Mathematical Sciences: Statistical Inference for Large Spatial and Space-Time Datasets

数学科学：大型空间和时空数据集的统计推断

• 批准号: 9504470
• 负责人: Michael Stein
• 金额: $ 15万
• 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: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504470&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Statistical; Inference; Large

Proposal: DMS 9504470 PI: Stein Institution: University of Chicago Title: Statistical Inference for Large Spatial and Space-Time Datasets Abstract: This research considers both applied and theoretical problems arising in statistical analysis of spatial and space-time data. The applied aspect is the detailed modeling and analysis of stratospheric ozone levels as measured via satellite at over 30,000 locations daily for over a decade. The goal is to model the data at the high level of spatial and temporal resolution it is taken and not to aggregate over space and/or time as has been done in all previous statistical analyses of these data. To reach this goal, it will be necessary to consider in detail the nature of the measurement process and the space-time variations of ozone concentrations due to such factors as long-term trends, seasonal effects, variations both within and across latitudes (which are quite different) and possibly the relationship of ozone to meteorological conditions. The immense size of this dataset provides a strong connection to the theoretical aspect of this proposal: the study of asymptotic problems in the analysis of spatial data. In particular, a fixed domain asymptotic approach, in which the number of observations in some fixed region of space increasing, is adopted. Using this approach, this research studies the asymptotic properties of spatial periodograms for estimating the high frequency behavior of the spectral density of a stationary random field and the effect of misspecifying spectral densities on prediction problems. The ultimate goal is to connect these two problems and to understand the effect of estimating spectral densities on subsequent predictions. Satellite based instruments measure numerous aspects of the earth and its atmosphere with high resolution in space and time. For example, the Total Ozone Monitoring Spectrometer (TOMS) measures ozone levels at over 30,000 locations daily, providing a much grea ter level of detail than can possibly be attained using ground-based instruments. However, this high spatial resolution has not been put to much use, as statistical analyses to date of this dataset have been on ozone levels averaged over large regions. Using 10 years of TOMS records as a test case, this project develops statistical and computational methods for analyzing the spatial-temporal structure of large, high-resolution geophysical datasets. This research aims to provide a better understanding of the space-time dynamics of stratospheric ozone and hence the opportunity to more accurately assess the effect of anthropogenic emissions on ozone levels, a problem of worldwide environmental concern. The methods developed in this research may prove useful in analyzing other large satellite based space-time datasets, such as meteorological conditions relevant to global climate change. In addition, this research studies theoretical properties of statistical methods when applied to large spatial and space-time datasets.

建议：DMS 9504470 PI：Stein机构：芝加哥大学标题：大型空间和时空数据集的统计推断摘要：本研究考虑了在空间和时空数据的统计分析中所产生的应用和理论问题。 应用的方面是通过卫星在超过30,000个位置测量的平流层臭氧水平的详细建模和分析。 目的是在高度和时间分辨率的高级别上对数据进行建模，而不是像在这些数据的所有统计分析中所做的那样在空间和/或时间上进行汇总。 为了实现这一目标，有必要详细考虑由于长期趋势，季节性效应，纬度内部和范围内的变化（这是完全不同的）以及臭氧与气象条件的关系，诸如长期趋势，季节性影响，季节性效应，季节性效应，季节性的变化等因素，臭氧浓度的变化。该数据集的巨大规模可与该提案的理论方面有很强的联系：在空间数据分析中对渐近问题的研究。 特别是，采用了一种固定领域渐近方法，其中采用了某些固定空间区域中的观测数量。 使用这种方法，本研究研究了空间周期图的渐近特性，用于估计固定随机场的光谱密度的高频行为以及误解光谱密度对预测问题的影响。最终目标是连接这两个问题，并了解估计光谱密度对随后预测的影响。 基于卫星的仪器以高分位和时间分辨率测量地球的许多方面及其大气层。 例如，总臭氧监测光谱仪（TOMS）每天在30,000个位置测量臭氧水平，提供的细节水平要比使用地面仪器所能达到的范围要多得多。但是，这种高空间分辨率尚未得到太多使用，因为该数据集的统计分析已在大型地区的臭氧水平上进行。使用10年的TOMS记录作为测试案例，该项目开发了用于分析大型高分辨率地球物理数据集的时空结构的统计和计算方法。 这项研究旨在更好地了解平流层臭氧的时空动态，因此有机会更准确地评估人为排放对臭氧水平的影响，这是全球环境问题的问题。这项研究中开发的方法可能被证明可用于分析其他基于卫星的大型时空数据集，例如与全球气候变化有关的气象条件。 此外，该研究研究统计方法的理论特性当应用于大型空间和时空数据集时。