Uncertainty quantification and partition for multivariate risk inferences through a factorial multimodel Bayesian copula (FMBC) system

Abstract In this study, a factorial multimodel Bayesian copula (FMBC) method is proposed to investigate various uncertainties in the copula-based multivariate risk models and further track the major contributors to the imprecise predictions for different risk indices. In FMBC, the copula models with different marginals and dependence structures will be firstly established with the parameter uncertainties being quantified by the adaptive Metropolis algorithm. A multilevel factorial analysis approach is then adopted to characterize the individual and interactive effects of marginals, copula functions and the associated parameter uncertainties on different risk indices. Moreover, a copula-based dependent sampling algorithm is proposed in the factorial analysis process to generate parameter samples under consideration of their correlation. The applicability of the FMBC approach is demonstrated through the multivariate flood risk analysis at two gauging stations in Wei River basin. The results indicate that extensive fluctuation exists in the inferences of multivariate return periods resulting from different marginal and dependence structures as well as the associated parameter uncertainties. For risk indices of the failure probabilities in AND and Kendall, their predictive variability can be mainly attributed to the uncertainties in model parameters and copula structure, with their total contribution more than 75%. In comparison, the failure probability in OR would be mainly influenced by the parameter uncertainty and also marginal structures, with their total contribution more than 80%. The copula structure would not have a visible effect on the failure probability in OR, with its contribution less than 5% for most scenarios. The obtained results can provide scientific support for reliable hydrological risk inferences within a multivariate context.