Optimal design for spatial models (Q2799898)

The authors present a survey of results on optimal designs for spatial sampling. They start with model-free sampling designs, especially with space-filling designs [\textit{M. E. Johnson} et al., ``Minimax and maximin distance designs'', J. Stat. Plann. Inference 26, 131--148 (1990)] and spatial probability-based sampling designs like simple random sampling, systematic sampling, stratified sampling, cluster sampling). The main part of the paper deals with model-based spatial sampling. The authors use the geostatistical context [\textit{N. Cressie}, in: Multivariate environmental statistics. Amsterdam: North-Holland. 99--107 (1993; Zbl 0825.62477)] and present results on designs for estimating the covariance structure [\textit{W. G. Müller} and \textit{D. L. Zimmermann}, ``Optimal designs for variogram estimation'', Environmetrics 10, 23--37 (1999; \url{doi:10.1002/(SICI)1099-095X(199901/02)10:1<23::AID-ENV333>3.0.CO;2-P})] and results on designs for spatial prediction [\textit{Z. Zhu} and \textit{M. L. Stein}, J. Stat. Plann. Inference 134, No. 2, 583--603 (2005; Zbl 1066.62092)]. Furthermore Bayesian designs and dynamic designs are discussed.NEWLINENEWLINEFor the entire collection see [Zbl 1327.62001].