Statistical Models for Spatial-Temporal Processes

• Activity Number: 389
• Type: Luncheons
• Date/Time: Wednesday, August 6, 2003 : 12:30 PM to 1:50 PM
• Sponsor: Section on Statistics & the Environment
• Author(s): Michael L. Stein*+
• Companies: University of Chicago
• Keywords: Covariance functions ; Physical models ; Markov processes ; Spectral densities ; Anisotropy

Abstract

Processes that vary in both space and time are ubiquitous in environmental science. Until recently, most efforts to model the covariance structure of such processes have made severe, simplifying assumptions, such as independence of the process at different observations times or separability of the spatial-temporal covariance function into a spatial term times a temporal term. Current research recognizes the inadequacy of such assumptions, which has led to the development of new, more flexible classes of spatial-temporal covariance functions. Other than applying such models to a large number of data sets and seeing how they work, are there any principled ways of deciding what kinds of spatial-temporal covariance functions might be appropriate in different circumstances? Other possible topics of discussion include models that recognize the often fundamental distinction between the vertical and horizontal dimensions in environmental processes and the role of deterministic physical models in statistical modeling of environmental processes.