Perfect simulation using dominated coupling from the past with application to area-interaction point processes and wavelet thresholding

TL;DR

This paper develops perfect simulation algorithms for complex point processes and applies them to model multiscale clustering in point patterns and dependencies in wavelet coefficients for improved nonparametric regression.

Contribution

It introduces a new perfect simulation algorithm for locally stable point processes that are neither purely attractive nor repulsive, including multiscale area-interaction processes.

Findings

Feasible simulation for complex point processes with varying clustering.

Improved wavelet coefficient modeling using area-interaction processes.

Promising results in nonparametric regression with dependent wavelet coefficients.

Abstract

We consider perfect simulation algorithms for locally stable point processes based on dominated coupling from the past, and apply these methods in two different contexts. A new 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. The other topic considered is nonparametric regression using wavelets, where we use a suitable area-interaction process on the discrete space of indices of wavelet coefficients to model the notion that if one wavelet coefficient is non-zero then it is more likely that neighbouring coefficients will be also. A method based on perfect simulation within this model shows promising results compared to the standard methods which threshold coefficients independently.