1st Edition

# Statistical Inference and Simulation for Spatial Point Processes

318 Pages 45 B/W Illustrations
by Chapman & Hall

Spatial point processes play a fundamental role in spatial statistics and today they are an active area of research with many new applications. Although other published works address different aspects of spatial point processes, most of the classical literature deals only with nonparametric methods, and a thorough treatment of the theory and applications of simulation-based inference is difficult to find. Written by researchers at the top of the field, this book collects and unifies recent theoretical advances and examples of applications. The authors examine Markov chain Monte Carlo algorithms and explore one of the most important recent developments in MCMC: perfect simulation procedures.

EXAMPLES OF SPATIAL POINT PATTERNS
INTRODUCTION TO POINT PROCESSES
Point Processes on R^d
Marked Point Processes and Multivariate Point Processes
Unified Framework
Space-Time Processes
POISSON POINT PROCESSES
Basic Properties
Further Results
Marked Poisson Processes
SUMMARY STATISTICS
First and Second Order Properties
Summary Statistics
Nonparametric Estimation
Summary Statistics for Multivariate Point Processes
Summary Statistics for Marked Point Processes
COX PROCESSES
Definition and Simple Examples
Basic Properties
Neyman-Scott Processes as Cox Processes
Shot Noise Cox Processes
Approximate Simulation of SNCPs
Log Gaussian Cox Processes
Simulation of Gaussian Fields and LGCPs
Multivariate Cox Processes
MARKOV POINT PROCESSES
Finite Point Processes with a Density
Pairwise Interaction Point Processes
Markov Point Processes
Extensions of Markov Point Processes to R^d
Inhomogeneous Markov Point Processes
Marked and Multivariate Markov Point Processes
METROPOLIS-HASTINGS ALGORITHMS
Description of Algorithms
Background Material for Markov Chains
Convergence Properties of Algorithms
SIMULATION-BASED INFERENCE
Monte Carlo Methods and Output Analysis
Estimation of Ratios of Normalising Constants
Approximate Likelihood Inference Using MCMC
Monte Carlo Error
Distribution of Estimates and Hypothesis Tests
Approximate MissingData Likelihoods
INFERENCE FOR MARKOV POINT PROCESSES
Maximum Likelihood Inference
Pseudo Likelihood
Bayesian Inference
INFERENCE FOR COX PROCESSES
Minimum Contrast Estimation
Conditional Simulation and Prediction
Maximum Likelihood Inference
Bayesian Inference
BIRTH-DEATH PROCESSES AND PERFECT SIMULATION
Spatial Birth-Death Processes
Perfect Simulation
APPENDICES
History, Bibliography, and Software
Measure Theoretical Details
Moment Measures and Palm Distributions
Perfect Simulation of SNCPs
Simulation of Gaussian Fields
Nearest-Neighbour Markov Point Processes
Results for Spatial Birth-Death Processes
References
Subject Index
Notation Index

### Biography

Jesper Moller

"This book is an extremely well-written summary of important topics in the analysis of spatial point processes. … The authors do an excellent job focusing on those theoretical concepts and methods that are most important in applied research. Although other good books on spatial point processes are available, this is the first text to tackle difficult issues of simulation-based inference for such processes … . [T]he text … is remarkably easy to follow. … The authors have a very impressive knack for explaining complicated topics very clearly … . [This book] will no doubt prove an outstanding resource for researchers and students … Its excellent survey of the vast array of models is reason enough to own it. As computer technology and speed advance … the authors' clear, detailed, and comprehensive survey of simulation methods for spatial point processes will become increasingly important."
- Journal of the American Statistical Association

"… [T]his monograph is a well-written and concisely presented journey through the primary types of spatial point process frameworks. There is a useful equal balance between theoretical development and inference centred on simulation-based methods. … This volume would be well suited for library purchase. … [A] worthwhile investment."
- Journal of the Royal Statistics Society

"The book is very well organized and clearly written. It provides both an introduction and a review of the subject in a very condensed form. Thus it is an excellent support for a systematic approach to and an orientation for the current extensive literature with its different branches."
-Mathematical Reviews Issue 2004

"This book provides an excellent and up-to-date review of developments in this area. It covers most, if not all, of the major classes of models, and discusses methods for their approximate and exact simulation."
-ISI Short Book Reviews, Aug 04

"The book is a landmark in the development of point process statistics and sets standards in its field. It will be the key reference for all which is related to simulation in point process statistics."
- Dietrich Stoyan, Institut für Stochastik, Begakademie, Freiberg, Germany, in Statistics in Medicine, 2004

"Well and clearly written…self-contained…accessible to a wide audience."
-Zentralblatt MATH 1044