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