Generating from the Strauss Process using stitching

TL;DR

This paper introduces Acceptance Rejection Stitching, a novel and efficient method for simulating Strauss processes with high interaction parameters, outperforming existing techniques in speed and scalability.

Contribution

The paper presents a new stitching-based acceptance rejection method that significantly improves simulation efficiency for Strauss processes with large interaction parameters.

Findings

Acceptance Rejection Stitching is faster than existing methods.

It enables simulation of Strauss processes with higher λ values.

The method scales well with increased process complexity.

Abstract

The STrauss process is a point process with unnormalized density with respect to a Poisson point process, where each pair of points within a specified distance $r$ of each other contributes a factor $\lambda \in (0, 1)$ to the density. Basic Acceptance Rejection works spectacularly poorly for this problem, which is why several other perfect simulation methods have been developed. these methods, however, also work poorly for reasonably large values of $\lambda$. *Acceptance Rejection Stitching* is a new method that works much faster, allowing the simulation of point processes with values of $\lambda$ much larger than ever before.