Spatial Prediction: The Importance of the Nugget

• Activity Number: 264
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Daniel Ries* and Mark Kaiser
• Companies: Iowa State University and Iowa State University
• Keywords: Kriging ; Variogram ; Nugget

Abstract

Ordinary kriging is a standard tool for spatial prediction. One can conduct ordinary kriging using either a variogram model or a covariance model. Variograms allow for a nice interpretation of the nugget where it represents the measurement error and microscale variation. The interpretation is less clear with covariance functions, and many models are used that do not include a parameter for the nugget. Even if a nugget is included in a covariance model, it may require multiple measurements at a distance of zero to be able to estimate it. Since one usually doesn't have this luxury, it is easy and often done that one constructs a covariance matrix and performs kriging without consideration for the nugget. Through a simulation study and the use of cross-validation, we investigate the effects of various sized nuggets on spatial prediction using the variogram and covariance function. Predictive performance using the covariance function suffers compared to the variogram as the size of the nugget grows. The implications of these phenomena for practical spatial prediction are discussed and presented in an application to the Tarrawarra data set.