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Simulation of cluster point processes without edge effects

Part of: Multivariate analysis Stochastic processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Anders Brix  and
Wilfrid S. Kendall
Anders Brix*
Affiliation:
Risk Management Solutions Ltd
Wilfrid S. Kendall*
Affiliation:
University of Warwick
*
∗ Postal address: Risk Management Solutions Ltd, 10 Eastcheap, London EC3N 1AJ, UK. Email address: [email protected]
∗∗ Postal address: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK.
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Abstract

The usual direct method of simulation for cluster processes requires the generation of the parent point process over a region larger than the actual observation window, since we have to allow for all possible parents giving rise to observed daughter points, and some of these parents may fall outwith the observation window. When there is no a priori bound on the distance between parent and child then we have to take care to control approximations arising from edge effects. In this paper, we present a simulation method which requires simulation only of those parent points actually giving rise to observed daughter points, thus avoiding edge effect approximation. The idea is to replace the cluster distribution by one which is conditioned to plant at least one daughter point in the observation window, and to modify the parent process to have an inhomogeneous intensity exactly balancing the effect of the conditioning. We furthermore show how the method extends to cases involving infinitely many potential parents, for example gamma-Poisson processes and shot-noise G-Cox processes, allowing us to avoid approximation due to truncation of the parent process.

Keywords

Cox processshot-noise processgamma-Poisson process

MSC classification

Primary: 60G55: Point processes
Secondary: 60D05: Geometric probability and stochastic geometry 62H11: Directional data; spatial statistics
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 34 , Issue 2 , June 2002 , pp. 267 - 280
Copyright
Copyright © Applied Probability Trust 2002 

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