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

提案：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： 本研究考虑了空间和时空数据的统计分析中出现的应用和理论问题。 应用方面是对平流层臭氧水平进行详细建模和分析，十多年来每天通过卫星在30，000多个地点进行测量。 目标是以高水平的空间和时间分辨率对数据进行建模，而不是像以前对这些数据的所有统计分析那样在空间和/或时间上进行汇总。 为实现这一目标，必须详细考虑测量过程的性质以及由于长期趋势、季节效应、纬度内部和纬度之间的变化等因素造成的臭氧浓度的时空变化 （这是完全不同的）和可能的臭氧与气象条件的关系。这个数据集的巨大规模提供了 与这项建议的理论方面有很强的联系： 空间数据分析中的渐近问题。 特别地，采用了一种固定区域渐近方法，在该方法中，在空间的某个固定区域中的观测值的数目增加。 利用这种方法，本研究研究了估计平稳随机场谱密度高频行为的空间周期图的渐近性质以及错误指定的影响 谱密度预测问题。最终目标是连接 这两个问题，并了解估计谱密度的影响， 随后的预测。 基于卫星的仪器测量地球及其大气层的许多方面，在空间和时间上具有高分辨率。 例如，臭氧总量监测光谱仪（TOMS）每天测量30，000多个地点的臭氧水平，提供的详细程度远远超过地面仪器。然而，这种高空间分辨率并没有得到太多的应用， 由于迄今为止对这一数据集的统计分析是针对大面积区域的平均臭氧水平进行的，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。 这项研究旨在更好地了解平流层臭氧的时空动态，从而有机会更准确地评估 人为排放对臭氧水平的影响，这是一个全球环境关注的问题。这项研究中开发的方法可以证明， 用于分析其他大型卫星空时数据集，例如 与全球气候变化有关的气象条件。 此外，本研究还研究了统计方法的理论性质 当应用于大型空间和时空数据集时。

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.