Brix, Anders and Kendall, W. S. (2002) Simulation of cluster point processes without edge effects. Advances in Applied Probability, Vol.34 (No.2). pp. 267-280. doi:10.1239/aap/1025131217 ISSN 0001-8678.

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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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH):	Cluster analysis
Journal or Publication Title:	Advances in Applied Probability
Publisher:	Applied Probability Trust
ISSN:	0001-8678
Official Date:	June 2002
Dates:	Date Event June 2002 Published
Volume:	Vol.34
Number:	No.2
Number of Pages:	14
Page Range:	pp. 267-280
DOI:	10.1239/aap/1025131217
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC), European Union (EU), European Science Foundation (ESF)
Grant number:	GR/L56831 (EPSRC), GR/M75785 (EPSRC), ERB-FMRXCT96-0095 (EU)

Data sourced from Thomson Reuters' Web of Knowledge

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