Library Subscription: Guest
Begell Digital Portal Begell Digital Library eBooks Journals References & Proceedings Research Collections
International Journal for Uncertainty Quantification
IF: 3.259 5-Year IF: 2.547 SJR: 0.417 SNIP: 0.8 CiteScore™: 1.52

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2019029511
pages 311-319

A WEIGHT-BOUNDED IMPORTANCE SAMPLING METHOD FOR VARIANCE REDUCTION

Tenchao Yu
School of Mathematical Sciences and Institute of Natural Sciences, Shanghai Jiao Tong University, 800 Dongchuan Rd, Shanghai 200240, China
Linjun Lu
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
Jinglai Li
Institute of Natural Sciences and School of Mathematical Sciences Shanghai Jiaotong University, Shanghai 200240, China

ABSTRACT

Importance sampling (IS) is an important technique to reduce the estimation variance in Monte Carlo simulations. In many practical problems, however, the use of the IS method may result in unbounded variance, and thus fail to provide reliable estimates. To address the issue, we propose a method which can prevent the risk of unbounded variance; the proposed method performs the standard IS for the integral of interest in a region only in which the IS weight is bounded and we use the result as an approximation to the original integral. It can be verified that the resulting estimator has a finite variance. Moreover, we also provide a normality test based method to identify the region with bounded IS weight (termed as the safe region) from the samples drawn from the standard IS distribution. With numerical examples, we demonstrate that the proposed method can yield a rather reliable estimate when the standard IS fails, and it also outperforms the defensive IS, a popular method to prevent unbounded variance.

REFERENCES

  1. Liu, J.S., Monte Carlo Strategies in Scientific Computing, New York: Springer Science & Business Media, 2008.

  2. Robert, C. and Casella, G., Monte Carlo Statistical Methods, New York: Springer Science & Business Media, 2013.

  3. Landau, D.P. and Binder, K., A Guide to Monte Carlo Simulations in Statistical Physics, Cambridge, UK: Cambridge University Press, 2014.

  4. Glasserman, P., Monte Carlo Methods in Financial Engineering, vol. 53, New York: Springer Science & Business Media, 2013.

  5. Glasserman, P. and Wang, Y., Counterexamples in Importance Sampling for Large Deviations Probabilities, Ann. Appl. Probab., 7(3):731-746, 1997.

  6. Hesterberg, T., Weighted Average Importance Sampling and Defensive Mixture Distributions, Technometrics, 37(2):185-194, 1995.

  7. Owen, A. and Zhou, Y., Safe and Effective Importance Sampling, J. Am. Stat. Assoc, 95(449):135-143, 2000.

  8. Anderson, T.W. and Darling, D.A., Asymptotic Theory of Certain "Goodness of Fit" Criteria based on Stochastic Processes, Ann. Math. Stat., pp. 193-212, 1952.

  9. Yazici, B. and Yolacan, S., A Comparison of Various Tests ofNormality, J. Stat. Comput. Simul., 77(2):175-183, 2007.

  10. Glasserman, P. and Li, J., Importance Sampling for Portfolio Credit Risk, Manag. Sci., 51(11):1643-1656, 2005.

  11. de Boer, P.T., Kroese, D., Mannor, S., and Rubinstein, R., A Tutorial on Cross-Entropy Method, Ann. Oper. Res, 134:19-67, 2005.

  12. Rubinstein, R. and Kroese, D., The Cross-Entropy Method, New York: Springer Science & Business Media, Inc., 2004.


Articles with similar content:

DATA ASSIMILATION FOR NAVIER-STOKES USING THE LEAST-SQUARES FINITE-ELEMENT METHOD
International Journal for Uncertainty Quantification, Vol.8, 2018, issue 5
Richard P. Dwight, Alexander Schwarz
A GRADIENT-BASED SAMPLING APPROACH FOR DIMENSION REDUCTION OF PARTIAL DIFFERENTIAL EQUATIONS WITH STOCHASTIC COEFFICIENTS
International Journal for Uncertainty Quantification, Vol.5, 2015, issue 1
Miroslav Stoyanov, Clayton G. Webster
AN ADAPTIVE MULTIFIDELITY PC-BASED ENSEMBLE KALMAN INVERSION FOR INVERSE PROBLEMS
International Journal for Uncertainty Quantification, Vol.9, 2019, issue 3
Tao Zhou, Liang Yan
Mathematical Manipulation of the Interface Region of Multilayer Flows
Journal of Porous Media, Vol.12, 2009, issue 5
M. A. Hajji, F. Allan
MODELING OF THE ABSORPTION COEFFICIENT IN THE EXPONENTIAL WIDE BAND MODEL (EWBM)
ICHMT DIGITAL LIBRARY ONLINE, Vol.16, 2004, issue
Bengt Sunden, M. Bahador