Publicou 6 edições por ano
ISSN Imprimir: 2152-5080
ISSN On-line: 2152-5099
Indexed in
A WEIGHT-BOUNDED IMPORTANCE SAMPLING METHOD FOR VARIANCE REDUCTION
RESUMO
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.
-
Liu, J.S., Monte Carlo Strategies in Scientific Computing, New York: Springer Science & Business Media, 2008.
-
Robert, C. and Casella, G., Monte Carlo Statistical Methods, New York: Springer Science & Business Media, 2013.
-
Landau, D.P. and Binder, K., A Guide to Monte Carlo Simulations in Statistical Physics, Cambridge, UK: Cambridge University Press, 2014.
-
Glasserman, P., Monte Carlo Methods in Financial Engineering, vol. 53, New York: Springer Science & Business Media, 2013.
-
Glasserman, P. and Wang, Y., Counterexamples in Importance Sampling for Large Deviations Probabilities, Ann. Appl. Probab., 7(3):731-746, 1997.
-
Hesterberg, T., Weighted Average Importance Sampling and Defensive Mixture Distributions, Technometrics, 37(2):185-194, 1995.
-
Owen, A. and Zhou, Y., Safe and Effective Importance Sampling, J. Am. Stat. Assoc, 95(449):135-143, 2000.
-
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.
-
Yazici, B. and Yolacan, S., A Comparison of Various Tests ofNormality, J. Stat. Comput. Simul., 77(2):175-183, 2007.
-
Glasserman, P. and Li, J., Importance Sampling for Portfolio Credit Risk, Manag. Sci., 51(11):1643-1656, 2005.
-
de Boer, P.T., Kroese, D., Mannor, S., and Rubinstein, R., A Tutorial on Cross-Entropy Method, Ann. Oper. Res, 134:19-67, 2005.
-
Rubinstein, R. and Kroese, D., The Cross-Entropy Method, New York: Springer Science & Business Media, Inc., 2004.
-
Zhang Hongjie, Qu Cheng, Zhang Jindou, Li Jing, Self-Adaptive Priority Correction for Prioritized Experience Replay, Applied Sciences, 10, 19, 2020. Crossref