#### Get Citation

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

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

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

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

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

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