About: Estimation of the Intensity Parameter of the Germ-Grain Quermass-Interaction Model when the Number of Germs is not Observed

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	The Quermass-interaction model allows to generalize the classical germ-grain Boolean model in adding a morphological interaction between the grains. It enables to model random structures with specific morphologies, which are unlikely to be generated from a Boolean model. The Quermass-interaction model depends in particular on an intensity parameter, which is impossible to estimate from classical likelihood or pseudo-likelihood approaches because the number of points is not observable from a germ-grain set. In this paper, we present a procedure based on the Takacs–Fiksel method, which is able to estimate all parameters of the Quermass-interaction model, including the intensity. An intensive simulation study is conducted to assess the efficiency of the procedure and to provide practical recommendations. It also illustrates that the estimation of the intensity parameter is crucial in order to identify the model. The Quermass-interaction model is finally fitted by our method to P. Diggle’s heather data set. The Quermass-interaction model allows to generalize the classical germ-grain Boolean model in adding a morphological interaction between the grains. It enables to model random structures with specific morphologies, which are unlikely to be generated from a Boolean model. The Quermass-interaction model depends in particular on an intensity parameter, which is impossible to estimate from classical likelihood or pseudo-likelihood approaches because the number of points is not observable from a germ-grain set. In this paper, we present a procedure based on the Takacs–Fiksel method, which is able to estimate all parameters of the Quermass-interaction model, including the intensity. An intensive simulation study is conducted to assess the efficiency of the procedure and to provide practical recommendations. It also illustrates that the estimation of the intensity parameter is crucial in order to identify the model. The Quermass-interaction model is finally fitted by our method to P. Diggle’s heather data set. (en)
Title	Estimation of the Intensity Parameter of the Germ-Grain Quermass-Interaction Model when the Number of Germs is not Observed Estimation of the Intensity Parameter of the Germ-Grain Quermass-Interaction Model when the Number of Germs is not Observed (en)
skos:prefLabel	Estimation of the Intensity Parameter of the Germ-Grain Quermass-Interaction Model when the Number of Germs is not Observed Estimation of the Intensity Parameter of the Germ-Grain Quermass-Interaction Model when the Number of Germs is not Observed (en)
skos:notation	RIV/68407700:21230/14:00222636!RIV15-GA0-21230___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GP13-05466P)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Staňková Helisová, Kateřina
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	České vysoké učení technické v Praze / Fakulta elektrotechnická
http://linked.open...dnocenehoVysledku	15075
http://linked.open...ai/riv/idVysledku	RIV/68407700:21230/14:00222636
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Area-Interaction Process; Germ-Grain Model; Gibbs Point Process; Perimeter Interaction Process; Quermass-Interaction Process; Takacs–Fiksel Estimator (en)
http://linked.open.../riv/klicoveSlovo	Area-Interaction Process Germ-Grain Model Gibbs Point Process Perimeter Interaction Process Quermass-Interaction Process Takacs–Fiksel Estimator
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[218D55C0EC36]
http://linked.open...i/riv/nazevZdroje	Scandinavian Journal of Statistics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Stochastické modelování a statistická analýza náhodných množin
http://linked.open...UplatneniVysledku	2014
http://linked.open...v/svazekPeriodika	41
http://linked.open...iv/tvurceVysledku	Helisová, Kateřina Dereudre, D. Lavancier, F.
http://linked.open...ain/vavai/riv/wos	000340493800014
issn	0303-6898
number of pages	21 (xsd:int)
http://bibframe.org/vocab/doi	10.1111/sjos.12064
http://localhost/t...ganizacniJednotka	21230

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