research. While good books on spatial point processes currently exist, this is the first to tackle difficult issues of simulation and simulation-based inference for such processes, including methods based on MCMC and related techniques. As the authors correctly note, as computer power and speed increase, and since analytic expressions for expectations of statistics for complex point process models are often unavailable, simulation-based approaches for spatial point processes should become increasingly important and widespread.Readers will find the text moderately difficult to read. It is about halfway between Brian Ripley's brilliantly simplistic "Spatial Statistics" and the far more theoretical "An Introduction to the Theory of Point Processes" by Daley and Vere-Jones, the latter of which deals little with spatial point processes but is widely (and correctly) considered the indispensable book on point processes in general. While Møller and Waagepetersen's book focuses on important practical topics such as simulation and inference, it is less a manual for applied statistics than a description of key concepts and mathematical results justifying important techniques used in applied research. Considering that the text states most results in their full mathematical precision and includes proofs of key theorems, it is remarkably easy to

We view the locations and times of a collection of crime events as a space-time point pattern. So, with either a nonhomogeneous Pois-son process or with a more general Cox process, we need to specify a space-time intensity. For the latter, we need a random intensity which we model as a realization of a spatio-temporal log Gaussian process. Importantly, we view time as circular not linear, necessitating valid separable and nonseparable covariance functions over a bounded spatial region crossed with circular time. In addition, crimes are classified by crime type. Furthermore, each crime event is recorded by day of the year which we convert to day of the week marks. The contribution here is to develop models to accommodate such data. Our specifications take the form of hierarchical models which we fit within a Bayesian framework. In this regard, we consider model comparison between the nonhomogeneous Poisson process and the log Gaussian Cox process. We also compare separable vs. nonseparable covariance specifications. Our motivating dataset is a collection of crime events for the city of San Francisco during the year 2012. We have location, hour, day of the year, and crime type for each event. We investigate models to enhance our understanding of the set of incidences.

We develop methods for analysing the`interaction' or dependence between points in a spatial point pattern, when the pattern is spatially inhomogeneous. Completely non-parametric study of interactions is possible using an analogue of the K -function. Alternatively one may assume a semi-parametric model in which a (parametrically speci®ed) homogeneous Markov point process is subjected to (non-parametric) inhomogeneous independent thinning. The effectiveness of these approaches is tested on datasets representing the positions of trees in forests.

This article is concerned with inference for a certain class of inhomogeneous Neyman-Scott point processes depending on spatial covariates. Regression parameter estimates obtained from a simple estimating function are shown to be asymptotically normal when the "mother" intensity for the Neyman-Scott process tends to infinity. Clustering parameter estimates are obtained using minimum contrast estimation based on the K-function. The approach is motivated and illustrated by applications to point pattern data from a tropical rain forest plot.

The paper is concerned with parameter estimation for inhomogeneous spatial point processes with a regression model for the intensity function and tractable second-order properties ("K"-function). Regression parameters are estimated by using a Poisson likelihood score estimating function and in the second step minimum contrast estimation is applied for the residual clustering parameters. Asymptotic normality of parameter estimates is established under certain mixing conditions and we exemplify how the results may be applied in ecological studies of rainforests. Copyright (c) 2009 Royal Statistical Society.