Majorisation as a theory for uncertainty

IF 1.5 4区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY International Journal for Uncertainty Quantification Pub Date : 2020-07-21 DOI:10.1615/int.j.uncertaintyquantification.2022035476

V. Volodina, Nikki Sonenberg, E. Wheatcroft, H. Wynn

引用次数: 0

Abstract

Majorisation, also called rearrangement inequalities, yields a type of stochastic ordering in which two or more distributions can be then compared. This method provides a representation of the peakedness of probability distributions and is also independent of the location of probabilities. These properties make majorisation a good candidate as a theory for uncertainty. We demonstrate that this approach is also dimension free by obtaining univariate decreasing rearrangements from multivariate distributions, thus we can consider the ordering of two, or more, distributions with different support. We present operations including inverse mixing and maximise/minimise to combine and analyse uncertainties associated with different distribution functions. We illustrate these methods for empirical examples with applications to scenario analysis and simulations.

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专业化作为不确定性理论

Majorisation，也称为重排不等式，产生了一种随机排序，其中可以比较两个或多个分布。该方法提供了概率分布的峰值性的表示，并且与概率的位置无关。这些特性使多数化成为不确定性理论的一个很好的候选者。我们通过从多变量分布中获得单变量递减重排来证明这种方法也是无量纲的，因此我们可以考虑具有不同支持的两个或多个分布的排序。我们介绍了包括反向混合和最大化/最小化在内的操作，以组合和分析与不同分布函数相关的不确定性。我们举例说明了这些方法在情景分析和模拟中的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal for Uncertainty Quantification ENGINEERING, MULTIDISCIPLINARY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.60

自引率

5.90%

发文量

期刊介绍： The International Journal for Uncertainty Quantification disseminates information of permanent interest in the areas of analysis, modeling, design and control of complex systems in the presence of uncertainty. The journal seeks to emphasize methods that cross stochastic analysis, statistical modeling and scientific computing. Systems of interest are governed by differential equations possibly with multiscale features. Topics of particular interest include representation of uncertainty, propagation of uncertainty across scales, resolving the curse of dimensionality, long-time integration for stochastic PDEs, data-driven approaches for constructing stochastic models, validation, verification and uncertainty quantification for predictive computational science, and visualization of uncertainty in high-dimensional spaces. Bayesian computation and machine learning techniques are also of interest for example in the context of stochastic multiscale systems, for model selection/classification, and decision making. Reports addressing the dynamic coupling of modern experiments and modeling approaches towards predictive science are particularly encouraged. Applications of uncertainty quantification in all areas of physical and biological sciences are appropriate.