PRONÓSTICOS BAYESIANOS USANDO SIMULACIÓN ESTOCÁSTICA*

Authors

  • David F. Muñoz Negrón Instituto Tecnológico Autónomo de México (México). Ph. D. en Investigación de Operaciones de Stanford University, California.

DOI:

https://doi.org/10.46631/jefas.2009.v14n26.01

Keywords:

Forecasting, simulation output analysis, Bayesian estimation, quantile estimation

Abstract

In this article, we present a general framework to construct forecasts using simulation. This framework allows us to incorporate available data into a forecasting model in order to assess parameter uncertainty through a posterior distribution, which is then used to estimate a point forecast in the form of a conditional (given the data) expectation. The uncertainty on the point forecast is assessed through the estimation of a conditional variance and a prediction interval. We discuss how to construct asymptotic confidence intervals to assess the estimation error for the estimators obtained using simulation. We illustrate how this approach is consistent with Bayesian forecasting by presenting two examples, and experimental results that confirm our analytical results are discussed.

Downloads

Download data is not yet available.

References

Asmussen, S. (2003). Applied probability and queues (2.a ed.).New York: Springer.

Asmussen, S. & Glynn, P. W. (2007). Stochastic simulation algorithms and analysis. New York: Springer.

Berger, J. O., Bernardo, J. M. & Sun, D. (2009). The formal definition of reference priors. Annals of Statistics, 37 (2), 905-938.

Bernardo, J. M. & Smith, A. F. M. (2000). Bayesian theory. Chichester: Wiley.

Cheng, R. C. H. & Holland, W. (1998). Two points methods for assessing variability in simulation output.Journal of Statistical Computation and Simulation, 60 (3), 183-205.

Cheng, R. C. H. & Holland, W. (2004). Calculation of confidence intervals for simulation output. ACM Transactions on Modeling and Computer Simulation, 14 (4), 344-362.

Chick, S. E. (2001). Input distribution selection for simulation experiments: accounting for input uncertainty. Operations Research, 49 (5), 744-758.

Chick, S. E. (2004). Bayesian methods for discrete event simulation. En R. G. Ingalls, M. D. Rossetti, J. S. Smith, B. A. Peters (eds.). Proceedings of the 2004 winter simulation conference (89-100). New Jersey: IEEE.

Fisher, M. L., Raman, A., McClelland, A. S. (2000). Rocket science retailing is almost here. Harvard Business Review, 78(4), 115-124.

Glynn, P. W. (1996). Importance sampling for Monte Carlo estimation of quantiles. En Proceedings of the second international workshop on mathematical methods in stochastic simulation and experimental design (San Petersburgo), 180-185.

Glynn, P. W. & Iglehart, D. L. (1989). Importance sampling for stochastic simulations. Management Science, 35 (11), 1367-1392.

Glynn, P. W. & Iglehart, D. L. (1991). Simulation output analysis using standardized time series. Mathematics of Operations Research, 15 (1), 1-16.

Iglehart, D. L. (1976). Simulating stable stochastic systems, VI: Quantile estimation. Journal of the Association for Computing Machinery, 23 (2), 347-360.

Kalchschmidt, M., Verganti, R. & Zotteri, G. (2006). Forecasting demand from heterogeneous customers. International Journal of Operations & Production Management, 26 (6), 619-638.

Kraan, B. & Bedford, T. (2005). Probabilistic inversion of expert judgments in the quantification of model uncertainty. Management Science, 51 (6), 995-1006.

Montgomery, D. C. (1998). Design and analysis of experiments. New York: Wiley.

Muñoz, D. F. & Glynn, P. W. (1997). A batch means methodology for estimation of a nonlinear function of a steadystate mean. Management Science, 43 (8), 1121-1135.

Muñoz, D. F. & Muñoz, D. G. (2008). A Bayesian framework for the incorporations of priors and sample data in simulation experiments. The Open Operational Research Journal, 2, 44-51.

Muñoz, D. F. (2009). On the validity of the batch quantile method in Markov chains. Aceptado para su publicación en Operations Research Letters.

Muñoz, D. F., Romero-Hernández, O., Detta-Silveira, J. E. & Mu-ñoz, D. G. (2009). Forecasting demand for educational material for adult learners in Mexico. Aceptado para su publicación en la International Transactions in Operational Research.

O’Hagan, A. & Forster, J. (2004). J. Kendall’s advanced theory of statistics volume 2B Bayesian inference (2.a ed.). London: Arnold.

Rossi, P. E., Allenby, G. M. & McCulloch, R. (2005).Bayesian statistics and marketing. Chichester: Wiley.

Schmeiser, B. (1982). Batch size effects in the analysis of simulation output. Operations Research, 30 (3), 556-568.

Serfling, R. J. (1980). Approximation theorems of mathematical statistics. New York: John Wiley.

Song, T. W. & Chih, M. (2008). Implementable mse-optimal dynamic partial-overlapping batch means estimators for steady-state simulations. En S. J. Mason, R. R.

Hill, L. Mönch, O. Rose, T. Jefferson & J. W. Fowler (eds.). Proceedings of the 2008 winter simulation conference (426-435). New Jersey: IEEE.

Zouaoui, F. & Wilson, J. R. (2003). Accounting for parameter uncertainty in simulation input modeling. IIE Transactions, 35 (9), 781-792.

Downloads

Published

2009-06-30

How to Cite

Muñoz Negrón, D. F. (2009). PRONÓSTICOS BAYESIANOS USANDO SIMULACIÓN ESTOCÁSTICA*. Journal of Economics, Finance and Administrative Science, 14(26), 7–26. https://doi.org/10.46631/jefas.2009.v14n26.01