Title: The impacts of sampling design on model inference and spatial prediction
Abstract: Informative sampling designs are broadly used across many application areas of statistical modeling, and can have a large impact on model inference and prediction. In spatial modeling, informative sampling can result in biased spatial covariance parameter estimation, which in turn can bias spatial kriging estimates. Even with unbiased estimates of the spatial covariance parameters, since the kriging variance is a function of the observation locations, these estimates will vary based on the sample and overestimate the population-based estimates. To address these biases, we develop a weighted composite likelihood approach to improve spatial covariance parameter estimation under informative sampling designs. Then, given these parameter estimates, we propose three approaches to quantify the effects of the sampling design on the variance estimates in spatial prediction in order to make informed decisions for population-based inference. We apply our methods to perform spatial prediction of nitrate concentration in wells located throughout central California.
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