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MaPhySto
Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 1999-11
March 1999




Perfect Metropolis-Hastings simulation of locally stable point processes

by:

Jesper Møller

Wilfrid S. Kendall

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 MetropolisHastings 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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This paper has now been published in Has appeared in revised form as Perfect simulation using dominating processes as ordered spaces, with application to locally stable point processes. Adv. Appl. Prob., 32, 844-865 (2000)