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International Journal for Uncertainty Quantification

年間 6 号発行

ISSN 印刷: 2152-5080

ISSN オンライン: 2152-5099

The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.7 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.9 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 0.5 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.0007 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.5 SJR: 0.584 SNIP: 0.676 CiteScore™:: 3 H-Index: 25

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DISTANCES AND DIAMETERS IN CONCENTRATION INEQUALITIES: FROM GEOMETRY TO OPTIMAL ASSIGNMENT OF SAMPLING RESOURCES

巻 2, 発行 1, 2012, pp. 21-38
DOI: 10.1615/Int.J.UncertaintyQuantification.v2.i1.30
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要約

This note reviews, compares and contrasts three notions of "distance" or "size" that arise often in concentration-of-measure inequalities. We review Talagrand′s convex distance and McDiarmid′s diameter, and consider in particular the normal distance on a topological vector space 𝒳, which corresponds to the method of Chernoff bounds, and is in some sense "natural" with respect to the duality structure on 𝒳. We show that, notably, with respect to this distance, concentration inequalities on the tails of linear, convex, quasiconvex and measurable functions on 𝒳 are mutually equivalent. We calculate the normal distances that correspond to families of Gaussian and of bounded random variables in ℝN, and to functions of N empirical means. As an application, we consider the problem of estimating the confidence that one can have in a quantity of interest that depends upon many empirical—as opposed to exact—means and show how the normal distance leads to a formula for the optimal assignment of sampling resources.

によって引用された
  1. Hemez François M., Stull Christopher J., Optimal Inequalities to Bound a Performance Probability, in Topics in Model Validation and Uncertainty Quantification, Volume 5, 2013. Crossref

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