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Screening: From tornado diagrams to effective dimensions

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  • Borgonovo, Emanuele
  • Rabitti, Giovanni

Abstract

Popular sensitivity analysis techniques such as Tornado Diagrams or the Morris method are based on one-at-a-time input variations (local main effects, henceforth). We evidence a link between local main effects of screening methods and global sensitivity measures. The link allows analysts to obtain insights on interactions on the local and global scales simultaneously. We evidence a mirroring effect according to which a local main effect calculated from the base case to the sensitivity case is equal in magnitude to the local total effect in the opposite direction, and their difference yields an overall local interaction index. We then obtain the exact relationship between Morris sensitivity measures and Sobol’ total indices and discuss its implications on the choice of the sampling scheme. We show that the non-diagonal elements of the variance-covariance matrix of main effects computed at randomized locations yield Liu and Owen’s global interaction indices. Asymptotic results are derived with particular reference to confidence intervals for the mean dimension. We illustrate findings and insights through numerical experiments on two well known simulators.

Suggested Citation

  • Borgonovo, Emanuele & Rabitti, Giovanni, 2023. "Screening: From tornado diagrams to effective dimensions," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1200-1211.
    • Handle: RePEc:eee:ejores:v:304:y:2023:i:3:p:1200-1211
    DOI: 10.1016/j.ejor.2022.05.003
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    References listed on IDEAS

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    1. Kucherenko, S. & Rodriguez-Fernandez, M. & Pantelides, C. & Shah, N., 2009. "Monte Carlo evaluation of derivative-based global sensitivity measures," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1135-1148.
    2. Wen Shi & Xi Chen & Jennifer Shang, 2019. "An Efficient Morris Method-Based Framework for Simulation Factor Screening," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 745-770, October.
    3. Barry L. Nelson, 2013. "Foundations and Methods of Stochastic Simulation," International Series in Operations Research and Management Science, Springer, edition 127, number 978-1-4614-6160-9, December.
    4. Xiaoqun Wang & Ken Seng Tan, 2013. "Pricing and Hedging with Discontinuous Functions: Quasi-Monte Carlo Methods and Dimension Reduction," Management Science, INFORMS, vol. 59(2), pages 376-389, July.
    5. Pesenti, Silvana M. & Millossovich, Pietro & Tsanakas, Andreas, 2019. "Reverse sensitivity testing: What does it take to break the model?," European Journal of Operational Research, Elsevier, vol. 274(2), pages 654-670.
    6. Harvey M. Wagner, 1995. "Global Sensitivity Analysis," Operations Research, INFORMS, vol. 43(6), pages 948-969, December.
    7. Shi, Wen & Chen, Xi, 2019. "Controlled Morris method: A new factor screening approach empowered by a distribution-free sequential multiple testing procedure," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 299-314.
    8. Michael A. Zazanis & Rajan Suri, 1993. "Convergence Rates of Finite-Difference Sensitivity Estimates for Stochastic Systems," Operations Research, INFORMS, vol. 41(4), pages 694-703, August.
    9. Andreas Tsanakas & Pietro Millossovich, 2016. "Sensitivity Analysis Using Risk Measures," Risk Analysis, John Wiley & Sons, vol. 36(1), pages 30-48, January.
    10. Xiaoqun Wang & Ian H. Sloan, 2011. "Quasi-Monte Carlo Methods in Financial Engineering: An Equivalence Principle and Dimension Reduction," Operations Research, INFORMS, vol. 59(1), pages 80-95, February.
    11. J. E. Jacoby & S. Harrison, 1962. "Multi‐variable experimentation and simulation models," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 9(2), pages 121-136, June.
    12. Ted G. Eschenbach, 1992. "Spiderplots versus Tornado Diagrams for Sensitivity Analysis," Interfaces, INFORMS, vol. 22(6), pages 40-46, December.
    13. E. Borgonovo & C. L. Smith, 2011. "A Study of Interactions in the Risk Assessment of Complex Engineering Systems: An Application to Space PSA," Operations Research, INFORMS, vol. 59(6), pages 1461-1476, December.
    14. Ronald A. Howard, 1988. "Decision Analysis: Practice and Promise," Management Science, INFORMS, vol. 34(6), pages 679-695, June.
    15. Liu, Ruixue & Owen, Art B., 2006. "Estimating Mean Dimensionality of Analysis of Variance Decompositions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 712-721, June.
    16. Wen Shi & Xi Chen, 2018. "Efficient budget allocation strategies for elementary effects method in stochastic simulation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(3), pages 218-241, April.
    17. Xiaoqun Wang, 2006. "On the Effects of Dimension Reduction Techniques on Some High-Dimensional Problems in Finance," Operations Research, INFORMS, vol. 54(6), pages 1063-1078, December.
    18. Xiaoqun Wang, 2016. "Handling Discontinuities in Financial Engineering: Good Path Simulation and Smoothing," Operations Research, INFORMS, vol. 64(2), pages 297-314, April.
    19. Saltelli, Andrea & Campolongo, Francesca & Cariboni, Jessica, 2009. "Screening important inputs in models with strong interaction properties," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1149-1155.
    20. Sobol’, I.M. & Kucherenko, S., 2009. "Derivative based global sensitivity measures and their link with global sensitivity indices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3009-3017.
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