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Uncertainty Quantification using Exponential Epi-Splines
"... ABSTRACT: We quantify uncertainty in complex systems by a flexible, nonparametric framework for estimating probability density functions of output quantities of interest. The framework systematically incorporates soft information about the system from engineering judgement and experience to improve ..."
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the estimates and ensure that they are consistent with prior knowledge. The framework is based on a maximum likelihood criterion, with epi-splines facilitating rapid solution of the resulting optimization problems. In four numerical examples with few realizations of the system output, we identify the main
DENSITY ESTIMATION OF SIMULATION OUTPUT USING EXPONENTIAL EPI-SPLINES
"... The density of stochastic simulation output provides more information on system performance than the mean alone. However, density estimation methods may require large sample sizes to achieve a certain accuracy or desired structural properties. A nonparametric estimation method based on exponential e ..."
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epi-splines has shown promise to overcome this difficulty by incorporating qualitative and quantitative information that reduces the space of possible density estimates substantially. Such ‘soft ’ information may come in the form of the knowledge of a non-negative support, unimodality
