Equivalent Kriging

• Activity Number: 87
• Type: Invited
• Date/Time: Sunday, August 3, 2014 : 8:30 PM to 10:30 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): William Kleiber*+ and Douglas Nychka
• Companies: University of Colorado and NCAR
• Keywords: Equivalent kernel ; Kriging ; Kernel smoothing ; Massive dataset ; Spatial statistics

Abstract

Most modern spatially indexed datasets are very large, with sizes commonly ranging from tens of thousands to millions of locations. Spatial analysis often focuses 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 analysis infeasible or impossible with large datasets. We introduce an approach to kriging in the presence of large datasets called equivalent kriging, which relies on approximating the kriging weight function using an equivalent kernel. Resulting kriging calculations are extremely fast and feasible in the presence of massive spatial datasets. We derive closed form kriging approximations for multiresolution classes of spatial processes, as well as under any stationary model, including popular choices such as the Matern. Estimation can proceed by either cross-validation or generalized cross-validation. Equivalent kriging is illustrated on simulated datasets, and a monthly average precipitation dataset whose size prohibits traditional geostatistical approaches.