A Kernel Method for Smoothing Point Process Data

By Peter J. Diggle. 1985

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Citations in the corpus

Trend analysis of climate time series: A review of methods (2019, background): “On the other hand, the choice of K (Epanechnikov, Gaussian, and so forth), is more of “cosmetic” (Diggle, 1985) interest.”
Residual analysis for spatial point processes (with discussion) (2005, methodology): “Clustered models cannot be fitted by using the techniques of Diggle (1990) and Diggle and Rowlingson (1994), which apply only to Poisson processes. Although the model checking techniques in Diggle (1990), section 3.”
Nonparametric estimation of the dependence of a spatial point process on spatial covariates (2012, background): “An exception is the special case of spatial relative risk or spatial residual risk where the covariates are the Cartesian coordinates [12, 13, 25, 38, 43, 44] and/or the time coordinate [28, 57].”
Rings, circles, and null-models for point pattern analysis in ecology (2004, background): “where C(x, y)(R) is a circular moving window with radius R that is centered in cell (x, y). This is basically a kernel estimate with fixed bandwidth R ( Diggle 1985, Bailey and Gatrell 1995).”
On Consistent Nonparametric Intensity Estimation for Inhomogeneous Spatial Point Processes (2008, methodology): “Diggle (1985) and Berman and Diggle (1989) developed data-driven procedures to select the bandwidth.”
Variational Inference for Gaussian Process Modulated Poisson Processes (2014, methodology): “Our kernel smoothing method is similar to standard kernel density estimation except we use truncated normal kernels to account for our explicit knowledge of the domain—the latter is referred to as “end-correction” in some literature (Diggle, 1985).”
Modern Statistics for Spatial Point Processes * (2007, background): “In the inhomogeneous case, a non-parametric kernel estimate is ̂(u)= n∑ i =1 k(u −xi) /∫ W k(v−u) dv (35) where k is a kernel with finite bandwidth, and where the denominator is an edge correction factor ensuring that ∫ W ̂(u) du is an unbiased estimate of (W ) (Diggle, 1985).”
Tractable nonparametric Bayesian inference in Poisson processes with Gaussian process intensities (2009, methodology): “A sum of an exponential and a Gaussian bump: We compared the SGCP to the classical kernel smoothing (KS) approach of Diggle (1985).”
A non-model-based approach to bandwidth selection for kernel estimators of spatial intensity functions (2018, methodology): “The global edge correction factor proposed in Berman & Diggle (1989) and Diggle (1985) corresponds to wh(x, y) = h−d ∫ W κ ( x − u h ) du, whereas the choice of the local factor wh(x, y) = h−d ∫ W κ ( u − y h ) du, suggested in van Lieshout (2012), results in the mass preservation property that∫ W…”
Structured Spatio‐Temporal Shot‐Noise Cox Point Process Models, with a View to Modelling Forest Fires (2010, methodology): “Equations (17) and (18) follow straightforwardly from (11) and (13), or alternatively by using (9) and the Slivnyak-Mecke Theorem.”
On Estimation of the Intensity Function of a Point Process (2011, unknown): “…of specific information on the intensity function λ , it is natural to apply ideas from density estimation theory, as in the classic and widely used Berman– Diggle estimator (Diggle 1985; Berman and Diggle 1989) In the sequel, we assume that the point locations are not subject to measurement error.”
Synergistic effects of ground cover and adjacent vegetation on natural enemies of olive insect pests (2013, methodology): “A bivariate Gaussian kernel density funcion (Diggle, 1985) was computed from the 1 m × 1 m grid and its alue was calculated for each plot in order to obtain a distance eighted measure of the influence of each natural vegetation type n that plot.”
Estimating Second-Order Characteristics of Inhomogeneous Spatio-Temporal Point Processes (2013, methodology): “There is an extensive literature on edge correction for inter-points distancemethods in the spatial case; see for instance Baddeley (1999), Cressie (1993), Diggle (2003), Illian et al.”
Space‐time Multi Type Log Gaussian Cox Processes with a View to Modelling Weeds (2001, background): “However, non-parametric kernel estimators ~ri of ri can be obtained as discussed in Diggle (1985).”