A Study on the Cross-Entropy Method for Rare-Event Probability Estimation
Published Online:20 Jul 2007https://doi.org/10.1287/ijoc.1060.0176
References
- A classified bibliography of research on stochastic PERT networks: 1966–1987. INFOR (1989) 27:272–296Google Scholar
- Applied Probability and Queues (2003) 2nd ed.(Springer-Verlag, Berlin, Germany) Google Scholar
- Perturbation Analysis of Optimization Problems (2000) (Springer-Verlag, New York) Springer Series in Operations ResearchCrossref, Google Scholar
- Large Deviation Techniques in Decision, Simulation, and Estimation (1990) (Wiley, New York) Google Scholar
- Analysis and efficient simulation of queueing models of telecommunications systems. (2000) . Ph.D. thesis, Department of Computer Science, Univ. of Twente, The NetherlandsGoogle Scholar
- A tutorial on the cross-entropy method. Ann. Oper. Res. (2005) 134:19–67Crossref, Google Scholar
- Large Deviations Techniques and Applications (1998) (Springer-Verlag, New York) Crossref, Google Scholar
- Monte Carlo: Concepts, Algorithms and Applications (1997) (Springer-Verlag, New York) Google Scholar
- Monte Carlo Methods in Financial Engineering. Applications of Mathematics (2004) 53(Springer-Verlag, New York) Google Scholar
- Multilevel splitting for estimating rare event probabilities. Oper. Res. (1999) 47:585–600Link, Google Scholar
- Importance sampling for stochastic simulations. Management Sci. (1989) 35:1367–1392Link, Google Scholar
- Fast simulation of rare events in queueing and reliability models. ACM Trans. Model. Comput. Simulation (1995) 5:43–85Crossref, Google Scholar
- , 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:310–319Crossref, Google Scholar
- Finding optimal material release times using simulation based optimization. Management Sci. (1999) 45:86–102Link, Google Scholar
- , 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.:1616–1624Crossref, Google Scholar
- Simulating heavy tailed processes using delayed hazard rate twisting. ACM Trans. Model. Comput. Simulation (2002) 12:94–118Crossref, Google Scholar
- Asymptotics and fast simulation for tail probabilities of maximum of sums of few random variables. ACM Trans. Model. Comput. Simulation (2007) 17(2). Article 7Crossref, Google Scholar
- Methods of reducing the sample size in Monte Carlo computations. J. Oper. Res. Soc. (1953) 1:263–278Abstract, Google Scholar
- Probabilistic bounds (via large deviations) for the solutions of stochastic programming problems. Ann. Oper. Res. (1995) 56:189–208Crossref, Google Scholar
- Entropy Optimization Principles with Applications (1992) (Academic Press, New York) Crossref, Google Scholar
- The transform likelihood ratio method for rare event simulation with heavy tails. Queueing Systems (2004) 46:317–351Crossref, Google Scholar
- On information and sufficiency. Ann. Math. Statist. (1951) 22:79–86Crossref, Google Scholar
- Simulation Modeling and Analysis (2000) 3rd ed.(McGraw-Hill, New York) Google Scholar
- Adaptive importance sampling in Monte Carlo integration. J. Statist. Comput. Simulation (1992) 41:143–168Crossref, Google Scholar
- Integration of multimodal functions by Monte Carlo importance sampling. J. Amer. Statist. Assoc. (1993) 88:450–456Crossref, Google Scholar
- Convex Analysis (1970) (Princeton Univ. Press, Princeton, NJ) Crossref, Google Scholar
- The cross-entropy method for combinatorial and continuous optimization. Methodology Comput. Appl. Probab. (1999) 2:127–190Crossref, Google Scholar
- Cross-entropy and rare events for maximal cut and partition problems. ACM Trans. Model. Comput. Simulation (2002) 12:27–53Crossref, Google Scholar
- Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Method (1993) (Wiley, Chichester, UK) Google Scholar
- Approximation Theorems in Mathematical Statistics (1980) (Wiley, New York) Crossref, Google Scholar
- , 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
- On the rate of convergence of Monte Carlo approximations of stochastic programs. SIAM J. Optim. (2000) 11:70–86Crossref, Google Scholar
- , 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.:1493–1500Crossref, Google Scholar
- About the efficiency of RESTART. Proc. RESIM Workshop (1999) Univ. of Twente, The Netherlands:99–128Google Scholar
- Nonparametric importance sampling. J. Amer. Statist. Assoc. (1996) 91:1245–1253Crossref, Google Scholar

