Perfect sampling for Gibbs point processes using partial rejection sampling

Sarat B. Moka, Dirk P. Kroese

Research output: Contribution to journalArticlepeer-review

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 Θ(1/rd) parallel processor units are available.

Original languageEnglish
Pages (from-to)2082-2104
Number of pages23
JournalBernoulli
Volume26
Issue number3
DOIs
Publication statusPublished - Aug 2020
Externally publishedYes

Keywords

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

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