4.7 Article

On the quantification and efficient propagation of imprecise probabilities resulting from small datasets

期刊

MECHANICAL SYSTEMS AND SIGNAL PROCESSING
卷 98, 期 -, 页码 465-483

出版社

ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ymssp.2017.04.042

关键词

Uncertainty quantification; Uncertainty propagation; Epistemic uncertainty; Imprecise probability; Bayesian inference; Importance sampling; Akaike information criterion; Kullback-Leibler information theory

资金

  1. Office of Naval Research [N00014-15-1-2754]

向作者/读者索取更多资源

This paper addresses the problem of uncertainty quantification and propagation when data for characterizing probability distributions are scarce. We propose a methodology wherein the full uncertainty associated with probability model form and parameter estimation are retained and efficiently propagated. This is achieved by applying the information theoretic multimodel inference method to identify plausible candidate probability densities and associated probabilities that each method is the best model in the Kullback-Leibler sense. The joint parameter densities for each plausible model are then estimated using Bayes' rule. We then propagate this full set of probability models by estimating an optimal importance sampling density that is representative of all plausible models, propagating this density, and reweighting the samples according to each of the candidate probability models. This is in contrast with conventional methods that try to identify a single probability model that encapsulates the full uncertainty caused by lack of data and consequently underestimate uncertainty. The result is a complete probabilistic description of both aleatory and epistemic uncertainty achieved with several orders of magnitude reduction in computational cost. It is shown how the model can be updated to adaptively accommodate added data and added candidate probability models. The method is applied for uncertainty analysis of plate buckling strength where it is demonstrated how dataset size affects the confidence (or lack thereof) we can place in statistical estimates of response when data are lacking. (C) 2017 Elsevier Ltd. All rights reserved.

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