Adrian Baddeley

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

TL;DR: ‘Vertical’ sections are plane sections longitudinal to a fixed (but arbitrary) axial direction that can be generated by placing the object on a table and taking sections perpendicular to the plane of the table.

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.

TL;DR: In this article, the authors develop methods for analysing the interaction or dependence between points in a spatial point pattern, when the pattern is spatially inhomogeneous, using an analogue of the K-function.

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.