Accounting for Input Uncertainty in Discrete-Event Simulation

Abstract

The primary objectives of this research are formulation and evaluation ofa Bayesian approach for selecting input models in discrete-eventstochastic simulation. This approach takes into account the model,parameter, and stochastic uncertainties that are inherent in mostsimulation experiments in order to yield valid predictive inferences aboutthe output quantities of interest. We use prior information to specify theprior plausibility of each candidate input model that adequately fits thedata, and to construct prior distributions on the parameters of eachmodel. We combine prior information with the likelihood function of thedata to compute the posterior model probabilities and the posteriorparameter distributions using Bayes' rule. This leads to a BayesianSimulation Replication Algorithm in which: (a) we estimate the parameteruncertainty by sampling from the posterior distribution of each model'sparameters on selected simulation runs; (b) we estimate the stochasticuncertainty by multiple independent replications of those selected runs;and (c) we estimate model uncertainty by weighting the results of (a) and(b) using the corresponding posterior model probabilities. We alsoconstruct a confidence interval on the posterior mean response from theoutput of the algorithm, and we develop a replication allocation procedurethat optimally allocates simulation runs to input models so as to minimizethe variance of the mean estimator subject to a budget constraint oncomputer time. To assess the performance of the algorithm, we propose someevaluation criteria that are reasonable within both the Bayesian andfrequentist paradigms. An experimental performance evaluation demonstratesthe advantages of the Bayesian approach versus conventional frequentisttechniques.