Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-05-09T08:07:13.217Z Has data issue: false hasContentIssue false
  • English
  • Français

Deep-Penetration Calculations for Scattering Neutrons by Importance Sampling

Published online by Cambridge University Press:  27 July 2009

Craig Kollman
Craig Kollman
Affiliation:
Department of Statistics, Sequoia Hall, Stanford University, Stanford, California 94305
Get access Rights & Permissions [Opens in a new window]

Abstract

Neutron scatter in a homogeneous solid is modelled as a one-dimensional i.i.d. random walk with killing. Importance sampling is used to estimate the extremely small probability that the random walk crosses a large level before killing occurs. The theory of large deviations provides insight into the selection of the probability measure used in the simulations. A sample problem demonstrates the variance reduction possible when this technique is used.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 8 , Issue 2 , April 1994 , pp. 201 - 211
Copyright
Copyright © Cambridge University Press 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Bucklew, J.A. (1990). Large deviation techniques in decision, simulation, and estimation. New York: Wiley Interscience.Google Scholar
2.Cramer, S.N., Gonnord, J., & Hendricks, J.S. (1986). Monte Carlo techniques for analyzing deep-penetration problems. Nuclear Science and Engineering 92: 280–288.CrossRefGoogle Scholar
3.Glynn, P.W. & Iglehart, D.L. (1989). Importance sampling for stochastic simulations. Management Science 35: 1367–1392.CrossRefGoogle Scholar
4.Lehtonen, T. & Nyrhinen, H. (1992). Simulating level-crossing probabilities by importance sampling. Advances in Applied Probability 24: 858–874.CrossRefGoogle Scholar
5.Murthy, K.P.N. & Indira, R. (1986). Analytical results of variance reduction characteristics of biased Monte Carlo for deep-penetration problems. Nuclear Science and Engineering 92: 482–487.CrossRefGoogle Scholar
6.Ripley, B.D. (1987). Stochastic simulation. New York: John Wiley & Sons.CrossRefGoogle Scholar
7.Rockafellar, R.T. (1970). Convex analysis. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
8.Siegmund, D. (1976). Importance sampling in the Monte Carlo study of sequential tests. Annals of Statistics 4: 673–684.CrossRefGoogle Scholar
9.Siegmund, D. (1985). Sequential analysis. New York: Springer-Verlag.CrossRefGoogle Scholar