Statistical Inference and Simulation for Spatial Point Processes: 1st Edition (Hardback) book cover

Statistical Inference and Simulation for Spatial Point Processes

1st Edition

By Jesper Moller, Rasmus Plenge Waagepetersen

Chapman and Hall/CRC

320 pages | 45 B/W Illus.

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Hardback: 9781584882657
pub: 2003-09-25
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Description

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.

Reviews

"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

Table of Contents

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

About the Series

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General
MAT029010
MATHEMATICS / Probability & Statistics / Bayesian Analysis