Periodic version of the minimax distance criterion for Monte Carlo integration

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dc.contributor.authorEliáš, Jancs
dc.contributor.authorVořechovský, Miroslavcs
dc.contributor.authorSadílek, Václavcs
dc.coverage.issue1cs
dc.coverage.volume149cs
dc.date.issued2020-11-01cs
dc.description.abstractThe selection of points for numerical integration of the Monte Carlo type, largely used in analysis of engineering problems, is developed. It is achieved by modification of the metric in the minimax optimality criterion. The standard minimax criterion ensures the design exhibits good space-filling property and therefore reduces the variance of the estimator of the integral. We, however, show that the points are not selected with the same probability over the space of sampling probabilities: some regions are over- or under-sampled when designs are generated repetitively. This violation of statistical uniformity may lead to systematically biased integral estimators. We propose that periodic metric be considered for calculation of the minimax distance. Such periodic minimax criterion provides statistically uniform designs leading to unbiased integration results and also low estimator variance due to retained space-filling property. These conclusions are demonstrated by examples integrating analytical functions. The designs are constructed by two different algorithms: (i) a new time-stepping algorithm resembling a damped system of attracted particles developed here, and (ii) the heuristic swapping of coordinates. The designs constructed by the time-stepping algorithm are attached to the paper as a supplementary material. The computer code for construction of the designs is attached too.en
dc.formattextcs
dc.format.extent1-13cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationADVANCES IN ENGINEERING SOFTWARE. 2020, vol. 149, issue 1, p. 1-13.en
dc.identifier.doi10.1016/j.advengsoft.2020.102900cs
dc.identifier.issn0965-9978cs
dc.identifier.orcid0000-0001-9453-4078cs
dc.identifier.orcid0000-0002-3366-5557cs
dc.identifier.orcid0000-0001-6695-2168cs
dc.identifier.other165338cs
dc.identifier.researcheridC-1179-2014cs
dc.identifier.researcheridA-1759-2010cs
dc.identifier.researcheridF-8950-2018cs
dc.identifier.scopus36131177500cs
dc.identifier.scopus57260228700cs
dc.identifier.scopus26027265100cs
dc.identifier.urihttp://hdl.handle.net/11012/196691
dc.language.isoencs
dc.publisherElseviercs
dc.relation.ispartofADVANCES IN ENGINEERING SOFTWAREcs
dc.relation.urihttps://www.sciencedirect.com/science/article/pii/S0965997820300508cs
dc.rightsCreative Commons Attribution-NonCommercial-NoDerivatives 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/0965-9978/cs
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/cs
dc.subjectNumerical integrationen
dc.subjectDesign of experimentsen
dc.subjectSpace-filling designsen
dc.subjectLatin hypercube samplingen
dc.subjectVorono tessellationen
dc.subjectPeriodic spaceen
dc.titlePeriodic version of the minimax distance criterion for Monte Carlo integrationen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionacceptedVersionen
sync.item.dbidVAV-165338en
sync.item.dbtypeVAVen
sync.item.insts2025.02.03 15:45:25en
sync.item.modts2025.01.17 15:17:19en
thesis.grantorVysoké učení technické v Brně. Fakulta stavební. Ústav stavební mechanikycs
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