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Informative sampling designs can impact spatial prediction, or kriging, intwo important ways. First, the sampling design can bias spatial covarianceparameter estimation, which in turn can bias spatial kriging estimates. Second,even with unbiased estimates of the spatial covariance parameters, since thekriging variance is a function of the observation locations, these estimateswill vary based on the sample and overestimate the population-based estimates.In this work, we develop a weighted composite likelihood approach to improvespatial covariance parameter estimation under informative sampling designs.Then, given these parameter estimates, we propose three approaches to quantifythe effects of the sampling design on the variance estimates in spatialprediction. These results can be used to make informed decisions forpopulation-based inference. We illustrate our approaches using a comprehensivesimulation study. Then, we apply our methods to perform spatial prediction onnitrate concentration in wells located throughout central California.

Correcting spatial Gaussian process parameter and prediction variance estimation under informative sampling