Rolf Turner

TL;DR: This paper is a general description of spatstat and an introduction for new users.

TL;DR: Point patterns Statistical methodology for point patterns Statistical inference for Poisson models Alternative fitting methods More flexible models Theory Coarse quadrature approximation Fine pixel approximation Conditional logistic regression Approximate Bayesian inference Non-loglinear models Local likelihood FAQ Hypothesis Tests and Simulation Envelopes Introduction concepts and terminology.

Abstract: Summary This paper describes a technique for computing approximate maximum pseudolikelihood estimates of the parameters of a spatial point process. The method is an extension of Berman & Turner’s (1992) device for maximizing the likelihoods of inhomogeneous spatial Poisson processes. For a very wide class of spatial point process models the likelihood is intractable, while the pseudolikelihood is known explicitly, except for the computation of an integral over the sampling region. Approximation of this integral by a finite sum in a special way yields an approximate pseudolikelihood which is formally equivalent to the (weighted) likelihood of a loglinear model with Poisson responses. This can be maximized using standard statistical software for generalized linear or additive models, provided the conditional intensity of the process takes an ‘exponential family’ form. Using this approach a wide variety of spatial point process models of Gibbs type can be fitted rapidly, incorporating spatial trends, interaction between points, dependence on spatial covariates, and mark information.

TL;DR: In this paper, the authors define residuals for point process models fitted to spatial point pattern data, and propose diagnostic plots based on them, which apply to any point process model that has a conditional intensity and may exhibit spatial heterogeneity, interpoint interaction and dependence on spatial covariates.

TL;DR: In this paper, the authors describe a technique for computing approximate maximum pseudolikelihood estimates of the parameters of a spatial point process, which is an extension of Berman and Turner's device for maximising the likelihoods of inhomogeneous spatial Poisson processes.