Thinning spatial point processes into Poisson processes

Jesper Møller, Frederic Paik Schoenberg

Research output: Contribution to journalJournal articleResearchpeer-review

6 Citations (Scopus)

Abstract

In this paper we describe methods for randomly thinning certain classes of spatial point processes. In the case of a Markov point process, the proposed method involves a dependent thinning of a spatial birth-and-death process, where clans of ancestors associated with the original points are identified, and where we simulate backwards and forwards in order to obtain the thinned process. In the case of a Cox process, a simple independent thinning technique is proposed. In both cases, the thinning results in a Poisson process if and only if the true Papangelou conditional intensity is used, and, thus, can be used as a graphical exploratory tool for inspecting the goodness-of-fit of a spatial point process model. Several examples, including clustered and inhibitive point processes, are considered.
Original languageEnglish
JournalAdvances in Applied Probability
Volume42
Issue number2
Pages (from-to)347-358
Number of pages12
ISSN0001-8678
DOIs
Publication statusPublished - Jun 2010

Fingerprint

Spatial Point Process
Thinning
Poisson process
Point Process
Cox Process
Birth and Death Process
Spatial Process
Goodness of fit
Markov Process
Process Model
If and only if
Dependent

Keywords

  • area-interaction point process
  • Cox process
  • dependent and independent thinning
  • Markov point process
  • Papangelou conditional intensity
  • Poisson process
  • Thomas process

Cite this

Møller, Jesper ; Schoenberg, Frederic Paik. / Thinning spatial point processes into Poisson processes. In: Advances in Applied Probability. 2010 ; Vol. 42, No. 2. pp. 347-358.
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Thinning spatial point processes into Poisson processes. / Møller, Jesper; Schoenberg, Frederic Paik.

In: Advances in Applied Probability, Vol. 42, No. 2, 06.2010, p. 347-358.

Research output: Contribution to journalJournal articleResearchpeer-review

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