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

Part of: Special processes Inference from stochastic processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Wilfrid S. Kendall  and
Jesper Møller
Wilfrid S. Kendall*
Affiliation:
University of Warwick
Jesper Møller*
Affiliation:
Aalborg University
*
∗ 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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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.

Keywords

Coupling from the Past (CFTP)dominated CFTPexact simulationlocal stabilityMarkov chain Monte CarloMetropolis-Hastingsperfect simulationPapangelou conditional intensityrealizable monotonicityspatial birth-and-death processspatial point processstochastic monotonicityStrauss process

MSC classification

Primary: 62M30: Spatial processes 60G55: Point processes 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 32 , Issue 3 , September 2000 , pp. 844 - 865
Copyright
Copyright © Applied Probability Trust 2000 

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