On Ignorability of Preferential Sampling in Geostatistics

TL;DR

This paper reveals that under certain conditions, ignoring preferential sampling in geostatistics can still yield unbiased estimates, offering a computationally efficient alternative to likelihood-based methods.

Contribution

It demonstrates that non-likelihood-based methods ignoring preferential sampling can be valid, providing simpler and faster estimation procedures with reliable results.

Findings

Non-likelihood methods can produce unbiased estimators under certain conditions.

Simulation studies show reduced error and better confidence coverage.

Application to real data confirms practical utility.

Abstract

Preferential sampling has attracted considerable attention in geostatistics since the pioneering work of Diggle et al. (2010). A variety of likelihood-based approaches have been developed to correct estimation bias by explicitly modelling the sampling mechanism. While effective in many applications, these methods are often computationally expensive and can be susceptible to model misspecification. In this paper, we present a surprising finding: some existing non-likelihood-based methods that ignore preferential sampling can still produce unbiased and consistent estimators under the widely used framework of Diggle et al. (2010) and its extensions. We investigate the conditions under which preferential sampling can be ignored and develop relevant estimators for both regression and covariance parameters without specifying the sampling mechanism parametrically. Simulation studies demonstrate clear advantages of our approach, including reduced estimation error, improved confidence interval coverage, and substantially lower computational cost. To show the practical utility, we further apply it to a tropical forest data set.