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Input Distribution Selection for Simulation Experiments: Accounting for Input Uncertainty

Department of Industrial and Operations Engineering, The University of Michigan, 1205 Beal Avenue, Ann Arbor, Michigan 48109-2117
Stephen.E.Chick{at}umich.edu

A number of authors have identified problematic issues with techniques used in current simulation practice for selecting probability distributions and their parameters for input to stochastic simulations. A major goal of this paper is to address some of those issues by presenting a self-consistent evaluation of the uncertainty about the mean value of the simulation output, when there is uncertainty in both the parameters and functional form of input distributions (structural uncertainty), and uncertainty due to the stochastic nature of simulation output (stochastic uncertainty), as is common in simulation practice. The analysis leads to an algorithm for randomly sampling input distributions and parameters before each simulation replication, using a Bayesian posterior distribution for input distributions and parameters, given historical data. Mechanisms for addressing issues of importance to the discrete-event simulation community are illustrated by example, such as the specification of prior distributions, and analysis for shifted distributions.

Subject classifications: Simulation, Statistical Analysis: input distribution selection, uncertainty analysis; Statistics, Bayesian: model selection, prior distribution assessment.
History: Received November 1996; revision received February 1998; revision received February 1999; revision received January 2000; accepted June 2000.