### Abstract

Original language | English |
---|---|

Journal | Scandinavian Journal of Statistics |

Volume | 37 |

Issue number | 3 |

Pages (from-to) | 365-381 |

Number of pages | 17 |

ISSN | 0303-6898 |

DOIs | |

Publication status | Published - 2010 |

### Fingerprint

### 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

*Scandinavian Journal of Statistics*,

*37*(3), 365-381. https://doi.org/10.1111/j.1467-9469.2009.00660.x

}

*Scandinavian Journal of Statistics*, vol. 37, no. 3, pp. 365-381. https://doi.org/10.1111/j.1467-9469.2009.00660.x

**Likelihood inference for unions of interacting discs.** / Møller, Jesper; Helisova, K.

Research output: Contribution to journal › Journal article › Research › peer-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

N2 - 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.

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

KW - edge effects

KW - germ-grain model

KW - quermass-interaction process

KW - spatial Markov property

KW - simulation-based maximum likelihood

KW - summry statistics

KW - random closed set

U2 - 10.1111/j.1467-9469.2009.00660.x

DO - 10.1111/j.1467-9469.2009.00660.x

M3 - Journal article

VL - 37

SP - 365

EP - 381

JO - Scandinavian Journal of Statistics

JF - Scandinavian Journal of Statistics

SN - 0303-6898

IS - 3

ER -