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

Abstract

Informative sampling designs can impact spatial prediction, or kriging, in two important ways. First, the sampling design can bias spatial covariance parameter estimation, which in turn can bias spatial kriging estimates. Second, 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. In this work, 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. These results can be used to make informed decisions for population-based inference. We illustrate our approaches using a comprehensive simulation study. Then, we apply our methods to perform spatial prediction on nitrate concentration in wells located throughout central California.

A Look into the Problem of Preferential Sampling from the Lens of Survey Statistics

“…While the use of weighted likelihoods remains far less prevalent in the PS literature, the application in Zidek et al (2014) suggests that many of the relevant developments in the survey literature could well be carried over to the PS problem. In fact, more recently, Schliep et al (2021) have studied the use of weighted composite likelihoods in the context of spatial kriging under biased sampling schemes.…”