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August 2012 Spatial birth–death swap chains
Mark Huber
Bernoulli 18(3): 1031-1041 (August 2012). DOI: 10.3150/10-BEJ350


Markov chains have long been used for generating random variates from spatial point processes. Broadly speaking, these chains fall into two categories: Metropolis–Hastings type chains running in discrete time and spatial birth–death chains running in continuous time. These birth–death chains only allow for removal of a point or addition of a point. In this paper it is shown that the addition of transitions where a point is moved from one location to the other can aid in shortening the mixing time of the chain. Here the mixing time of the chain is analyzed through coupling, and use of the swap moves allows for analysis of a broader class of chains. Furthermore, these swap moves can be employed in perfect sampling algorithms via the dominated coupling from the past procedure of Kendall and Møller. This method can be applied to any pairwise interaction model with repulsion. In particular, an application to the Strauss process is developed in detail, and the swap chains are shown to be much faster than standard birth–death chains.


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Mark Huber. "Spatial birth–death swap chains." Bernoulli 18 (3) 1031 - 1041, August 2012.


Published: August 2012
First available in Project Euclid: 28 June 2012

zbMATH: 1254.60080
MathSciNet: MR2948911
Digital Object Identifier: 10.3150/10-BEJ350

Rights: Copyright © 2012 Bernoulli Society for Mathematical Statistics and Probability


Vol.18 • No. 3 • August 2012
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