Characterization results and Markov chain Monte Carlo algorithms including exact simulation for some spatial point processes

Olle Häggström*, Marie-Colette van Lieshout, Jesper Møller

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

55 Citations (Scopus)

Abstract

The area-interaction process and the continuum random-cluster model are characterized in terms of certain functional forms of their respective conditional intensities. In certain cases, these two point process models can be derived from a bivariate point process model which in many respects is simpler to analyse and simulate. Using this correspondence we devise a two-component Gibbs sampler, which can be used for fast and exact simulation by extending the recent ideas of Propp and Wilson. We further introduce a Swendsen-Wang type algorithm. The relevance of the results within spatial statistics as well as statistical physics is discussed.

Original languageEnglish
JournalBernoulli
Volume5
Issue number4
Pages (from-to)641-658
Number of pages18
ISSN1350-7265
Publication statusPublished - 1999

Keywords

  • Area-interaction process
  • Continuum random-cluster model
  • Exact simulation
  • Gibbs sampling
  • Markov chain Monte Carlo
  • Nearest-neighbour Markov point process
  • Papangelou conditional intensity

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