Open Access
August 2020 Perfect sampling for Gibbs point processes using partial rejection sampling
Sarat B. Moka, Dirk P. Kroese
Bernoulli 26(3): 2082-2104 (August 2020). DOI: 10.3150/19-BEJ1184


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.


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Sarat B. Moka. Dirk P. Kroese. "Perfect sampling for Gibbs point processes using partial rejection sampling." Bernoulli 26 (3) 2082 - 2104, August 2020.


Received: 1 March 2019; Revised: 1 August 2019; Published: August 2020
First available in Project Euclid: 27 April 2020

zbMATH: 07193953
MathSciNet: MR4091102
Digital Object Identifier: 10.3150/19-BEJ1184

Keywords: area-interaction process , hard-core process , pairwise interaction process , partial-rejection sampling , penetrable spheres mixture model , perfect sampling , Strauss process

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 3 • August 2020
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