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Perfect simulation using dominating processes on ordered spaces, with application to locally stable point processes

  • Wilfrid S. Kendall (a1) and Jesper Møller (a2)
Abstract

In this paper we investigate the application of perfect simulation, in particular Coupling from the Past (CFTP), to the simulation of random point processes. We give a general formulation of the method of dominated CFTP and apply it to the problem of perfect simulation of general locally stable point processes as equilibrium distributions of spatial birth-and-death processes. We then investigate discrete-time Metropolis-Hastings samplers for point processes, and show how a variant which samples systematically from cells can be converted into a perfect version. An application is given to the Strauss point process.

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Corresponding author
Postal address: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK. Email address: wsk@stats.warwick.ac.uk
∗∗ Postal address: Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7E, DK-9220 Aalborg, Denmark. Email address: jm@math.auc.dk
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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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