientists and oceanographers on data assimilationproblems and on assessment of the performance of weather, ocean, andair quality numerical models. The methods proposed here for spacetime processes are also applicable to other fields. Past interactionsof the PI with various scientists at the Environmental ProtectionAgency (EPA), the National Oceanic and Atmospheric Administration(NOAA), and the National Center for Atmospheric Research (NCAR) areevidence that previous work of the PI has had an impact on variousfields. At NCSU there is ahigh proportion of women, American and African-American studentscompared to other Statistics departments. Five out of the seven PhDstudents currently working on their dissertations under the PI'ssupervision are women. The PI will continue her efforts to broaden theparticipation of minorities and women.

M. FUENTES: DMS - 0353029 摘要经典地质统计学和傅立叶谱方法是研究平稳和可分离过程的时空结构的有力工具。 然而，人们普遍认识到，在实际应用中，时空过程很少是静止的和可分离的。 因此，这些谱方法的一个重要扩展是非平稳和不可分离的过程。 在这项工作中，研究者提出了一些新的谱方法和工具来估计、建模和测试非平稳性和不可分离性。研究者引入了非参数方法和拟合算法来估计连续空间上定义的非平稳和不可分离空间过程的时空结构，并研究了这些估计的渐近性质。该方法基于谱方法，使用时空相关的谱函数。 这里提出的研究最重要的科学贡献是：一般情况下（非平稳性、各向异性、不可分离性）环境过程的复杂时空依赖性的参数和非参数估计；引入使用光谱方法进行环境过程空间预测的灵活模型；以及在海量数据存在下进行空间预测和估计的新方法。空间过程是许多环境和科学问题的重要建模工具。 然而，处理时空数据的环境科学家通常并不认为真实数据满足目前在实践中使用的简单模型假设，例如可分离性和平稳性。因此，统计学家必须开发不使用这些假设的方法，特别是对于使用具有海量时空（环境）数据集。 通过与科学家的合作，研究者提出的用于估计和预测时空过程的新统计模型和方法将通过改善天气和空气质量绘图来增强科学。 研究人员将与大气科学家和海洋学家合作开发数据同化问题以及天气、海洋和空气质量数值模型性能评估的应用程序。 这里提出的时空过程方法也适用于其他领域。 PI 过去与美国环境保护署 (EPA)、美国国家海洋和大气管理局 (NOAA) 以及国家大气研究中心 (NCAR) 各科学家的互动证明了 PI 之前的工作对各个领域产生了影响。 与其他统计系相比，北卡罗来纳州立大学的女性、美国和非裔美国学生比例很高。 目前在 PI 的指导下撰写论文的七名博士生中有五名是女性。首席检察官将继续努力扩大少数族裔和妇女的参与。