Accounting for parameter uncertainty in large-scale stochastic simulations with correlated inputs

Operations Research

Volumn 59, Issue 3, 2011, Pages 661-673

  Biller, Bahar ^a   Corlu, Canan G ^b  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b BILKENT UNIVERSITY   (Turkey)

Author keywords

Bayesian; Correlation; Design of experiments; Sampling; Statistical analysis

Indexed keywords

BAYESIAN; BAYESIAN MODEL; CONFIDENCE INTERVAL; CORRELATED DEMAND; DISCRETE EVENTS; DISTRIBUTION PARAMETERS; EXCHANGE RATES; GLOBAL SUPPLY CHAIN; INPUT DATAS; MANUFACTURING FACILITY; MARGINAL DISTRIBUTION; MULTI-PRODUCTS; PARAMETER UNCERTAINTY; PERFORMANCE MEASURE; PRIMARY CONTRIBUTION; PROCESSING TIME; PRODUCT DEMAND; SIMULATION REPLICATION; STOCHASTIC SIMULATIONS; STOCHASTIC UNCERTAINTIES; WORK PIECES;

BAYESIAN NETWORKS; COMPUTER SIMULATION; DESIGN OF EXPERIMENTS; FINANCIAL DATA PROCESSING; PARAMETER ESTIMATION; SAMPLING; STOCHASTIC MODELS; STOCHASTIC SYSTEMS; SUPPLY CHAINS;

UNCERTAINTY ANALYSIS;

EID: 79960505236     PISSN: 0030364X     EISSN: 15265463     Source Type: Journal    
DOI: 10.1287/opre.1110.0915     Document Type: Article

References (45)

1. Barnard, J., R. McCulloch, X. Meng. 2000. Modeling covariance matrices in terms of standard deviations and correlations with applications to shrinkage. Statistica Sinica 10(4) 1281-1311.
2. Barton, R. R., L. W. Schruben. 2001. Resampling methods for input modeling. B. A. Peters, J. S. Smith, D. J. Medeiros, M. W. Rohrer, eds. Proc. 2001 Winter Simulation Conf., IEEE, Piscataway, NJ, 372-378. (Pubitemid 34091318)
3. Bedford, T., R. M. Cooke. 2001. Probabilistic Risk Analysis: Foundations and Methods. Cambridge University Press, Cambridge, UK.
4. Bedford, T., R. M. Cooke. 2002. Vines-A new graphical model for dependent random variables. Ann. Statist. 30(4) 1031-1068. (Pubitemid 37095337)
5. Berger, J. O., D. Sun. 2008. Objective priors for the bivariate normal model. Ann. Statist. 36(2) 963-982.
6. Bernardo, J. M., A. F. M. Smith. 1994. Bayesian Theory. John Wiley & Sons, Inc., New York.
7. Biller, B., S. Ghosh. 2006. Multivariate input processes. B. L. Nelson, S. G. Henderson, eds. Simulation. Handbooks in Operations Research and Management Science. Elsevier Science, Amsterdam.
8. Cario, M. C., B. L. Nelson. 1997. Modeling and generating random vectors with arbitrary marginal distributions and correlation matrix. Working paper, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL.
9. Carlin, B. P., T. A. Louis. 2000. Bayes and Empirical Bayes Methods for Data Analysis. Chapman & Hall, London.
10. Cheng, R. C. H., W. Holland. 1997. Sensitivity of computer simulation experiments to errors in input data. J. Statist. Comput. Simulation 57(1-4) 327-335.
11. Cheng, R. C. H., W. Holland. 1998. Two-point methods for assessing variability in simulation output. J. Statist. Comput. Simulation 60(3) 183-205. (Pubitemid 128433495)
12. Cheng, R. C. H., W. Holland. 2004. Calculation of confidence intervals for simulation output. ACM Trans. Modeling Comput. Simulation 14(4) 344-362. (Pubitemid 40016108)
13. Chick, S. E. 1997. Bayesian analysis for simulation input and output. S. Andradottir, K. J. Healy, D. H. Withers, B. L. Nelson, eds. Proc. 1997 Winter Simulation Conf., IEEE, Piscataway, NJ, 253-260.
14. Chick, S. E. 1999. Steps to implement Bayesian input distribution selection. P. A. Farrington, H. B. Nembhard, D. T. Sturrock, G. W. Evans, eds. Proc. 1999 Winter Simulation Conf., IEEE, Piscataway, NJ, 317-324.
15. Chick, S. E. 2001. Input distribution selection for simulation experiments: Accounting for input uncertainty. Oper. Res. 49(5) 744-758. (Pubitemid 34011325)
16. Cooke, R. M. 1997. Markov and entropy properties of tree- and vine-dependent variables. Proc. ASA Section Bayesian Statist. Sci., American Statistical Association, Alexandria, VA, 166-175.
17. Daniels, M. J. 1999. A prior for the variance in hierarchical models. Canadian J. Statist. 27(3) 567-578.
18. Draper, D. 1995. Assessment of propagation of model uncertainty (with discussion). J. Roy. Statist. Soc. Ser. B 56(1) 501-514.
19. Gelfand, A., A. Smith. 1990. Sampling based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85(410) 398-409.
20. Gelman, A., J. B. Carlin, H. S. Stern, D. B. Rubin. 2000. Bayesian Data Analysis. Chapman & Hall, London.
21. Geman, S., A. Geman. 1984. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Machine Intelligence 6(6) 721-740.
22. George, E. I. 1999. Bayesian model selection. S. Kotz, C. Read, D. Banks, eds. Encyclopedia of Statistical Sciences, Vol. 3. Wiley, New York, 39-46.
23. Gilks, W. R., S. Richardson, D. J. Spiegelhalter. 1996. Markov Chain Monte Carlo in Practice. Chapman & Hall, London.
24. Helton, J. C. 1997. Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty. J. Statist. Comput. Simulation 57(1-4) 3-76.
25. Hoeting, J. A., D. Madigan, A. E. Raftery, C. T. Volinsky. 1999. Bayesian model averaging: A tutorial. Technical Report 9814, Department of Statistics, Colorado State University, Fort Collins, CO.
26. Jeffreys, H. 1961. Theory of Probability. Oxford University Press, Oxford, UK.
27. Joe, H. 1997. Multivariate Models and Dependence Concepts. Chapman & Hall, London.
28. Kass, R. E., L. Wasserman. 1996. The selection of prior distributions by formal rules. J. Amer. Statist. Assoc. 91(435) 1343-1370.
29. Kouvelis, P., P. Su. 2007. The Structure of Global Supply Chains. Research monograph for Foundations and Trends® in Technology, Information, and Operations Management. Now Publishers, Boston.
30. Kurowicka, D., R. Cooke. 2003. A parameterization of positive definite matrices in terms of partial correlation vines. Linear Algebra Appl. 372(1) 225-251.
31. Kurowicka, D., R. Cooke. 2006. Uncertainty Analysis with High Dimensional Dependence Modeling. Wiley Series in Probability and Statistics. John Wiley & Sons, Hoboken, NJ.
32. Law, A. M. 2007. Simulation Modeling and Analysis, 4th ed. McGraw- Hill, New York.
33. Leonard, T., J. S. Hsu. 1992. Bayesian inference for a covariance matrix. Ann. Statist. 20(4) 1669-1696.
34. Liechty, J. C., M. W. Liechty, P. Muller. 2004. Bayesian correlation estimation. Biometrika 91(1) 1-14. (Pubitemid 41309833)
35. Morales, O., D. Kurowicka, A. Roelen. 2006. Elicitation procedures for conditional and unconditional rank correlations. Resources for the Future, Expert Judgement Policy Symposium and Technical Workshop, Washington, DC, March 13-14.
36. Nelsen, R. B. 2006. An Introduction to Copulas. Springer-Verlag, New York.
37. Raftery, A. E., D. Madigan, C. T. Volinsky. 1996. Accounting for model uncertainty in survival analysis improves predictive performance (with discussion). J. M. Bernardo, J. O. Berger, A. P. David, A. F. M. Smith, eds. Bayesian Statistics 5. Oxford University Press, Oxford, UK, 323-349.
38. Rossi, P. E., G. M. Allenby, R. McCulloch. 2006. Bayesian Statistics and Marketing. Wiley Series in Probability and Statistics. John Wiley & Sons, Hoboken, NJ.
39. Schweizer, B. 1991. Thirty years of copulas. G. Dall'Aglio, S. Kotz, G. Salinetti, eds. Advances in Probability Distributions with Given Marginals. Kluwer, Dordrecht, The Netherlands, 13-50.
40. Son, Y. S., M. Oh. 2006. Bayesian estimation of the two-parameter gamma distribution. Comm. Statist.- Simulation Comput. 35(2) 285-293.
41. Tong, Y. L. 1990. The Multivariate Normal Distribution. Springer-Verlag, New York.
42. Xu, S. H. 1999. Structural analysis of a queueing system with multiclasses of correlated arrivals and blocking. Oper. Res. 47(2) 264-276.
43. Yule, G., M. G. Kendall. 1965. An Introduction to the Theory of Statistics. Charles Griffin & Company, Belmont, CA.
44. Zouaoui, F., J. R. Wilson. 2003. Accounting for parameter uncertainty in simulation input modeling. IIE Trans. 35(9) 781-792.
45. Zouaoui, F., J. R. Wilson. 2004. Accounting for input-model and inputparameter uncertainties in simulation. IIE Trans. 36(11) 1135-1151.