Ensemble Copula Coupling for Multivariate Input Modeling and Uncertainty Quantification

We consider the problem of estimating a multivariate distribution based on multiple data sources, which include both joint and marginal-only data. Specifically, we introduce a nonparametric approach called Ensemble Copula Coupling (ECC), which can be viewed as a data fusion approach that combines joint and marginal information. The particular setting of interest is input modeling for output analysis of simulated stochastic systems. We apply an ECC-based input model to address uncertainty quantification with correlated inputs. We prove the consistency of ECC and provide limit theorems that can be used to construct confidence intervals for the estimators. Resampling schemes are proposed to improve the accuracy of the confidence intervals. Simulation experiments on queueing and finance examples illustrate the advantages of using the proposed approach and demonstrate that the ECC-based input model can be applied to higher-dimensional problems at lower computational cost compared with existing approaches.

Funding: K.-K. Kim received financial support from the National Research Foundation of Korea funded by the Korea Government (Ministry of Science and ICT) [Grant RS-2023-00278082]. The research of T. Kim was substantially supported by the Hong Kong Research Grant Council Junior Research Fellow Scheme [Grant JRFS2526-6H03]. M. C. Fu was financially supported by the U.S. National Science Foundation [Grant CMMI-2146067].

Supplemental Material: The online appendix is available at https://doi.org/10.1287/moor.2024.0827.