DISTINGUISHING AND INTEGRATING ALEATORIC AND EPISTEMIC VARIATION IN UNCERTAINTY QUANTIFICATION
DISTINGUISHING AND INTEGRATING ALEATORIC AND EPISTEMIC VARIATION IN UNCERTAINTY QUANTIFICATION
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DOI：
10.1051/m2an/2012038
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发表时间：
2013-05-01
期刊：
影响因子：
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通讯作者：
Dupuis, Paul
中科院分区：
文献类型：
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作者：
Chowdhary, Kamaljit;Dupuis, Paul
迄今为止，许多不确定性量化都集中于确定概率建模的变量对某些物理或工程系统的影响，这些变量具有已知的分布。当某些变量的分布是准确已知的，其他变量的分布仅是近似已知的，或者其他变量的分布可能根本没有被建模为随机变量时，我们开发了获取系统信息的方法。使用的主要工具是风险敏感积分和相对熵之间的对偶性，并且我们获得了分布族的标准绩效度量（方差、超出概率）的明确界限，这些分布族与名义分布的距离是通过相对熵来测量的。风险敏感期望的评估基于多项式混沌展开，这有助于保持计算方面的易于处理。
Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the system when the distributions of some variables are known exactly, others are known only approximately, and perhaps others are not modeled as random variables at all. The main tool used is the duality between risk-sensitive integrals and relative entropy, and we obtain explicit bounds on standard performance measures (variances, exceedance probabilities) over families of distributions whose distance from a nominal distribution is measured by relative entropy. The evaluation of the risk-sensitive expectations is based on polynomial chaos expansions, which help keep the computational aspects tractable.