Spatial sampling design under the infill asymptotic framework

Abstract

SUMMARYWe study optimal sample designs for prediction with estimated parameters. Recent advances in the infill asymptotic theory provide a deeper understanding of the finite sample behavior of prediction and estimation. By incorporating these known asymptotic results, we modify some existing design criteria for estimation of covariance function and best linear unbiased prediction. These modified criteria could significantly reduce the computation time necessary for finding an optimal design. We illustrate our approach through both a real experiment in agriculture and simulation.

Spatial designs and properties of spatial correlation: Effects on covariance estimation

“…We specifically chose the lattice design since most in-fill and increasing domain asymptotic results for the exponential covariance model are based on sampling points on a lattice (Zhang and Zimmerman 2005). Also, for comparison we used a cluster design, which Zimmerman (2006) and others (Zhu and Stein 2005;Zhu and Zhang 2006) have found to be the optimal design for covariance parameter estimation of the exponential-with-nugget model. Finally, we included the random design because the EMAP sample, which prompted this investigation, is similar to a random spatial design.…”

“…Cluster designs are found to be the optimal design for spatial covariance estimation by several authors (Pettitt and McBratney 1993;Muller and Zimmerman 1999;Zhu and Stein 2005;Xia et al 2006;Zimmerman 2006;Zhu and Zhang 2006). Some of these contain "clusters" that are really linear strands of sample points.…”

“…Some of these contain "clusters" that are really linear strands of sample points. The values of the range parameter and the nugget-to-partial sill ratio influence the configuration of the clusters in terms of location and number of points within the cluster (Zhu and Stein 2005;Zimmerman 2006;Zhu and Zhang 2006). We have chosen sample locations for our cluster design that mimic the optimal design found by Zimmerman (2006) for covariance parameter estimation.…”

“…To mimic in-fill asymptotics with n = 361 we increased the number of clusters but kept the number of points within the cluster the same. We have only used one cluster design which cannot be optimal for all of the parameter combinations investigated (Zhu and Stein 2005;Zimmerman 2006;Zhu and Zhang 2006). …”

A Kriging and Stochastic Collocation ensemble for uncertainty quantification in engineering applications

“…Once the covariance function is estimated, a Kr model can predict the values of the system response at new points in the sample space. To estimate the covariance function, it is well known that space filling sampling is an advantage [42,43].…”