Spatial Prediction for Large Datasets
Will Kleiber, Unviersity of Colorado at Boulder
Most modern spatially indexed datasets are very large, with sizes commonly ranging from tens of thousands to millions of locations. Spatial analyses often focus on spatial smoothing using the geostatistical technique known as kriging. Kriging requires covariance matrix computations whose complexity scales with the cube of the number of spatial locations, making such analyses infeasible or impossible with large datasets. By casting kriging as a variational problem, we develop an approximate technique called "equivalent kriging" which avoids costly covariance matrix manipulations. We derive closed form approximations for multiresolution classes of spatial processes, as well as under any stationary model, including popular choices such as the Matern. The theoretical justification leads to a convenient method for asymptotic calculations; we additionally discuss some implications of model misspecification.