2020
DOI: 10.1214/19-aos1896
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Isotropic covariance functions on graphs and their edges

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Cited by 27 publications
(52 citation statements)
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“…We expect that the same techniques could be applied on a linear network. We have not attempted this because there are some unresolved difficulties in constructing Cox models on a linear network (Baddeley et al 2017;Anderes et al 2020). Gibbs point process models on a network are in the early stages of development (van Lieshout 2018).…”
Section: Discussionmentioning
confidence: 99%
“…We expect that the same techniques could be applied on a linear network. We have not attempted this because there are some unresolved difficulties in constructing Cox models on a linear network (Baddeley et al 2017;Anderes et al 2020). Gibbs point process models on a network are in the early stages of development (van Lieshout 2018).…”
Section: Discussionmentioning
confidence: 99%
“…This highlights the fact that dealing with DPPs in non-Euclidean spaces S can be quite challenging (cf. Anderes et al, 2020).…”
Section: Determinantal Point Processesmentioning
confidence: 99%
“…Moreover, in Euclidean space, a covariance function is called isotropic if it is a function of the Euclidean norm of the difference between locations. Unlike its counterpart in Euclidean space, the definition of stationarity is less clear on networks (Anderes et al, 2020). Nevertheless, a space-time covariance function is said to be isotropic within components if C(s 1 , s…”
Section: Parametric Space-time Covariance Modelsmentioning
confidence: 99%
“…Covariance functions receive special attention due to the fact that a Gaussian random process is completely determined by its first-and second-order moments (Porcu et al, 2020). Although a broad range of classes of space-time covariance models are available in Euclidean space (De Iaco et al, 2013) and a thorough review has recently been given by Porcu et al (2020), corresponding results for pure spatial linear networks are few and far between -a recent exception being Anderes et al (2020) -and space-time results on networks are practically non-existent. To fill this gap, in this article we develop Fourier-free space-time covariance functions on generalized linear networks, using space embedding and scale mixture approaches.…”
Section: Introduction 1backgroundmentioning
confidence: 99%