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Sensitivity Analysis for Simulations via Likelihood Ratios

Author

Listed:
  • Martin I. Reiman

    (AT&T Bell Laboratories, Murray Hill, New Jersey)

  • Alan Weiss

    (AT&T Bell Laboratories, Murray Hill, New Jersey)

Abstract

We present a simple method of estimating the sensitivity of quantities obtained from simulation with respect to a class of parameters. Here sensitivity means the derivative of an expectation with respect to a parameter. The class of parameters includes, for example, Poisson rates, discrete probabilities, and the mean and variance of a Normal distribution. The method is extremely well suited to regenerative simulation, and can be implemented on extant simulations with little effort, increase in running time, or memory requirements. It is based on some change-of-measure formulas derived from likelihood ratios. In addition to the theorems that underly the technique, we present some numerical examples.

Suggested Citation

  • Martin I. Reiman & Alan Weiss, 1989. "Sensitivity Analysis for Simulations via Likelihood Ratios," Operations Research, INFORMS, vol. 37(5), pages 830-844, October.
    • Handle: RePEc:inm:oropre:v:37:y:1989:i:5:p:830-844
    DOI: 10.1287/opre.37.5.830
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    Cited by:

    1. Felisa J. Vazquez-Abad & Bernd Heidergott, 2003. "Gradient Estimation for a Class of Systems with Bulk Services: A Problem in Public Transportation," Tinbergen Institute Discussion Papers 03-057/4, Tinbergen Institute.
    2. J. Vazquez-Abad, Felisa, 2000. "RPA pathwise derivative estimation of ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 269-288, May.
    3. Gilles Pages & Olivier Pironneau & Guillaume Sall, 2015. "Vibrato and Automatic Differentiation for High Order Derivatives and Sensitivities of Financial Options," Working Papers hal-01234637, HAL.
    4. Detemple, Jerome & Rindisbacher, Marcel, 2007. "Monte Carlo methods for derivatives of options with discontinuous payoffs," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3393-3417, April.
    5. Soumyadip Ghosh & Henry Lam, 2019. "Robust Analysis in Stochastic Simulation: Computation and Performance Guarantees," Operations Research, INFORMS, vol. 67(1), pages 232-249, January.
    6. Sridhar Bashyam & Michael C. Fu, 1994. "Application of perturbation analysis to a class of periodic review (s, S) inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(1), pages 47-80, February.
    7. Kleijnen, Jack P. C. & Rubinstein, Reuven Y., 1996. "Optimization and sensitivity analysis of computer simulation models by the score function method," European Journal of Operational Research, Elsevier, vol. 88(3), pages 413-427, February.
    8. Sarazin, Gabriel & Morio, Jérôme & Lagnoux, Agnès & Balesdent, Mathieu & Brevault, Loïc, 2021. "Reliability-oriented sensitivity analysis in presence of data-driven epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    9. Marvin K. Nakayama & Perwez Shahabuddin, 1998. "Likelihood Ratio Derivative Estimation for Finite-Time Performance Measures in Generalized Semi-Markov Processes," Management Science, INFORMS, vol. 44(10), pages 1426-1441, October.
    10. Calvin, James M. & Nakayama, Marvin K., 2004. "Permuted derivative and importance-sampling estimators for regenerative simulations," European Journal of Operational Research, Elsevier, vol. 156(2), pages 390-414, July.
    11. L. Jeff Hong, 2009. "Estimating Quantile Sensitivities," Operations Research, INFORMS, vol. 57(1), pages 118-130, February.
    12. Michael C. Fu, 2008. "What you should know about simulation and derivatives," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(8), pages 723-736, December.
    13. Jacobson, Sheldon H., 1997. "The effect of initial transient on the steady-state simulation harmonic analysis gradient estimators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 43(2), pages 209-221.
    14. Abbas, K. & Heidergott, B.F. & Aissani, D., 2011. "A Taylor series expansion approach to the functional approximation of finite queues," Serie Research Memoranda 0049, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    15. Gilles Pag`es & Olivier Pironneau & Guillaume Sall, 2016. "Vibrato and automatic differentiation for high order derivatives and sensitivities of financial options," Papers 1606.06143, arXiv.org.
    16. Mark J. Cathcart & Steven Morrison & Alexander J. McNeil, 2011. "Calculating Variable Annuity Liability 'Greeks' Using Monte Carlo Simulation," Papers 1110.4516, arXiv.org.
    17. Xin Yun & L. Jeff Hong & Guangxin Jiang & Shouyang Wang, 2019. "On gamma estimation via matrix kriging," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(5), pages 393-410, August.
    18. Kleijnen, J.P.C. & Rubinstein, R.Y., 1996. "Optimization and Sensitivity Analysis of Computer Simulation Models by the Score Function Method," Other publications TiSEM 958c9b9a-544f-48f3-a3d1-c, Tilburg University, School of Economics and Management.
    19. Laub, Patrick J. & Salomone, Robert & Botev, Zdravko I., 2019. "Monte Carlo estimation of the density of the sum of dependent random variables," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 161(C), pages 23-31.
    20. Akiyama, Naho & Yamada, Toshihiro, 2024. "A weak approximation for Bismut’s formula: An algorithmic differentiation method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 386-396.
    21. Li, Jinghui & Mosleh, Ali & Kang, Rui, 2011. "Likelihood ratio gradient estimation for dynamic reliability applications," Reliability Engineering and System Safety, Elsevier, vol. 96(12), pages 1667-1679.
    22. Jingxu Xu & Zeyu Zheng, 2023. "Gradient-Based Simulation Optimization Algorithms via Multi-Resolution System Approximations," INFORMS Journal on Computing, INFORMS, vol. 35(3), pages 633-651, May.
    23. Yijie Peng & Li Xiao & Bernd Heidergott & L. Jeff Hong & Henry Lam, 2022. "A New Likelihood Ratio Method for Training Artificial Neural Networks," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 638-655, January.
    24. Yongqiang Wang & Michael C. Fu & Steven I. Marcus, 2012. "A New Stochastic Derivative Estimator for Discontinuous Payoff Functions with Application to Financial Derivatives," Operations Research, INFORMS, vol. 60(2), pages 447-460, April.

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