Perfect sampling for Gibbs point processes using partial rejection sampling

Abstract

We present a perfect sampling algorithm for Gibbs point processes, based on the partial rejection sampling of Guo, Jerrum and Liu (In STOC’17 – Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing (2017) 342–355 ACM). Our particular focus is on pairwise interaction processes, penetrable spheres mixture models and area-interaction processes, with a finite interaction range. For an interaction range $2r$ of the target process, the proposed algorithm can generate a perfect sample with $O(\log(1/r))$ expected running time complexity, provided that the intensity of the points is not too high and $\Theta(1/r^{d})$ parallel processor units are available.