Statistical Inference and Simulation for Spatial Point Processes

Statistical Inference and Simulation for Spatial Point Processes

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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.show more

Product details

  • Hardback | 320 pages
  • 154.94 x 231.14 x 22.86mm | 521.63g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 45 black & white illustrations
  • 1584882654
  • 9781584882657
  • 2,389,606

Review quote

"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. Itcovers 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." - Statistics in Medicine, 2004 "Well and clearly writtenself-containedaccessible to a wide audience." -Zentralblatt MATH 1044show more

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 Indexshow more

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