Properties of residuals for spatial point processes

Abstract

Distributional equivalence, Georgii-Nguyen-Zessin formula, Gibbs point process, Set-indexed martingale, Papangelou conditional intensity, Pearson residuals, Scan statistic, Smoothed residual field,

Nonparametric estimation of the dependence of a spatial point process on spatial covariates

“…For a general point process, the variance of the kernel estimators can be expressed in terms of the intensity and pair correlation function of the point process, using the second order Campbell formula, e.g. [6,33]. If the point process is regular (negatively associated) then the Poisson assumption leads to overestimates of the variance ofρ, and conservative confidence intervals.…”

Almost sure behavior of functionals of stationary Gibbs point processes

“…(a) The functional G W corresponds to the concept of innovations of a spatial point process, introduced by Baddeley et al (2005Baddeley et al ( , 2008. This functional plays a fundamental role in parametric estimation procedures as well as in procedures to judge the quality of a model.…”

“…Møller and Waagepetersen, 2004). Functionals of Gibbs point processes of the form L h − R h have been considered in Baddeley et al (2005Baddeley et al ( , 2008 and in Coeurjolly and Lavancier (2013). Correctly renormalized, such functionals have been shown to converge almost surely to zero as the window of observation expands to R d .…”

Filaments in observed and mock galaxy catalogues

“…Still, although quite simple, this definition allows us a general treatement using marked point processes. Very recent work in marked point process literature presents methodological ideas leading to statistical model validation (Baddeley et al 2005(Baddeley et al , 2008. This gives hope and perspective to incorporate these ideas into our method.…”