Infilling Sparse Records of Spatial Fields Craig J. Johns Douglas Nychka Timothy G.F. Kittel Chris Daly ∗ September 15, 2003 Abstract Historical records of weather such as monthly precipitation and temperatures from the last century are an invaluable database to study 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 irregularly observed 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 to 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 the overall approach has merit, treading a line along computational feasibility and statistical validity. Furthermore, we are able to produce reliable measures of uncertainty for the estimates. Keywords: Bayesian Spatial Interpolation, Cross-validation, Prediction, Geostatistics. 1 INTRODUCTION Understanding climate variability and its effect on environmental processes is important not only to increase our scientific understanding of the earth system but also to assess the impact of a ∗ Craig J. Johns is Assistant Professor, Mathematics Department, University of Colorado, Denver, CO, 80217-3364, Douglas Nychka is Director, Geophysical Statistics Project, National Center for Atmospheric Research, Boulder, CO, Timothy G.F. Kittel is Scientist, Terrestrial Sciences Section, National Center for Atmospheric Science, Boulder, CO, and Chris Daly is Director, Spatial Climate Analysis Service, Department of Geosciences, Oregon State University, Corvallis, OR. The authors gratefully acknowledge support from the National Science Foundation under Grants DMS 9815344 and DMS 9312686 for the Geophysical Statistics Project and its research and support from NOAA grant NA76GP0558 . VEMAP was supported by NASA, EPRI, USDA Forest Service, and the US Deptartment of Energy. 1