{"data":{"id":"10.6084/m9.figshare.1266500","type":"dois","attributes":{"doi":"10.6084/m9.figshare.1266500","prefix":"10.6084","suffix":"m9.figshare.1266500","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Chevalier, Clément","nameType":"Personal","givenName":"Clément","familyName":"Chevalier","affiliation":[],"nameIdentifiers":[]},{"name":"Bect, Julien","nameType":"Personal","givenName":"Julien","familyName":"Bect","affiliation":[],"nameIdentifiers":[]},{"name":"Ginsbourger, David","nameType":"Personal","givenName":"David","familyName":"Ginsbourger","affiliation":[],"nameIdentifiers":[]},{"name":"Vazquez, Emmanuel","nameType":"Personal","givenName":"Emmanuel","familyName":"Vazquez","affiliation":[],"nameIdentifiers":[]},{"name":"Picheny, Victor","nameType":"Personal","givenName":"Victor","familyName":"Picheny","affiliation":[],"nameIdentifiers":[]},{"name":"Richet, Yann","nameType":"Personal","givenName":"Yann","familyName":"Richet","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Fast Parallel Kriging-Based Stepwise Uncertainty Reduction With Application to the Identification of an Excursion Set"}],"publisher":"Taylor \u0026 Francis","container":{},"publicationYear":2014,"subjects":[{"subject":"Science Policy"},{"subject":"Cancer"},{"subject":"Mathematics"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Mathematics","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Information and Computing Sciences"},{"subject":"Biological Sciences"},{"subject":"Chemistry"},{"subject":"Earth and Environmental Sciences"},{"subject":"Medicine"}],"contributors":[],"dates":[{"date":"2014-12-11","dateType":"Created"},{"date":"2015-12-02","dateType":"Updated"},{"date":"2014","dateType":"Issued"}],"language":null,"types":{"ris":"DATA","bibtex":"misc","citeproc":"dataset","schemaOrg":"Dataset","resourceType":"Dataset","resourceTypeGeneral":"Dataset"},"relatedIdentifiers":[{"relationType":"IsSupplementTo","relatedIdentifier":"10.1080/00401706.2013.860918","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":["1494865 Bytes"],"formats":[],"version":null,"rightsList":[{"rights":"Creative Commons Attribution 4.0 International","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rightsIdentifier":"cc-by-4.0","rightsIdentifierScheme":"SPDX"}],"descriptions":[{"description":"Stepwise uncertainty reduction (SUR) strategies aim at constructing a sequence of points for evaluating a function \u003ci\u003ef\u003c/i\u003e in such a way that the residual uncertainty about a quantity of interest progressively decreases to zero. Using such strategies in the framework of Gaussian process modeling has been shown to be efficient for estimating the volume of excursion of \u003ci\u003ef\u003c/i\u003e above a fixed threshold. However, SUR strategies remain cumbersome to use in practice because of their high computational complexity, and the fact that they deliver a single point at each iteration. In this article we introduce several multipoint sampling criteria, allowing the selection of batches of points at which \u003ci\u003ef\u003c/i\u003e can be evaluated in parallel. Such criteria are of particular interest when \u003ci\u003ef\u003c/i\u003e is costly to evaluate and several CPUs are simultaneously available. We also manage to drastically reduce the computational cost of these strategies through the use of closed form formulas. We illustrate their performances in various numerical experiments, including a nuclear safety test case. Basic notions about kriging, auxiliary problems, complexity calculations, R code, and data are available online as supplementary materials.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"https://tandf.figshare.com/articles/dataset/Fast_Parallel_Kriging_Based_Stepwise_Uncertainty_Reduction_With_Application_to_the_Identification_of_an_Excursion_Set/1266500","contentUrl":null,"metadataVersion":3,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"viewsOverTime":[],"downloadCount":0,"downl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