Infilling Sparse Records of Spatial Fields

Abstract

Historical records of weather, such as monthly precipitation and temperatures from the last century, are an invaluable database to use in studying changes and variability in climate. These data also provide the starting point for understanding and modeling the relationship among climate, ecological processes, and human activities. However, these data are observed irregularly over space and time. The basic statistical problem is to create a complete data record that is consistent with the observed data and is useful for other scientific disciplines. We modify the Gaussian-inverted Wishart spatial field model to accommodate irregular data patterns and to facilitate computations. Novel features of our implementation include the use of cross-validation to determine the relative prior weight given to the regression and geostatistical components and the use of a space-filling subset to reduce the computations for some parameters. We feel that the overall approach has merit, treading a line between computational feasibility and statistical validity. Furthermore, we are able to produce reliable measures of uncertainty for the estimates.