Statistical Inference and Simulation for Spatial Point Processes

By Jesper Møller. 2003

931 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/25bf09f0b1f3732c72be51db289424b897ca8cf5

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In Applied Mathematics

Citations in the corpus

Bayesian Inference and Model Assessment for Spatial Point Patterns Using Posterior Predictive Samples (2017, neutral): “…theoretical development and computational tools for analyzing many types of point patterns, including simple point patterns, multivariate point patterns, marked point patterns, and spatiotemporal point patterns (see, e.g., Møller and Waagepetersen, 2003; Illian et al., 2008; Gelfand et al., 2010).”
Perfect simulation and moment properties for the Matérn type III process (2010, neutral): “(Slivnyak, 1962; Mecke, 1967) (see also Moller and Waagepetersen, 2004, pp.20 ‐22),”
Residual analysis for spatial point processes (with discussion) (2005, neutral): “Parametric inference, model selection, and goodness-of-fit testing are also feasible with Markov Chain Monte Carlo methods [50, 79].”
Joint Learning of Set Cardinality and State Distribution (2017, neutral): “For further details on point processes, we refer the reader to textbooks such as (Chiu et al. 2013; Daley and Vere-Jones 2007; Moller and Waagepetersen 2003).”
Perfect simulation of Hawkes processes (2005, positive): “Assuming, for the moment, that F (the CDF for the length of a cluster) is known, the following algorithm for perfect simulation of the marked Hawkes process is similar to the algorithm for simulation of Poisson cluster processes without edge effects given in [6] (see also [17] and [21]).”
Fitting complex ecological point process models with integrated nested Laplace approximation (2013, neutral): “We exploit this here and focus on log-Gaussian Cox processes, as considered inMøller, Syversveen &Waagepetersen (1998) and Møller & Waagepetersen (2004, 2007).”
Model-based classification and novelty detection for point pattern data (2016, neutral): “A random finite set (RFS) X of X is a random variable taking values in F(X ) [19], [11], [12], [20], [13].”
Two‐step estimation for inhomogeneous spatial point processes (2009, neutral): “Regarding the choice of r, plots of the empirical pair correlation function (e.g. expression (4.21) in Møller and Waagepetersen (2003)) may be helpful.”
Strong plant-soil associations in a heterogeneous subtropical broad-leaved forest (2011, positive): “In particular, spatial point process models are a particularly promising method recently developed to address this issue (Moller and Waagepetersen 2003; Waagepetersen 2007).”
Lecture Notes: Temporal Point Processes and the Conditional Intensity Function (2018, neutral): “Here it would be more appropriate to base the model checking on other aspects of the model (such as the summary statistics given for example in Møller and Waagepetersen (2004)), which may not be caught so well by the conditional intensity function.”
On Consistent Nonparametric Intensity Estimation for Inhomogeneous Spatial Point Processes (2008, neutral): “For a non-Poisson process, we can fit a parametric model for the pair correlation function involved in the second term by using a “minimum contrast estimation” procedure (e.g., Møller and Waagepetersen 2003), say, and then plug it back into the variance expression.”
Generalised shot noise Cox processes (2005, neutral): “2 of [34]), but a closed form expression for ρcent is in general unknown (except in the Poisson case, where λ∗( cent, ξ) does not actually depend on cent).”
Clustering for point pattern data (2017, neutral): “The probability density p : F(X ) → [0,∞) of an RFS is the Radon-Nikodym derivative of its probability distribution relative to the dominating measure μ, defined for each (measurable) T ⊆ F(X ), by [24], [26], [36], [37]:”
spatstat: An R Package for Analyzing Spatial Point Patterns (2005, neutral): “These functions return a point pattern (as an object of class "ppp Møller and Waagepetersen (2003); Stoyan and Stoyan (1995) for information about these models.”