Statistical Inference and Simulation for Spatial Point Processes (Hardcover)

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