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

TL;DR

This paper introduces a weighted composite likelihood method to correct bias in spatial covariance estimation caused by informative sampling, and proposes approaches to accurately quantify prediction variance, enhancing population-based spatial inference.

Contribution

It develops a novel weighted composite likelihood approach for unbiased spatial covariance estimation under informative sampling and proposes methods to adjust kriging variance estimates.

Findings

Improved covariance parameter estimates under informative sampling.

Enhanced accuracy of spatial prediction variance estimates.

Validated methods through simulation and real data application.

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.