Optimal Design in Geostatistics under Preferential Sampling

TL;DR

This paper investigates how preferential sampling influences optimal design decisions in Geostatistics, proposing a Bayesian utility-based approach, with simulations and real rainfall data illustrating significant effects on sampling strategies and estimation accuracy.

Contribution

It introduces a Bayesian utility-based method for optimal design under preferential sampling, accounting for sampling bias in Geostatistics, and demonstrates its impact through simulations and real data.

Findings

Preferential sampling significantly alters optimal sampling strategies.

The proposed method effectively incorporates sampling bias into design decisions.

Application to rainfall data shows substantial differences in optimal design under preferential sampling.

Abstract

This paper analyses the effect of preferential sampling in Geostatistics when the choice of new sampling locations is the main interest of the researcher. A Bayesian criterion based on maximizing utility functions is used. Simulated studies are presented and highlight the strong influence of preferential sampling in the decisions. The computational complexity is faced by treating the new local sampling locations as a model parameter and the optimal choice is then made by analysing its posterior distribution. Finally, an application is presented using rainfall data collected during spring in Rio de Janeiro. The results showed that the optimal design is substantially changed under preferential sampling effects. Furthermore, it was possible to identify other interesting aspects related to preferential sampling effects in estimation and prediction in Geostatistics. With the Rejoinder to Comments [arXiv:1509.04817], [arXiv:1509.04819], [arXiv:1509.04821].