Bayesian design for minimizing prediction uncertainty in bivariate spatial responses with applications to air quality monitoring.

Autor: Senarathne SGJ; School of Mathematical Sciences, Faculty of Science, Queensland University of Technology, Gardens Point campus, Brisbane, Australia., Müller WG; Department of Applied Statistics, Johannes Kepler University Linz, Austria., McGree JM; School of Mathematical Sciences, Faculty of Science, Queensland University of Technology, Gardens Point campus, Brisbane, Australia.
Jazyk: angličtina
Zdroj: Biometrical journal. Biometrische Zeitschrift [Biom J] 2023 Apr; Vol. 65 (4), pp. e2100386. Date of Electronic Publication: 2023 Jan 15.
DOI: 10.1002/bimj.202100386
Abstrakt: Model-based geostatistical design involves the selection of locations to collect data to minimize an expected loss function over a set of all possible locations. The loss function is specified to reflect the aim of data collection, which, for geostatistical studies, could be to minimize the prediction uncertainty at unobserved locations. In this paper, we propose a new approach to design such studies via a loss function derived through considering the entropy about the model predictions and the parameters of the model. The approach includes a multivariate extension to generalized linear spatial models, and thus can be used to design experiments with more than one response. Unfortunately, evaluating our proposed loss function is computationally expensive so we provide an approximation such that our approach can be adopted to design realistically sized geostatistical studies. This is demonstrated through a simulated study and through designing an air quality monitoring program in Queensland, Australia. The results show that our designs remain highly efficient in achieving each experimental objective individually, providing an ideal compromise between the two objectives. Accordingly, we advocate that our approach could be adopted more generally in model-based geostatistical design.
(© 2023 The Authors. Biometrical Journal published by Wiley-VCH GmbH.)
Databáze: MEDLINE
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