Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
research-article

Green Simulation: Reusing the Output of Repeated Experiments

Published: 27 October 2017 Publication History

Abstract

We introduce a new paradigm in simulation experiment design and analysis, called “green simulation,” for the setting in which experiments are performed repeatedly with the same simulation model. Green simulation means reusing outputs from previous experiments to answer the question currently being asked of the simulation model. As one method for green simulation, we propose estimators that reuse outputs from previous experiments by weighting them with likelihood ratios, when parameters of distributions in the simulation model differ across experiments. We analyze convergence of these estimators as more experiments are repeated, while a stochastic process changes the parameters used in each experiment. As another method for green simulation, we propose an estimator based on stochastic kriging. We find that green simulation can reduce mean squared error by more than an order of magnitude in examples involving catastrophe bond pricing and credit risk evaluation.

References

[1]
Bruce Ankenman, Barry L. Nelson, and Jeremy Staum. 2010. Stochastic kriging for simulation metamodeling. Operat. Res. 58, 2 (2010), 371--382.
[2]
Russell R. Barton, Barry L. Nelson, and Wei Xie. 2014. Quantifying input uncertainty via simulation confidence intervals. INFORMS J. Comput. 26, 1 (2014), 74--87.
[3]
Richard J. Beckman and Michael D. McKay. 1987. Monte Carlo estimation under different distributions using the same simulation. Technometrics 29, 2 (1987), 153--160.
[4]
George D. Birkhoff. 1931. Proof of the ergodic theorem. In Proceedings of the National Academy of Sciences, Vol. 17. National Academy of Sciences, 656--660.
[5]
Eric S. Blake and Ethan J. Gibney. 2011. The Deadliest, Costliest, and Most Intense United States Tropical Cyclones from 1851 to 2010 (and Other Frequently Requested Hurricane Facts). Retrieved July 25, 2017 from http://www.nhc.noaa.gov/dcmi.shtml.
[6]
Joshua D. Coval, Jakub W. Jurek, and Erik Stafford. 2009. Economic catastrophe bonds. Amer. Econ. Rev. 99, 3 (June 2009), 628--666.
[7]
Angelos Dassios and Ji-Wook Jang. 2003. Pricing of catastrophe reinsurance and derivatives using the Cox process with shot noise intensity. Fin. Stochast. 7, 1 (January 2003), 73--95.
[8]
Mingbin Feng and Jeremy Staum. 2015. Green simulation designs for repeated experiments. In Proceedings of the 2015 Winter Simulation Conference, L. Yilmaz, W. K. V. Chan, I. Moon, T. M. K. Roeder, C. Macal, and M. D. Rossetti (Eds.). IEEE Press, Piscataway, NJ, 403--413.
[9]
Michael Fu and others. 2015. Handbook of Simulation Optimization. Vol. 216. Springer, New York.
[10]
Paul Glasserman and Xingbo Xu. 2014. Robust risk measurement and model risk. Quant. Fin. 14, 1 (2014), 29--58.
[11]
Tim Hesterberg. 1988. Advances in Importance Sampling. Ph.D. Dissertation. Stanford University.
[12]
Tim Hesterberg. 1995. Weighted average importance sampling and defensive mixture distributions. Technometrics 37, 2 (1995), 185--194.
[13]
Jack P. C. Kleijnen and Reuven Y. Rubinstein. 1996. Optimization and sensitivity analysis of computer simulation models by the score function method. Eur. J. Operat. Res. 88 (1996), 413--427.
[14]
Stuart A. Klugman, Harry H. Panjer, and Gordon E. Willmot. 2012. Loss Models: From Data to Decisions (4 ed.). John Wiley 8 Sons.
[15]
Andrea Laforgia. 1991. Bounds for modified Bessel functions. J. Comput. Appl. Math. 34, 3 (1991), 263--267.
[16]
Pierre L’Ecuyer. 1990. A unified view of the IPA, SF, and LR gradient estimation techniques. Manage. Sci. 36, 11 (1990), 1364--1383.
[17]
Pierre L’Ecuyer. 1993. Two approaches for estimating the gradient in functional form. In Proceedings of the 25th Conference on Winter Simulation. ACM, New York, 338--346.
[18]
Yudell L. Luke. 1972. Inequalities for generalized hypergeometric functions. J. Approx. Theory 5, 1 (1972), 41--65.
[19]
Alvaro Maggiar, Andreas Wächter, Irina S. Dolinskaya, and Jeremy Staum. 2015. A Derivative-Free Algorithm for the Optimization of Functions Smoothed via Gaussian Convolution Using Multiple Importance Sampling. Retrieved May 27, 2017 from http://www.optimization-online.org/DB_HTML/2015/07/5017.html.
[20]
Luca Martino, Victor Elvira, David Luengo, and Jukka Corander. 2015. An adaptive population importance sampler: Learning from uncertainty. IEEE Trans. Signal Process. 63, 16 (2015), 4422--4437.
[21]
Alexander J. McNeil, Rüdiger Frey, and Paul Embrechts. 2005. Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton University Press, Princeton, NJ.
[22]
Robert C. Merton. 1974. On the pricing of corporate debt: The risk structure of interest rates. J. Fin. 29, 2 (1974), 449--470.
[23]
Sean Meyn and Richard L. Tweedie. 2009. Markov Chains and Stochastic Stability (2 ed.). Cambridge University Press, New York, NY.
[24]
Munich Re Geo Risks Research. 2015. Loss Events Worldwide 1980--2014, 10 Costliest Events Ordered by Overall Losses. Technical Report. Munich Re.
[25]
Esa Nummelin. 2004. General Irreducible Markov Chains and Non-Negative Operators. Cambridge Tracts in Mathematics, Vol. 83. Cambridge University Press.
[26]
Art B. Owen and Yi Zhou. 2000. Safe and effective importance sampling. J. Amer. Statist. Assoc. 95, 449 (2000), 135--143.
[27]
Reuven Y. Rubinstein and Alexander Shapiro. 1993. Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Method. John Wiley 8 Sons, New Jersey.
[28]
Peter Salemi, Jeremy Staum, and Barry L. Nelson. 2013. Generalized integrated Brownian fields for simulation metamodeling. In Proceedings of the 2013 Winter Simulation Conference: Simulation: Making Decisions in a Complex World, R. Pasupathy, S.-H. Kim, R. Hill, A. Tolk, and M. E. Kuhl (Eds.). IEEE Press, 543--554.
[29]
Jeremy Staum. 2009. Better simulation metamodeling: The why, what, and how of stochastic kriging. In Proceedings of the 2015 Winter Simulation Conference, M. D. Rossetti, B. Johansson R. R. Hill, A. Dunkin, and R. G. Ingalls (Eds.). IEEE Press, Piscataway, NJ, 119--133.
[30]
Eric Veach. 1997. Robust Monte Carlo Methods for Light Transport Simulation. Ph.D. Dissertation. Stanford University.
[31]
Eric Veach and Leonidas J. Guibas. 1995. Optimally combining sampling techniques for Monte Carlo rendering. In Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH’95). ACM, New York, NY, 419--428.
[32]
Wei Xie, Barry L. Nelson, and Russell R. Barton. 2014. A Bayesian framework for quantifying uncertainty in stochastic simulation. Operat. Res. 62, 6 (2014), 1439--1452.

Cited By

View all

Index Terms

  1. Green Simulation: Reusing the Output of Repeated Experiments

      Recommendations

      Comments

      Information & Contributors

      Information

      Published In

      cover image ACM Transactions on Modeling and Computer Simulation
      ACM Transactions on Modeling and Computer Simulation  Volume 27, Issue 4
      October 2017
      158 pages
      ISSN:1049-3301
      EISSN:1558-1195
      DOI:10.1145/3155315
      Issue’s Table of Contents
      Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication Notes

      Badge change: Article originally badged under Version 1.0 guidelines https://www.acm.org/publications/policies/artifact-review-badging

      Publication History

      Published: 27 October 2017
      Accepted: 01 July 2017
      Revised: 01 May 2017
      Received: 01 October 2016
      Published in TOMACS Volume 27, Issue 4

      Permissions

      Request permissions for this article.

      Check for updates

      Badges

      Author Tags

      1. Likelihood ratio method
      2. multiple importance sampling
      3. score function method
      4. simulation metamodeling

      Qualifiers

      • Research-article
      • Research
      • Refereed

      Contributors

      Other Metrics

      Bibliometrics & Citations

      Bibliometrics

      Article Metrics

      • Downloads (Last 12 months)51
      • Downloads (Last 6 weeks)4
      Reflects downloads up to 10 Nov 2024

      Other Metrics

      Citations

      Cited By

      View all
      • (2024)Data-Driven Ranking and Selection Under Input UncertaintyOperations Research10.1287/opre.2022.237572:2(781-795)Online publication date: 1-Mar-2024
      • (2024)Efficient Nested Simulation Experiment Design via the Likelihood Ratio MethodINFORMS Journal on Computing10.1287/ijoc.2022.0392Online publication date: 12-Jun-2024
      • (2024)Monte Carlo Methods for Economic CapitalINFORMS Journal on Computing10.1287/ijoc.2021.026136:1(266-284)Online publication date: Jan-2024
      • (2024)Context, Composition, Automation, and Communication: The C2AC Roadmap for Modeling and SimulationACM Transactions on Modeling and Computer Simulation10.1145/367322634:4(1-51)Online publication date: 13-Aug-2024
      • (2024)Selection of the Best in the Presence of Subjective Stochastic ConstraintsACM Transactions on Modeling and Computer Simulation10.1145/366481434:4(1-60)Online publication date: 12-Jul-2024
      • (2023)Generalized Importance Sampling for Nested SimulationProceedings of the Winter Simulation Conference10.5555/3643142.3643176(409-420)Online publication date: 10-Dec-2023
      • (2023)Achieving Stable Service-Level Targets in Time-Varying Queueing Systems: A Simulation-Based Offline Learning Staffing AlgorithmProceedings of the Winter Simulation Conference10.5555/3643142.3643169(327-338)Online publication date: 10-Dec-2023
      • (2023)Automatic Reuse, Adaption, and Execution of Simulation Experiments via Provenance PatternsACM Transactions on Modeling and Computer Simulation10.1145/356492833:1-2(1-27)Online publication date: 28-Feb-2023
      • (2023)Achieving Stable Service-Level Targets in Time-Varying Queueing Systems: A Simulation-Based Offline Learning Staffing Algorithm2023 Winter Simulation Conference (WSC)10.1109/WSC60868.2023.10408273(327-338)Online publication date: 10-Dec-2023
      • (2023)Generalized Importance Sampling for Nested Simulation2023 Winter Simulation Conference (WSC)10.1109/WSC60868.2023.10408062(409-420)Online publication date: 10-Dec-2023
      • Show More Cited By

      View Options

      Get Access

      Login options

      Full Access

      View options

      PDF

      View or Download as a PDF file.

      PDF

      eReader

      View online with eReader.

      eReader

      Media

      Figures

      Other

      Tables

      Share

      Share

      Share this Publication link

      Share on social media