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

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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.