On the quantification and efficient propagation of imprecise probabilities with copula dependence

Zhang, Jiaxin; Shields, Michael

doi:10.1016/j.ijar.2020.04.002

Title: On the quantification and efficient propagation of imprecise probabilities with copula dependence

Journal Article · Thu Apr 30 00:00:00 EDT 2020 · International Journal of Approximate Reasoning

DOI:https://doi.org/10.1016/j.ijar.2020.04.002· OSTI ID:1651315

^[1]; Shields, Michael ^[2]

Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Johns Hopkins Univ., Baltimore, MD (United States)

This paper addresses the problem of quantification and propagation of uncertainties associated with dependence modeling when data for characterizing probability models are limited. Practically, the system inputs are often assumed to be mutually independent or correlated by a multivariate Gaussian distribution. However, this subjective assumption may introduce bias in the response estimate if the real dependence structure deviates from this assumption. In this work, we overcome this limitation by introducing a flexible copula dependence model to capture complex dependencies. Here, a hierarchical Bayesian multimodel approach is proposed to quantify uncertainty in dependence model-form and model parameters that result from small data sets. This approach begins by identifying, through Bayesian multimodel inference, a set of candidate marginal models and their corresponding model probabilities, and then estimating the uncertainty in the copula-based dependence structure, which is conditional on the marginals and their parameters. The overall uncertainties integrating marginals and copulas are probabilistically represented by an ensemble of multivariate candidate densities. A novel importance sampling reweighting approach is proposed to efficiently propagate the overall uncertainties through a computational model. Through an example studying the influence of constituent properties on the out-of-plane properties of transversely isotropic E-glass fiber composites, we show that the composite property with copula-based dependence model converges to the true estimate as data set size increases, while an independence or arbitrary Gaussian correlation assumption leads to a biased estimate.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); US Department of the Navy, Office of Naval Research (ONR)

Grant/Contract Number:: AC05-00OR22725; N00014-16-1-2582; ERKJ352; DEAC05-00OR22725

OSTI ID:: 1651315

Alternate ID(s):: OSTI ID: 1693549

Journal Information:: International Journal of Approximate Reasoning, Vol. 122, Issue NA; ISSN 0888-613X

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 11 works

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