Non‐ and semi‐parametric estimation of interaction in inhomogeneous point patterns

By Adrian Baddeley, Jesper Møller, Rasmus Waagepetersen. 2000

662 citations recorded by the source corpus.

Subfields: Applied Mathematics, Environmental Engineering, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/06e89be5040d1a067d55eeadc32700302a9808d0

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In Applied Mathematics

In Environmental Engineering

In Geometry and Topology

Citations in the corpus

Second‐order analysis of inhomogeneous spatio‐temporal point process data (2009, background): “Baddeley et al. (2000) defined a weaker form of stationarity for spatial point processes, called second-order intensity-reweighted stationarity.”
A Studentized Permutation Test for the Comparison of Spatial Point Patterns (2012, background): “One has to be aware that different point process models do not necessarily have different K-functions; in particular, the K-function is invariant under independent thinning of the point process; for example, see Baddeley, Møller, and Waagepetersen (2000).”
The permanental process (2006, background): “Non-parametric estimation of the inhomogenous K-function is less problematic (Baddeley et al. 2000): For the moment, assume that we extend the Cox process and the underlying Gaussian processes to R.”
Estimating functions for inhomogeneous spatial point processes with incomplete covariate data (2008, methodology): “Parameters of the density h may as suggested in Waagepetersen (2007) be estimated using a minimum contrast method based on the generalization of the K-function to the inhomogeneous case (Baddeley et al., 2000).”
Heterogeneity influences spatial patterns and demographics in forest stands (2008, background): “…thinning surface is in general not known and using an estimate of the intensity of the pattern itself as the thinning surface is problematic because in this case, both firstand second-order properties have to be determined from the same pattern simultaneously (Baddeley et al. 2000; Diggle 2003).”
Bayesian Inference and Model Assessment for Spatial Point Patterns Using Posterior Predictive Samples (2017, positive): “The usual distance-based measures such as the G- and K-functions (Illian et al., 2008) are defined through functions v(S,θ) such that E[v(S,θ)|θ] = G(d;θ) or E[v(S,θ)|θ] = K(d;θ) (Banerjee et al., 2014).”
A Thinned Block Bootstrap Variance Estimation Procedure for Inhomogeneous Spatial Point Patterns (2007, methodology): “As point out by one referee, we may simply estimate the PCF or the K-function using the original data (Baddeley et al. 2000). This will yield an estimate of the SOCF that in turn can be plugged into the expression for Bn in Theorem 1 to obtain an estimate for the asymptotic variance. Waagepetersen (”
Correction note: Poisson point process models solve the “pseudo-absence problem” for presence-only data in ecology (2010, methodology): “It is deﬁned over the region A as K inhom reduces to the usual K function for a stationary process, and like the usual K -function, can be used to diagnose whether there are interactions in the point pattern y [Baddeley, Moller and Waagepetersen (2000)].”
Structured Spatio‐Temporal Shot‐Noise Cox Point Process Models, with a View to Modelling Forest Fires (2010, methodology): “Sections 3-4 study various useful properties of the spatio-temporal shot-noise Cox process X relying only on the general structure (1)-(2) or (1)-(3).”
Point process diagnostics based on weighted second-order statistics and their asymptotic properties (2009, methodology): “…be a comparison between the various residual second-order statistics proposed here as well as comparison with other methods of residual analysis such as the first-order residuals of Baddeley et al. (2000) or the second-order statistics of the residual processes such as those in Schoenberg (2003).”
Two‐step estimation for inhomogeneous spatial point processes (2009, background): “2 Rasmus Waagepetersen and Yongtao Guan stationarity (Baddeley et al., 2000) in which case the so-called K-function is well-defined and given in terms of an integral involving g (cf. (1) in Section 2). A parametric model gψ is often imposed for the pair correlation function and hypotheses regarding ”
Shot noise Cox processes (2003, background): “Moreover, Ripley’sK-function [37], [38] for the stationary case and its extension [4] for the nonstationary case can be obtained by integrating the pair correlation function.”
Assessment of Point Process Models for Earthquake Forecasting (2013, methodology): “The raw or Pearson residuals may be smoothed, as in Baddeley et al. (2005), but such smoothing typically only reveals gross, large-scale inconsistencies between the model and data. If one is primarily interested in comparing competing models, then instead one may plot, in each pixel, the difference ”
Nonparametric estimation of the dependence of a spatial point process on spatial covariates (2012, methodology): “In this case, a more accurate variance estimate could be obtained by estimating the pair correlation function, provided we are willing to impose additional model assumptions, such as second-order reweighted stationarity [5] or a Cox process model [54].”