文章基本信息

标题：Uncertainty quantification via codimension one domain partitioning and a new concentration inequality
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作者：Timothy J. Sullivan ; Timothy J. Sullivan ; Mike McKerns 等
期刊名称：Procedia - Social and Behavioral Sciences
印刷版ISSN：1877-0428
出版年度：2010
卷号：2
期号：6
页码：7751-7752
DOI：10.1016/j.sbspro.2010.05.211
语种：English
出版社：Elsevier
摘要：In [LOO08], it was proposed that a concentration-of-measure inequality known as McDiarmid’s inequality [McD89] be used to provide upper bounds on the failure probabilityof a system of interest, the response of which depends on a collection of independentrandom inputs. McDiarmid’s inequality has the advantage of providing an upper boundin terms of only the mean response of the system, the failure threshold, and measures ofsystem spread known as the McDiarmid subdiameters. A disadvantage of McDiarmid’sinequality is that it that takes a global view of the response function: even if the responsefunction exhibits large plateaus of success with only small, localized regions of failure,McDiarmid’s inequality is unable to use this to any advantage. We propose a partitioning algorithm that uses McDiarmid diameters to generate “good” sequences of partitions,on which McDiarmid’s inequality can be applied to each partition element, yielding arbitrarily tight upper bounds. We also investigate some new concentration-of-measureinequalities that arise if mean performance is known only through sampling.