Shot noise Cox processes

Møller, Jesper

doi:10.1017/s0001867800012465

Cited by 67 publications

(155 citation statements)

References 37 publications

(63 reference statements)

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“…The most interesting situation, evidently, arises when Z is a location-dependent random field. In this case, one of the most mathematically tractable family of Cox processes, the shot noise Cox processes (SNCPs; Møller 2003, Møller andWaagepetersen 2007), is defined by the following random intensity surface:…”

Section: Review Of the Modelsmentioning

confidence: 99%

“…More specifically, we will focus on a family of Cox processes (Cressie 1993, Illian 2008: the shot noise Cox processes, SNCPs (Møller 2003). This class is rich enough to include a wide subfamily of Neyman-Scott processes (Thomas 1949, Neyman andScott 1958), Poisson/Gamma processes (Wolpert and Ickstadt 1998), and shot noise G Cox processes (Brix 1999).…”

Section: Introductionmentioning

confidence: 99%

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Downscaling species occupancy from coarse spatial scales

Azaele

Cornell

Kunin

2012

Ecological Applications

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Abstract. The measurement and prediction of species' populations at different spatial scales is crucial to spatial ecology as well as conservation biology. An efficient yet challenging goal to achieve such population estimates consists of recording empirical species' presence and absence at a specific regional scale and then trying to predict occupancies at finer scales. So far the majority of the methods have been based on particular species' distributional features deemed to be crucial for downscaling occupancy. However, only a minority of them have dealt explicitly with specific spatial features. Here we employ a wide class of spatial point processes, the shot noise Cox processes (SNCP), to model species occupancies at different spatial scales and show that species' spatial aggregation is crucial for predicting population estimates at fine scales starting from coarser ones. These models are formulated in continuous space and locate points regardless of the arbitrary resolution that one employs to study the spatial pattern. We compare the performances of nine models, calibrated at regional scales and demonstrate that a very simple class of SNCP, the Thomas process, is able to outperform other published models in predicting occupancies down to areas four orders of magnitude smaller than the ones employed for the parameterization. We conclude by explaining the ability of the approach to infer spatially explicit information from spatially implicit measures, the potential of the framework to combine niche and spatial models, and the possibility of reversing the method to allow upscaling.

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Section: Review Of the Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Downscaling species occupancy from coarse spatial scales

Azaele

Cornell

Kunin

2012

Ecological Applications

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“…Thus, S i (u) is formed by superposition of random impulses k i (u − v) for the points v ∈ i (Illian et al, 2008, p. 45). A Cox process X i driven by a random intensity function proportional to S i (u) is called a shot-noise Cox process with parent process i and dispersal kernel k i (Møller, 2003). Since ES i (u) = 1, the pair correlation function of X i is given by…”

Section: Shot-noise Fieldsmentioning

confidence: 99%

Multivariate Product-Shot-Noise Cox Point Process Models

et al. 2015

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Registro de acceso restringido Este recurso no está disponible en acceso abierto por política de la editorial. No obstante, se puede acceder al texto completo desde la Universitat Jaume I o si el usuario cuenta con suscripción. Registre d'accés restringit Aquest recurs no està disponible en accés obert per política de l'editorial. No obstant això, es pot accedir al text complet des de la Universitat Jaume I o si l'usuari compta amb subscripció. Restricted access item This item isn't open access because of publisher's policy. The full--text version is only available from Jaume I University or if the user has a running suscription to the publisher's contents.

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“…These are f l and s 2 l in the purely spatial case, with f c , s 2 c and θ for the spatiotemporal model. The minimum contrast approach is advocated in the seminal works of Møller et al (1998) and Brix and Diggle (2001) as the best, most convenient option currently available for estimation of these correlation parameters of the LGCP (as well as the SNCP in Møller, 2003;Møller and Díaz-Avalos, 2010;Proke sová and Dvo rák, 2013). As such, it has been employed in the applied modelling of real-world data such as in Møller et al (1998), Diggle et al (2005) and Møller and Díaz-Avalos (2010).…”

Section: Minimum Contrast Parameter Estimationmentioning

confidence: 99%

Assessing minimum contrast parameter estimation for spatial and spatiotemporal log‐Gaussian Cox processes

Davies

Hazelton

2013

Statistica Neerlandica

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The univariate log-Gaussian Cox process (LGCP) has shown considerable potential for the flexible modelling of the spatial, and more recently, spatiotemporal, intensity functions of planar point patterns within a restricted region in space. Its flexibility and mathematical tractability are partly offset by the need to acquire sensible estimates of the parameters controlling the dependence structure of the Gaussian field given the observed data. The method of minimum contrast, which compares theoretical descriptors of the process with their non-parametric counterparts in order to obtain the required estimates, is arguably the most popular in practice to date. This article provides a comprehensive set of simulation studies focused on gauging the performance and impact of minimum contrast methods for parameter estimation of these processes. Results indicate that concerns over arbitrariness of implementation of minimum contrast give way to satisfactory practical performance.

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Shot noise Cox processes

Cited by 67 publications

References 37 publications

Downscaling species occupancy from coarse spatial scales

Downscaling species occupancy from coarse spatial scales

Multivariate Product-Shot-Noise Cox Point Process Models

Assessing minimum contrast parameter estimation for spatial and spatiotemporal log‐Gaussian Cox processes

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