Revisiting the declustering of spatial data with preferential sampling

Preferential sampling is a form of data collection that may significantly distort the histogram and the semivariogram of spatially correlated data. Typical situations are a higher sampling density at high-valued areas favorable for mining, and highly contaminated areas in need of environmental remediation. Multiple statistical procedures are devoted to obtaining representative statistics, whose magnitudes should be close to the respective population values. This paper proposes a resampling method that can compensate for preferential sampling of spatially correlated data without using declustering weights. The application of the method herein generates a dataset of median estimates of quantiles of multiple stratified resamples that is free of preferential sampling. The methodology is illustrated with two examples. The first one involves values actually measured in the field and has the advantage of representing a real scenario of spatial fluctuations and preferential sampling. A second dataset is synthetic and has the main benefit of a priori knowledge of the underlying spatial distribution, thus allowing a satisfactory evaluation of the results against the known baseline. Access to computer code is offered for practical application of the method.