Perfect simulation and moment properties for the Matérn type III process

Jesper Møller, Mark L. Huber, Robert L. Wolpert

Research output: Contribution to journalJournal articleResearchpeer-review

21 Citations (Scopus)

Abstract

In a seminal work, Bertil Matérn introduced several types of processes for modeling repulsive point processes. In this paper an algorithm is presented for the perfect simulation of the Matérn III process within a bounded window in , fully accounting for edge effects. A simple upper bound on the mean time needed to generate each point is computed when interaction between points is characterized by balls of fixed radius R. This method is then generalized to handle interactions resulting from use of random grains about each point. This includes the case of random radii as a special case. In each case, the perfect simulation method is shown to be provably fast, making it a useful tool for analysis of such processes.
Original languageEnglish
JournalStochastic Processes and Their Applications
Volume120
Issue number11
Pages (from-to)2142-2158
Number of pages17
ISSN0304-4149
DOIs
Publication statusPublished - 2010

Fingerprint

Perfect Simulation
Moment
Radius
Edge Effects
Point Process
Interaction
Simulation Methods
Ball
Upper bound
Modeling

Keywords

  • cluster size
  • dependent thinning
  • hard core point process
  • packing density
  • random sequential adsorption model

Cite this

Møller, Jesper ; Huber, Mark L. ; Wolpert, Robert L. / Perfect simulation and moment properties for the Matérn type III process. In: Stochastic Processes and Their Applications. 2010 ; Vol. 120, No. 11. pp. 2142-2158.
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Perfect simulation and moment properties for the Matérn type III process. / Møller, Jesper; Huber, Mark L. ; Wolpert, Robert L.

In: Stochastic Processes and Their Applications, Vol. 120, No. 11, 2010, p. 2142-2158.

Research output: Contribution to journalJournal articleResearchpeer-review

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T1 - Perfect simulation and moment properties for the Matérn type III process

AU - Møller, Jesper

AU - Huber, Mark L.

AU - Wolpert, Robert L.

PY - 2010

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N2 - In a seminal work, Bertil Matérn introduced several types of processes for modeling repulsive point processes. In this paper an algorithm is presented for the perfect simulation of the Matérn III process within a bounded window in , fully accounting for edge effects. A simple upper bound on the mean time needed to generate each point is computed when interaction between points is characterized by balls of fixed radius R. This method is then generalized to handle interactions resulting from use of random grains about each point. This includes the case of random radii as a special case. In each case, the perfect simulation method is shown to be provably fast, making it a useful tool for analysis of such processes.

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KW - cluster size

KW - dependent thinning

KW - hard core point process

KW - packing density

KW - random sequential adsorption model

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DO - 10.1016/j.spa.2010.06.002

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