Applying Bayesian ideas in simulation

Abstract

The standard approach to analyzing the results of probabilistic simulation rests on the use of classical statistics. In this paper, we explore the use of Bayesian statistics as an alternative. This makes it possible to incorporate prior information into the analysis of simulation results in a formal and rigorous manner, through the use of prior distributions. The Bayesian approach will typically yield improved analyses, by better taking into account what is actually known and what is not known about the system to be simulated (assuming that the prior distributions themselves adequately represent this knowledge). We briefly review Bayesian methods for readers who are not familiar with this type of analysis and suggest ways in which these methods can be applied to simulation. Specifically, we explore the use of Bayesian statistics for verification and validation of simulation models and for simulation output analysis, in both cases using priors on the performance measures of interest. We then study the use of prior distributions on the input parameters to the simulation, as a way to quantify the effects of input uncertainties on both the mean and the uncertainty of the performance measures of interest, and discuss Bayesian and related methods for choosing input distributions. Finally, we briefly consider the use of a joint prior on both the input parameters and the resulting performance measures. Bayesian methods are particularly appropriate for use in practice when simulations are costly, or when input uncertainties are large. Our work provides guidance on the use of Bayesian methods for simulation analysis. We hope that it will stimulate readers to learn more about this important subject, and also encourage further research in this area.