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This paper addresses the problem of quantification and propagation ofuncertainties associated with dependence modeling when data for characterizingprobability models are limited. Practically, the system inputs are oftenassumed to be mutually independent or correlated by a multivariate Gaussiandistribution. However, this subjective assumption may introduce bias in theresponse estimate if the real dependence structure deviates from thisassumption. In this work, we overcome this limitation by introducing a flexiblecopula dependence model to capture complex dependencies. A hierarchicalBayesian multimodel approach is proposed to quantify uncertainty in dependencemodel-form and model parameters that result from small data sets. This approachbegins by identifying, through Bayesian multimodel inference, a set ofcandidate marginal models and their corresponding model probabilities, and thenestimating the uncertainty in the copula-based dependence structure, which isconditional on the marginals and their parameters. The overall uncertaintiesintegrating marginals and copulas are probabilistically represented by anensemble of multivariate candidate densities. A novel importance samplingreweighting approach is proposed to efficiently propagate the overalluncertainties through a computational model. Through an example studying theinfluence of constituent properties on the out-of-plane properties oftransversely isotropic E- glass fiber composites, we show that the compositeproperty with copula-based dependence model converges to the true estimate asdata set size increases, while an independence or arbitrary Gaussiancorrelation assumption leads to a biased estimate.

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