Abstract
Spatial data play an important role in many areas such as ecology, biology, environmental monitoring, agronomy, remote sensing, geology, to name a few. Sometimes observations are obtained on a regular lattice (see, e.g. Whittle in Biometrika 49:305–314, 1962; Bartlett in Adv. Appl. Prob. 6(2):336–358, 1974; Besag in J. R. Stat. Soc., Ser. B 36(2):192–236, 1974; Cressie in Statistics for spatial data, 1993; Christakos in Random field models in Earth sciences, 1992; Modern spatiotemporal geostatistics, 2000; Benson et al. in Water Resour. Res. 42(W01415):1–18, 2006; Sain and Cressie in J. Econom. 140(1):226–259, 2007, and references therein). This leads to considering spatial processes on a grid, or more specifically, random fields X t with index \(t\in\mathbb{Z}^{2}\). On the other hand, if the spatial points are not on a regular grid, then random fields with \(t\in\mathbb{R}^{2}\) are used.
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Beran, J., Feng, Y., Ghosh, S., Kulik, R. (2013). Spatial and Space-Time Processes. In: Long-Memory Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35512-7_9
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