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.
Publié le : 1999-08-14
Classification:
area-interaction process,
continuum random-cluster model,
exact simulation,
Gibbs sampling,
Markov chain Monte Carlo,
nearest-neighbour Markov point processes,
Papangelou conditional intensity,
penetrable sphere model,
phase transition,
spatial point processes,
Swendsen-Wang algorithm,
Widom-Rowlinson mixture model
@article{1171899321,
author = {H\"aggstr\"om,, Olle and Van Lieshout, Marie-Colette N.M. and M\o ller, Jesper},
title = {Characterization results and Markov chain Monte Carlo algorithms including exact simulation for some spatial point processes},
journal = {Bernoulli},
volume = {5},
number = {6},
year = {1999},
pages = { 641-658},
language = {en},
url = {http://dml.mathdoc.fr/item/1171899321}
}
Häggström,, Olle; Van Lieshout, Marie-Colette N.M.; Møller, Jesper. Characterization results and Markov chain Monte Carlo algorithms including exact simulation for some spatial point processes. Bernoulli, Tome 5 (1999) no. 6, pp. 641-658. http://gdmltest.u-ga.fr/item/1171899321/