Perfect simulation of spatial point processes using dominated coupling from the past with application to a multiscale area-interaction point process

2009/03/15 by Graeme K. Ambler, Ambler, Graeme K., Bernard W. Silverman +1 · 1 citation
Mathematics · #Applications (stat.AP) #Computation (stat.CO) #FOS: Computer and information sciences #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Point processes and geometric inequalities #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0903.2651

openalex publication_date 2009/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider perfect simulation algorithms for locally stable point processes based on dominated coupling from the past. A version of the algorithm is developed which is feasible for processes which are neither purely attractive nor purely repulsive. Such processes include multiscale area-interaction processes, which are capable of modelling point patterns whose clustering structure varies across scales. We prove correctness of the algorithm and existence of these processes. An application to the redwood seedlings data is discussed.

Cited by

• Perfect simulation for Bayesian wavelet thresholding with correlated coefficients

Related

• Perfect simulation using dominated coupling from the past with application to area-interaction point processes and wavelet thresholding
• Coupling methods for efficient simulation of spatial population dynamics
• Detecting multivariate interactions in spatial point patterns with Gibbs models and variable selection
• Modelling aggregation on the large scale and regularity on the small scale in spatial point pattern datasets
• Approximate Bayesian Computation and Model Validation for Repulsive Spatial Point Processes