1998
DOI: 10.1111/1467-9469.00115
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Log Gaussian Cox Processes

Abstract: We view the locations and times of a collection of crime events as a space-time point pattern. So, with either a nonhomogeneous Pois-son process or with a more general Cox process, we need to specify a space-time intensity. For the latter, we need a random intensity which we model as a realization of a spatio-temporal log Gaussian process. Importantly, we view time as circular not linear, necessitating valid separable and nonseparable covariance functions over a bounded spatial region crossed with circular tim… Show more

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Cited by 657 publications
(725 citation statements)
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“…As in Brix and Diggle (2001) and Diggle et al (2005), we assume that calls are made according to a log-Gaussian Cox process (Møller et al, 1998) and approximate the rate of calls during the ith day of the two-month period by…”
Section: Extensions and Applicationmentioning
confidence: 99%
“…As in Brix and Diggle (2001) and Diggle et al (2005), we assume that calls are made according to a log-Gaussian Cox process (Møller et al, 1998) and approximate the rate of calls during the ith day of the two-month period by…”
Section: Extensions and Applicationmentioning
confidence: 99%
“…The two most often used classes of spatial Cox point processes are the log Gaussian Cox processes (Møller et al, 1998) and the shot noise Cox processes (Møller, 2003). Even though these can be generalized and unified in the framework of Lévy based Cox processes (Hellmund et al, 2008) for ease of exposition we stick to the two classical models.…”
Section: Cox Processesmentioning
confidence: 99%
“…Condition (4) implies X can be viewed as the superposition Q ∪ R of a Cox process Q driven by γ = λ − ρ and an independent Poisson process R with intensity function ρ. For example, γ may be log Gaussian and Q then a log Gaussian Cox process (Møller, Syversveen and Waagepetersen, 1998), or a shot noise process and Q then a shot noise Cox process (Møller, 2003).…”
Section: Lower Bound On the Random Intensitymentioning
confidence: 99%
“…For example, if γ is log Gaussian, a Langevin-Hastings algorithm can be used (Møller et al, 1998;Møller and Waagepetersen, 2004), and if γ is a shot-noise process, a birth-death Metropolis-Hastings algorithm applies (Møller, 2003;Møller and Waagepetersen, 2004). We run one of these Metropolis-Hastings algorithms until it is effectively in equilibrium, and then return an (approximate) simulation of λ conditional on X = x.…”
Section: Independent Thinning Proceduresmentioning
confidence: 99%