A Look At Multilevel Splitting
This paper gives a non-technical overview of our work on the efficiency of a simple multilevel splitting technique for estimating rare event probabilities. For a particular class of stochastic models, this method is asymptotically optimal provided the splitting factor is properly chosen. However, for more general classes of processes, the method fails to be asymptotically optimal unless the splitting is done in a manner consistent with the dominant way in which the rare event happens (the large deviations behavior). In the absence of such consistency, the method also exhibits a kind of bias in which the estimate is too small with high probability. We briefly contrast our approach with one used in nuclear physics.
Unable to display preview. Download preview PDF.
- [Buc90]J.A. Bucklew. Large Deviation Techniques in Decision,Simulation and Estimation. Wiley, New York, 1990.Google Scholar
- [DGB86]A. Dubi, A. Goldfeld, and K. Burn. Application of the direct statistical approach on a multisurface splitting problem in Monte Carlo calculations. Nuclear Science and Engineering, 93:204–213, 1986..Google Scholar
- [GHSZ96a]P. Glasserman, P. Heidelberger, P. Shahabuddin, and T. Zajic. Multilevel splitting for estimating rare event probabilities. Technical Report RC 204–78, IBM T.J. Watson Research Center, Yorktown Heights, NY, 1996.Google Scholar
- [GHSZ96b]P. Glasserman, P. Heidelberger, P. Shahabuddin, and T. Zajic. Splitting for rare event simulation: Analysis of simple cases. In 1996 Winter Simulation Conference Proceedings, pages 302–308, San Diego, CA, 1996. IEEE Computer Society Press.Google Scholar
- [GHSZ97]P. Glasserman, P. Heidelberger, P. Shahabuddin, and T. Zajic. A large deviations perspective on the efficiency of multilevel splitting. Technical Report 20692, IBM T.J. Watson Research Center, Yorktown Heights, NY, 1997.Google Scholar
- [GW96]P. Glasserman and Y. Wang. Counterexamples in importance sampling for large deviations probabilities. Technical report, Columbia Business School, New York, NY, 1996. To appear in Annals of Applied Probability. Google Scholar
- [Hei95]P. Heidelberger. Fast simulation of rare events in queueing and reliability models. ACM Trans. Modeling and Computer Simulation, 5:43 — 85, 1995.Google Scholar
- [HH65]J.M. Hammersley and D.C. Handscomb. Monte Carlo Methods. Methuen and Co. Ltd., London, 1965.Google Scholar
- [KH51]H Kahn and T.E. Harris. Estimation of particle transmission by random sampling. National Bureau of Standards Applied Mathematics Series, 12:27–30, 1951.Google Scholar
- [Me193]V.B. Melas. Optimal simulation design by branching technique. In H.P. Wynn W.G. Muller and A.A. Zhigljaysky, editors, Model Oriented Data Analysis, pages 113–128. Physica-Verlag, Heidelberg, 1993.Google Scholar
- [VMMF94]M. Villén-Altamirano, A. Martinez-Marrón, J. Gamo, and F. Fernández-Cuesta. Enhancements of the accelerated simulation method RESTART by considering multiple thresholds. In J. Labetoulle and J.W. Roberts, editors,International Telecommunications Conference 14,pages 797–810, Amsterdam, 1994. Elsevier Science Publishers.Google Scholar
- [VV91]M. Villén-Altamirano and J. Villén-Altamirano. RESTART: A method for accelerating rare event simulations. In J.W. Cohen and C.D. Pack, editors, Queueing, Performance and Control in ATM, pages 71–76. Elsevier Science Publishers, Amsterdam, 1991.Google Scholar
- [VV94]M. Villén-Altamirano and J. Villén-Altamirano. RESTART: A straightforward method for fast simulation of rare events. In 1994 Winter Simulation Conference Proceedings, pages 282–289, Orlando, FL, 1994.Google Scholar