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august 1999 Characterization results and Markov chain Monte Carlo algorithms including exact simulation for some spatial point processes
Olle Häggström,, Marie-Colette N.M. Van Lieshout, Jesper Møller
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Bernoulli 5(4): 641-658 (august 1999).

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.

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Olle Häggström,. Marie-Colette N.M. Van Lieshout. Jesper Møller. "Characterization results and Markov chain Monte Carlo algorithms including exact simulation for some spatial point processes." Bernoulli 5 (4) 641 - 658, august 1999.

Information

Published: august 1999
First available in Project Euclid: 19 February 2007

zbMATH: 0981.65012
MathSciNet: MR1704559

Keywords: 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

Rights: Copyright © 1999 Bernoulli Society for Mathematical Statistics and Probability

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Vol.5 • No. 4 • august 1999
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