Likelihood Inference for Unions of Interacting Discs
本文首次利用胚芽-颗粒模型对随机集进行似然推断，其中单个颗粒不可观测且存在边缘效应，通过条件似然处理复杂情况，并用模拟最大似然分析石楠数据。
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.