指标函数的多项式型混沌展开的比较研究

IF 2.1 3区工程技术 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2022-10-25 DOI:10.1137/21m1413146

Florian Bourgey, E. Gobet, C. Rey

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引用次数: 2

摘要

针对一类阈值参数c∈R和随机变量X与经典正交多项式相关的形式为1c≤X的指标函数，我们提出了一种多项式混沌展开式(PCE)的全面比较。我们对PCE截断的结果提供了严密的全局和局部l2估计，数值实验支持误差估计的严密性。我们还比较了应用额外的分位数/概率变换时PCE的理论和数值精度，揭示了根据X分布的中心和尾部c的值不同的最优选择。

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A Comparative Study of Polynomial-Type Chaos Expansions for Indicator Functions

We propose a thorough comparison of polynomial chaos expansion (PCE) for indicator functions of the form 1 c ≤ X for some threshold parameter c ∈ R and a random variable X associated with classical orthogonal polynomials. We provide tight global and localized L 2 estimates for the resulting truncation of the PCE and numerical experiments support the tightness of the error estimates. We also compare the theoretical and numerical accuracy of PCE when extra quantile/probability transforms are applied, revealing diﬀerent optimal choices according to the value of c in the center and the tails of the distribution of X .

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来源期刊

Siam-Asa Journal on Uncertainty Quantification Mathematics-Statistics and Probability

CiteScore

3.70

自引率

0.00%

发文量

期刊介绍： SIAM/ASA Journal on Uncertainty Quantification (JUQ) publishes research articles presenting significant mathematical, statistical, algorithmic, and application advances in uncertainty quantification, defined as the interface of complex modeling of processes and data, especially characterizations of the uncertainties inherent in the use of such models. The journal also focuses on related fields such as sensitivity analysis, model validation, model calibration, data assimilation, and code verification. The journal also solicits papers describing new ideas that could lead to significant progress in methodology for uncertainty quantification as well as review articles on particular aspects. The journal is dedicated to nurturing synergistic interactions between the mathematical, statistical, computational, and applications communities involved in uncertainty quantification and related areas. JUQ is jointly offered by SIAM and the American Statistical Association.