Likelihood inference for unions of interacting discs

Jesper Møller, K. Helisova

Research output: Contribution to journalJournal articleResearchpeer-review

20 Citations (Scopus)

Abstract

This is probably the first paper which discusses likelihood inference for a random set using a germ-grain model, where the individual grains are unobservable, edge effects occur and other complications appear. We consider the case where the grains form a disc process modelled by a marked point process, where the germs are the centres and the marks are the associated radii of the discs. We propose to use a recent parametric class of interacting disc process models, where the minimal sufficient statistic depends on various geometric properties of the random set, and the density is specified with respect to a given marked Poisson model (i.e. a Boolean model). We show how edge effects and other complications can be handled by considering a certain conditional likelihood. Our methodology is illustrated by analysing Peter Diggle's heather data set, where we discuss the results of simulation-based maximum likelihood inference and the effect of specifying different reference Poisson models.
Original languageEnglish
JournalScandinavian Journal of Statistics
Volume37
Issue number3
Pages (from-to)365-381
Number of pages17
ISSN0303-6898
DOIs
Publication statusPublished - 2010

Fingerprint

Likelihood Inference
Edge Effects
Union
Random Sets
Poisson Model
Complications
Marked Point Process
Conditional Likelihood
Boolean Model
Sufficient Statistics
Reference Model
Process Model
Maximum Likelihood
Radius
Methodology
Inference
Simulation
Poisson model
Model

Keywords

  • Boolean model
  • connected component Markov process
  • disc process
  • edge effects
  • germ-grain model
  • quermass-interaction process
  • spatial Markov property
  • simulation-based maximum likelihood
  • summry statistics
  • random closed set

Cite this

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title = "Likelihood inference for unions of interacting discs",
abstract = "This is probably the first paper which discusses likelihood inference for a random set using a germ-grain model, where the individual grains are unobservable, edge effects occur and other complications appear. We consider the case where the grains form a disc process modelled by a marked point process, where the germs are the centres and the marks are the associated radii of the discs. We propose to use a recent parametric class of interacting disc process models, where the minimal sufficient statistic depends on various geometric properties of the random set, and the density is specified with respect to a given marked Poisson model (i.e. a Boolean model). We show how edge effects and other complications can be handled by considering a certain conditional likelihood. Our methodology is illustrated by analysing Peter Diggle's heather data set, where we discuss the results of simulation-based maximum likelihood inference and the effect of specifying different reference Poisson models.",
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Likelihood inference for unions of interacting discs. / Møller, Jesper; Helisova, K.

In: Scandinavian Journal of Statistics, Vol. 37, No. 3, 2010, p. 365-381.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Likelihood inference for unions of interacting discs

AU - Møller, Jesper

AU - Helisova, K.

N1 - Udgivelsesdato: Online 2009

PY - 2010

Y1 - 2010

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AB - This is probably the first paper which discusses likelihood inference for a random set using a germ-grain model, where the individual grains are unobservable, edge effects occur and other complications appear. We consider the case where the grains form a disc process modelled by a marked point process, where the germs are the centres and the marks are the associated radii of the discs. We propose to use a recent parametric class of interacting disc process models, where the minimal sufficient statistic depends on various geometric properties of the random set, and the density is specified with respect to a given marked Poisson model (i.e. a Boolean model). We show how edge effects and other complications can be handled by considering a certain conditional likelihood. Our methodology is illustrated by analysing Peter Diggle's heather data set, where we discuss the results of simulation-based maximum likelihood inference and the effect of specifying different reference Poisson models.

KW - Boolean model

KW - connected component Markov process

KW - disc process

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KW - germ-grain model

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KW - simulation-based maximum likelihood

KW - summry statistics

KW - random closed set

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