A Study on the Cross-Entropy Method for Rare-Event Probability Estimation

Published Online:https://doi.org/10.1287/ijoc.1060.0176

References

  • Adlakha V. G., Kulkarni V. G. A classified bibliography of research on stochastic PERT networks: 1966–1987. INFOR (1989) 27:272–296Google Scholar
  • Asmussen S.Applied Probability and Queues (2003) 2nd ed.(Springer-Verlag, Berlin, Germany) Google Scholar
  • Bonnans J. F., Shapiro A.Perturbation Analysis of Optimization Problems (2000) (Springer-Verlag, New York) Springer Series in Operations ResearchCrossrefGoogle Scholar
  • Bucklew J. A.Large Deviation Techniques in Decision, Simulation, and Estimation (1990) (Wiley, New York) Google Scholar
  • de Boer P. T. Analysis and efficient simulation of queueing models of telecommunications systems. (2000) . Ph.D. thesis, Department of Computer Science, Univ. of Twente, The NetherlandsGoogle Scholar
  • de Boer P. T., Kroese D. P., Mannor S., Rubinstein R. Y. A tutorial on the cross-entropy method. Ann. Oper. Res. (2005) 134:19–67CrossrefGoogle Scholar
  • Dembo A., Zeitouni O.Large Deviations Techniques and Applications (1998) (Springer-Verlag, New York) CrossrefGoogle Scholar
  • Fishman G.Monte Carlo: Concepts, Algorithms and Applications (1997) (Springer-Verlag, New York) Google Scholar
  • Glasserman P.Monte Carlo Methods in Financial Engineering. Applications of Mathematics (2004) 53(Springer-Verlag, New York) Google Scholar
  • Glasserman P., Heidelberger P., Shahabuddin P., Zajic T. Multilevel splitting for estimating rare event probabilities. Oper. Res. (1999) 47:585–600LinkGoogle Scholar
  • Glynn P. W., Iglehart D. L. Importance sampling for stochastic simulations. Management Sci. (1989) 35:1367–1392LinkGoogle Scholar
  • Heidelberger P. Fast simulation of rare events in queueing and reliability models. ACM Trans. Model. Comput. Simulation (1995) 5:43–85CrossrefGoogle Scholar
  • Homem-de-Mello T., Rubinstein R. Y., Yücesan E., Chen C.-H., Snowdon J. L., Charnes J. M. Estimation of rare event probabilities using cross-entropy. Proc. 2002 Winter Simulation Conf. (2002) San Diego, CA:310–319CrossrefGoogle Scholar
  • Homem-de-Mello T., Shapiro A., Spearman M. L. Finding optimal material release times using simulation based optimization. Management Sci. (1999) 45:86–102LinkGoogle Scholar
  • Huang Z., Shahabuddin P., Ingalis R. G., Rossetti M. D., Smith J. S., Peters B. A. A unified approach for finite dimensional, rare-event Monte Carlo simulation. Proc. 2004 Winter Simulation Conf. (2004) Washington, D.C.:1616–1624CrossrefGoogle Scholar
  • Juneja S., Shahabuddin P. Simulating heavy tailed processes using delayed hazard rate twisting. ACM Trans. Model. Comput. Simulation (2002) 12:94–118CrossrefGoogle Scholar
  • Juneja S., Karandikar R. L., Shahabuddin P. Asymptotics and fast simulation for tail probabilities of maximum of sums of few random variables. ACM Trans. Model. Comput. Simulation (2007) 17(2). Article 7CrossrefGoogle Scholar
  • Kahn H., Marshall A. W. Methods of reducing the sample size in Monte Carlo computations. J. Oper. Res. Soc. (1953) 1:263–278AbstractGoogle Scholar
  • Kaniovski Y. M., King A. J., Wets R. J.-B. Probabilistic bounds (via large deviations) for the solutions of stochastic programming problems. Ann. Oper. Res. (1995) 56:189–208CrossrefGoogle Scholar
  • Kapur J. N., Kesavan H. K.Entropy Optimization Principles with Applications (1992) (Academic Press, New York) CrossrefGoogle Scholar
  • Kroese D., Rubinstein R. Y. The transform likelihood ratio method for rare event simulation with heavy tails. Queueing Systems (2004) 46:317–351CrossrefGoogle Scholar
  • Kullback S., Leibler R. A. On information and sufficiency. Ann. Math. Statist. (1951) 22:79–86CrossrefGoogle Scholar
  • Law A. M., Kelton W. D.Simulation Modeling and Analysis (2000) 3rd ed.(McGraw-Hill, New York) Google Scholar
  • Oh M.-S., Berger J. O. Adaptive importance sampling in Monte Carlo integration. J. Statist. Comput. Simulation (1992) 41:143–168CrossrefGoogle Scholar
  • Oh M.-S., Berger J. O. Integration of multimodal functions by Monte Carlo importance sampling. J. Amer. Statist. Assoc. (1993) 88:450–456CrossrefGoogle Scholar
  • Rockafellar R. T.Convex Analysis (1970) (Princeton Univ. Press, Princeton, NJ) CrossrefGoogle Scholar
  • Rubinstein R. Y. The cross-entropy method for combinatorial and continuous optimization. Methodology Comput. Appl. Probab. (1999) 2:127–190CrossrefGoogle Scholar
  • Rubinstein R. Y. Cross-entropy and rare events for maximal cut and partition problems. ACM Trans. Model. Comput. Simulation (2002) 12:27–53CrossrefGoogle Scholar
  • Rubinstein R. Y., Shapiro A.Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Method (1993) (Wiley, Chichester, UK) Google Scholar
  • Serfling R.Approximation Theorems in Mathematical Statistics (1980) (Wiley, New York) CrossrefGoogle Scholar
  • Shahabuddin P., Alexopoulos C., Kang K., Lilegdon W. R., Goldsman D. Rare event simulation of stochastic systems. Proc. 1995 Winter Simulation Conf. (1995) Arlington, VA:178–185Google Scholar
  • Shapiro A., Homem-de-Mello T. On the rate of convergence of Monte Carlo approximations of stochastic programs. SIAM J. Optim. (2000) 11:70–86CrossrefGoogle Scholar
  • Vázquez-Abad F., Dufresne D., Medeiros D. J., Watson E. F., Carson J. S., Manivannan M. S. Accelerated simulation for pricing Asian options. Proc. 1998 Winter Simulation Conf. (1998) Washington, D.C.:1493–1500CrossrefGoogle Scholar
  • Villén-Altamirano M., Villén-Altamirano J. About the efficiency of RESTART. Proc. RESIM Workshop (1999) Univ. of Twente, The Netherlands:99–128Google Scholar
  • Zhang P. Nonparametric importance sampling. J. Amer. Statist. Assoc. (1996) 91:1245–1253CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.