Likelihood Inference for Unions of Interacting Discs

作者：Moller Jesper^*; Helisova Katerina

来源：Scandinavian Journal of Statistics, 2010, 37(3): 365-381.

DOI：10.1111/j.1467-9469.2009.00660.x

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

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.

• 出版日期2010-9