Geostatistical Modeling

Geostatistical modeling refers to methods of spatial and spatial-temporal statistics based on fitting a suitable covariance function (or variogram) to the data. They are usually the preferred method of analysis for data collected at point locations (as opposed to areal averages) and when these locations are not arranged on a regular lattice, as is typical of most environmental monitoring data. In this talk I will review the main steps of the methodology, in particular (a) defining models for spatial covariances and variograms, (b) model identification and parameter estimation, (c) prediction and interpolation ("kriging" and its extensions), (d) some of the simpler extensions to spatial-temporal models (the separable and "repeated measures" model). As an application, I shall consider the problem of estimating mean levels of fine particulate matter across a three-state region, to assess compliance with EPA air pollution standards.