Accounting for input-model and input-parameter uncertainties in simulation

To account for the input-model and input-parameter uncertainties inherent in many simulations as well as the usual stochastic uncertainty, we present a Bayesian input-modeling technique that yields improved point and confidence-interval estimators for a selected posterior mean response. Exploiting prior information to specify the prior probabilities of the postulated input models and the associated prior input-parameter distributions, we use sample data to compute the posterior input-model and input-parameter distributions. Our Bayesian simulation replication algorithm involves: (i) estimating parameter uncertainty by randomly sampling the posterior input-parameter distributions; (ii) estimating stochastic uncertainty by running independent replications of the simulation using each set of input-model parameters sampled in (i); and (iii) estimating input-model uncertainty by weighting the responses generated in (ii) using the corresponding posterior input-model probabilities. Sampling effort is allocated among input models to minimize final point-estimator variance subject to a computing-budget constraint. A queueing simulation demonstrates the advantages of this approach.