A tutorial on Palm distributions for spatial point processes

This tutorial provides an introduction to Palm distributions for spatial point processes. Initially, in the context of finite point processes , we give an explicit definition of Palm distributions in terms of their density functions. Then we review Palm distributions in the general case. Finally we discuss some examples of Palm distributions for specific models and some applications

Palm distributions for log Gaussian Cox processes

This paper establishes a remarkable result regarding Palmdistributions for a log Gaussian Cox process: the reduced Palmdistribution for a log Gaussian Cox process is itself a log Gaussian Coxprocess which only differs from the original log Gaussian Cox processin the intensity function. This new result is used to study functionalsummaries for log Gaussian Cox processes

Markov connected component fields

A new class of Gibbsian models with potentials associated with the connected components or homogeneous parts of images is introduced. The relationship with Markov random fields and marked point processes is explored and spatial Markov properties are established. Further, extensions to infinite lattices are studied. Statistical inference problems including geostatistical applications and statistical image analysis are also discussed. Finally, simulation studies are presented which show that the models may be appropriate for a variety of interesting patterns.</jats:p

Some recent developments in statistics for spatial point patterns

This article reviews developments in statistics for spatial point processes obtained within roughly the past decade. These developments include new classes of spatial point process models such as determinantal point processes, models incorporating both regularity and aggregation, and models where points are randomly distributed around latent geometric structures. Regarding parametric inference, the main focus is on various types of estimating functions derived from so-called innovation measures. Optimality of such estimating functions is discussed, as well as computational issues. Maximum likelihood inference for determinantal point processes and Bayesian inference are also briefly considered. Concerning nonparametric inference, we consider extensions of functional summary statistics to the case of inhomogeneous point processes as well as new approaches to simulation-based inference. </jats:p