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 language | English |
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Journal | Bernoulli |
Volume | 5 |
Issue number | 4 |
Pages (from-to) | 641-658 |
Number of pages | 18 |
ISSN | 1350-7265 |
Publication status | Published - 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