Capturing parameter uncertainty in simulations with correlated inputs

We consider a stochastic simulation with correlated inputs represented by a multivariate normal distribution. The objectives are to (i) account for parameter uncertainty (i.e., the uncertainty around the multivariate normal distribution parameters estimated from finite historical input data) in the mean performance estimate and the confidence interval of the simulation; and (ii) decompose the total variation of the simulation output into distinct terms representing stochastic and parameter uncertainties. We describe how to achieve these objectives using the Bayesian model of Biller and Gunes (2010) for capturing parameter uncertainty and the Bayesian simulation replication algorithm of Zouaoui and Wilson (2003) for output variance decomposition. We conclude with the extension of this study to arbitrary marginal distributions and dependence measures with positive tail dependencies.