A Nonparametric-based Approach for the Characterization and Propagation of Epistemic Uncertainty due to Small Datasets

Abstract

Quantification of uncertainty is ideally performed by the use of highly precise and consistent information, which is rarely available in many applications due to lack of knowledge and/or resources. When only small datasets are available for characterizing the underlying probability distributions of uncertainty sources, related epistemic uncertainty needs to be characterized and propagated with weaker assumptions and greater flexibility. This paper proposes a nonparametric-based approach to further facilitate the characterization and propagation of epistemic uncertainty due to the lack of sufficient data. The first part of this paper presents the use of Kernel Density Estimation (KDE) and Bootstrap to estimate probability distributions of random variables based on small datasets. Two types of density estimates are provided for uncertainty propagation: an optimal density estimate representing the best estimate of the true distribution, and a conservative density estimate representing risk and uncertainty that is inherent in small datasets. In the second part, copulas and inversion method are applied to model the dependence structure among random variables, to mitigate the overestimation or underestimation of uncertainty caused by incorrect independence assumption. The proposed method is illustrated by various illustrations and a challenging problem in aviation environmental impact analysis.

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