Bayesian methods: bayesian methods for simulation

ABSTRACT

This tutorial describes some ways that Bayesian methods address problems that arise during simulation studies. This includes quantifying uncertainty about input distributions and parameters, sensitivity analysis, and the selection of the best of several simulated alternatives. Focus is on illustrating the main ideas and their relevance to practical problems. Numerous citations for both introductory and more advanced material provide a launching pad into the Bayesian literature.

REFERENCES

• 1: Andradóttir, S., and V. M. Bier. 1997. Applying Bayesian ideas in simulation. Dept. of Industrial Engineering, University of Wisconsin-Madison, Technical Report 97-1.
• 2: Russell R. Barton , Lee W. Schruben, Uniform and bootstrap resampling of empirical distributions, Proceedings of the 25th conference on Winter simulation, p.503-508, December 12-15, 1993, Los Angeles, California, United States [doi>10.1145/256563.256699]
• 3: Barton, R. R., and L. W. Schruben. 2000. Simulating real systems. in submission.
• 4: Berger, J. O. 1985. Statistical decision theory and Bayesian analysis 2nd ed. New York: Springer-Verlag.
• 5: Berger, J. O. 1994. An overview of robust Bayesian analysis. TEST 3:5-124.
• 6: Berger, J. O., and L. R. Pericchi. 1996. The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association 91 (433): 109-122.
• 7: Bernardo, J. M., and A. F. M. Smith. 1994. Bayesian Theory. Chichester, UK: Wiley.
• 8: Carlin, B. P., and T. A. Louis. 1996. Bayes and empirical Bayes methods for data analysis. London: Chapman & Hall.
• 9: Chen, C.-H. 1996. A lower bound for the correct subset-selection probability and its application to discrete event simulations. IEEE Transactions on Automatic Control 41 (8): 1227-1231.
• 10: Chen, H., and B. Schmeiser. 1995. Monte Carlo estimation for guaranteed-coverage non-normal tolerance intervals. Journal of Statistical Computation and Simulation 51 (2-4): 223-238.
• 11: Hsiao-Chang Chen , Chun-Hung Chen , Jianwu Lin , Enver Yücesan, An asymptotic allocation for simultaneous simulation experiments, Proceedings of the 31st conference on Winter simulation: Simulation---a bridge to the future, p.359-366, December 05-08, 1999, Phoenix, Arizona, United States [doi>10.1145/324138.324242]
• 12: Russell C. H. Cheng, Regression metamodeling in simulation using Bayesian methods, Proceedings of the 31st conference on Winter simulation: Simulation---a bridge to the future, p.330-335, December 05-08, 1999, Phoenix, Arizona, United States [doi>10.1145/324138.324236]
• 13: Stephen E. Chick, Bayesian analysis for simulation input and output, Proceedings of the 29th conference on Winter simulation, p.253-260, December 07-10, 1997, Atlanta, Georgia, United States [doi>10.1145/268437.268488]
• 14: Stephen E. Chick, Input Distribution Selection for Simulation Experiments: Accounting for Input Uncertainty, Operations Research, v.49 n.5, p.744-758, September 2001 [doi>10.1287/opre.49.5.744.10606]
• 15: Chick, S. E., and K. Inoue. 2000a. New procedures for identifying the best simulated system using common random numbers. in resubmission.
• 16: Stephen E. Chick , Koichiro Inoue, New Two-Stage and Sequential Procedures for Selecting the Best Simulated System, Operations Research, v.49 n.5, p.732-743, September 2001 [doi>10.1287/opre.49.5.732.10615]
• 17: Chick, S. E., and S.-H. Ng. 2000. Input distribution selection for simulation experiments: Reducing input uncertainty. Technical report, University of Michigan, Ann Arbor, Dept. of Industrial & Operations Engineering.
• 18: H. Chipman , M. Hamada , C. F. J. Wu, A Bayesian variable-selection approach for analyzing designed experiments with complex aliasing, Technometrics, v.39 n.4, p.372-381, Nov. 1997 [doi>10.2307/1271501]
• 19: Cooke, R. M. 1994. Uncertainty in dispersion and deposition accident consequence modelling assessed with performance-based expert judgement. Reliability Engineering and System Safety 45:35-46.
• 20: de Finetti, B. 1990. Theory of probability, v. 2. New York: John Wiley & Sons, Inc.
• 21: de Groot, M. H. 1970. Optimal statistical decisions. New York: McGraw-Hill, Inc.
• 22: Draper, D. 1995. Assessment and propogation of model uncertainty (with discussion). Journal of the Royal Statistical Society, Series B 57 (1): 45-97.
• 23: Edwards, A. W. F. 1984. Likelihood. Cambridge: Cambridge University Press.
• 24: George, E. I., and R. E. McCulloch. 1996. Stochastic search variable selection. In Markov chain Monte Carlo in practice, ed. W. R. Gilks, S. Richardson, and D. J. Spiegelhalter. London: Chapman and Hall.
• 25: Gilks, W. R., N. G. Best, and K. K. C. Tan. 1995. Adaptive rejection metropolis sampling. Applied Statistics 44:455-472.
• 26: Gilks, W. R., S. Richardson, and D. J. Spiegelhalter. 1996. Markov chain Monte Carlo in practice. London: Chapman and Hall.
• 27: Peter W. Glynn, Problems in Bayesian analysis of stochastic simulation, Proceedings of the 18th conference on Winter simulation, p.376-379, December 08-10, 1986, Washington, D.C., United States [doi>10.1145/318242.318462]
• 28: David Goldsman , Barry L. Nelson, Statistical screening, selection, and multiple comparison procedures in computer simulation, Proceedings of the 30th conference on Winter simulation, p.159-166, December 13-16, 1998, Washington, D.C., United States
• 29: Gupta, S. S., and K. J. Miescke. 1996. Bayesian look ahead one-stage sampling allocations for selecting the best population. Journal of Statistical Planning and Inference 54:229-244.
• 30: Jon C. Helton, Computational structure of a performance assessment involving stochastic and subjective uncertainty, Proceedings of the 28th conference on Winter simulation, p.239-247, December 08-11, 1996, Coronado, California, United States [doi>10.1145/256562.256613]
• 31: Koichiro Inoue , Stephen E. Chick , Chun-Hung Chen, An empirical evaluation of several methods to select the best system, ACM Transactions on Modeling and Computer Simulation (TOMACS), v.9 n.4, p.381-407, Oct. 1999 [doi>10.1145/352222.352226]
• 32: Kahneman, D., P. Slovic, and A. Tversky. 1982. Judgment under uncertainty: Heuristics and biases. Cambridge: Cambridge University Press.
• 33: Kass, R. E., and L. Wasserman. 1996. The selection of prior distributions by formal rules. Journal of the American Statistical Association 91 (435): 1343-1370.
• 34: Averill M. Law , David M. Kelton, Simulation Modeling and Analysis, McGraw-Hill Higher Education, 1999
• 35: Shing-Hoi Lee , Peter W. Glynn, Computing the distribution function of a conditional expectation via Monte Carlo: discrete conditioning spaces, Proceedings of the 31st conference on Winter simulation: Simulation---a bridge to the future, p.1654-1663, December 05-08, 1999, Phoenix, Arizona, United States [doi>10.1145/324898.325356]
• 36: Lindley, D. V. 1972. Bayesian statistics, a review. Philadelphia: Society of Industrial and Applied Mathematics.
• 37: Nelson, B. L., B. W. Schmeiser, M. R. Taaffe, and J. Wang. 1997. Approximation-assisted point estimation. Operations Research Letters 20(3): 109-118.
• 38: Nelson, B. L., J. Swann, D. Goldsman, and W. Song. 2000. Simple procedures for selecting the best simulated system when the number of alternatives is large. Technical report, Northwestern University, Department of Industrial Engineering and Management Science, Evanston, IL.
• 39: O'Hagan, A. 1995. Fractional Bayes factors for model comparison (with discussion). Journal of the Royal Statistical Society, Series B 56:99-118.
• 40: Raftery, A. E. 1995. Bayesian model selection in social research (with discussion by Andrew Gelman & Donald B. Rubin, and Robert M. Hauser, and a rejoinder). In Sociological Methodology 1995, ed. P. V. Marsden. Cambridge, Mass.: Blackwells.
• 41: Raftery, A. E., D. Madigan, and J. A. Hoeting. 1997. Bayesian model averaging for linear regression models. Journal of the American Statistical Association 92 (437): 179-191.
• 42: Rinott, Y. 1978. On two-stage selection procedures and related probability-inequalities. Communications in Statistics A7:799-811.
• 43: Savage, L. J. 1972. The foundations of statistics. New York: Dover Publications, Inc.
• 44: E. Marian Scott, Uncertainty and sensitivity studies of models of environmental systems, Proceedings of the 28th conference on Winter simulation, p.255-259, December 08-11, 1996, Coronado, California, United States [doi>10.1145/256562.256618]
• 45: Mary Ann Flanigan Wagner , James R. Wilson, Graphical interactive simulation input modeling with bivariate Bézier distributions, ACM Transactions on Modeling and Computer Simulation (TOMACS), v.5 n.3, p.163-189, July 1995 [doi>10.1145/217853.217854]
• 46: Winkler, R. L. 1972. Introduction to Bayesian inference and decision. New York: Holt.