TY - RPRT
T1 - Likelihood inference for unions of interacting discs
AU - Møller, Jesper
AU - Helisová, Katarina
PY - 2008
Y1 - 2008
N2 - To the best of our knowledge, this is the first paper which discusses likelihood inference or 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 analyzing Peter Diggle's heather dataset, where we discuss the results of simulation-based maximum likelihood inference and the effect of specifying different reference Poisson models.
AB - To the best of our knowledge, this is the first paper which discusses likelihood inference or 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 analyzing Peter Diggle's heather dataset, where we discuss the results of simulation-based maximum likelihood inference and the effect of specifying different reference Poisson models.
M3 - Report
T3 - Research Report Series
BT - Likelihood inference for unions of interacting discs
PB - Department of Mathematical Sciences, Aalborg University
CY - Aalborg
ER -