About: On the Use of Particle Markov Chain Monte Carlo in Parameter Estimation of Space-Time Interacting Discs

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About: On the Use of Particle Markov Chain Monte Carlo in Parameter Estimation of Space-Time Interacting Discs Goto Sponge NotDistinct Permalink

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Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://link.springer.com/article/10.1007/s11009-013-9367-2
Description	A space-time random set is defined and methods of its parameters estimation are investigated. The evolution in discrete time is described by a state-space model. The observed output is a planar union of interacting discs given by a probability density with respect to a reference Poisson process of discs. The state vector is to be estimated together with auxiliary parameters of transitions caused by a random walk. Three methods of parameters estimation are involved, first of which is the maximum likelihood estimation (MLE) for individual outputs at fixed times. In the space-time model the state vector can be estimated by the particle filter (PF), where MLE serves to the estimation of auxiliary parameters. In the present paper the aim is to compare MLE and PF with particle Markov chain Monte Carlo (PMCMC). From the group of PMCMC methods we use specially the particle marginal Metropolis-Hastings (PMMH) algorithm which updates simultaneously the state vector and the auxiliary parameters. A simulation study is presented in which all estimators are compared by means of the integrated mean square error. New data are then simulated repeatedly from the model with parameters estimated by PMMH and the fit with the original model is quantified by means of the spherical contact distribution function. A space-time random set is defined and methods of its parameters estimation are investigated. The evolution in discrete time is described by a state-space model. The observed output is a planar union of interacting discs given by a probability density with respect to a reference Poisson process of discs. The state vector is to be estimated together with auxiliary parameters of transitions caused by a random walk. Three methods of parameters estimation are involved, first of which is the maximum likelihood estimation (MLE) for individual outputs at fixed times. In the space-time model the state vector can be estimated by the particle filter (PF), where MLE serves to the estimation of auxiliary parameters. In the present paper the aim is to compare MLE and PF with particle Markov chain Monte Carlo (PMCMC). From the group of PMCMC methods we use specially the particle marginal Metropolis-Hastings (PMMH) algorithm which updates simultaneously the state vector and the auxiliary parameters. A simulation study is presented in which all estimators are compared by means of the integrated mean square error. New data are then simulated repeatedly from the model with parameters estimated by PMMH and the fit with the original model is quantified by means of the spherical contact distribution function. (en)
Title	On the Use of Particle Markov Chain Monte Carlo in Parameter Estimation of Space-Time Interacting Discs On the Use of Particle Markov Chain Monte Carlo in Parameter Estimation of Space-Time Interacting Discs (en)
skos:prefLabel	On the Use of Particle Markov Chain Monte Carlo in Parameter Estimation of Space-Time Interacting Discs On the Use of Particle Markov Chain Monte Carlo in Parameter Estimation of Space-Time Interacting Discs (en)
skos:notation	RIV/68407700:21230/14:00222638!RIV15-MSM-21230___
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GAP201/10/0472)
http://linked.open...iv/cisloPeriodika	2
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	34533
http://linked.open...ai/riv/idVysledku	RIV/68407700:21230/14:00222638
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Model with Interacting Discs; Particle Metropolis-Hastings Algorithm; Spherical Contact Distribution Function (en)
http://linked.open.../riv/klicoveSlovo	Model with Interacting Discs Particle Metropolis-Hastings Algorithm Spherical Contact Distribution Function
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[655DE3F0E550]
http://linked.open...i/riv/nazevZdroje	METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY
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	Stochastic geometry - inhomogeneity, marking, dynamics and stereology
http://linked.open...UplatneniVysledku	2014
http://linked.open...v/svazekPeriodika	16
http://linked.open...iv/tvurceVysledku	Beneš, V. Helisová, Kateřina Zikmundová, M.
http://linked.open...ain/vavai/riv/wos	000335508800013
issn	1387-5841
number of pages	13 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/s11009-013-9367-2
http://localhost/t...ganizacniJednotka	21230

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