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Sensitivity Analysis of Model Output with Input Constraints: A Generalized Rationale for Local Methods

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  • Emanuele Borgonovo

Abstract

In this work, we introduce a generalized rationale for local sensitivity analysis (SA) methods that allows to solve the problems connected with input constraints. Several models in use in the risk analysis field are characterized by the presence of deterministic relationships among the input parameters. However, SA issues related to the presence of constraints have been mainly dealt with in a heuristic fashion. We start with a systematic analysis of the effects of constraints. The findings can be summarized in the following three effects. (i) Constraints make it impossible to vary one parameter while keeping all others fixed. (ii) The model output becomes insensitive to a parameter if a constraint is solved for that parameter. (iii) Sensitivity analysis results depend on which parameter is selected as dependent. The explanation of these effects is found by proposing a result that leads to a natural extension of the local SA rationale introduced in Helton (1993). We then extend the definitions of the Birnbaum, criticality, and the differential importance measures to the constrained case. In addition, a procedure is introduced that allows to obtain constrained sensitivity results at the same cost as in the absence of constraints. The application to a nonbinary event tree concludes the article, providing a numerical illustration of the above findings.

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  • Emanuele Borgonovo, 2008. "Sensitivity Analysis of Model Output with Input Constraints: A Generalized Rationale for Local Methods," Risk Analysis, John Wiley & Sons, vol. 28(3), pages 667-680, June.
    • Handle: RePEc:wly:riskan:v:28:y:2008:i:3:p:667-680
    DOI: 10.1111/j.1539-6924.2008.01052.x
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    1. Isadora Antoniano‐Villalobos & Emanuele Borgonovo & Sumeda Siriwardena, 2018. "Which Parameters Are Important? Differential Importance Under Uncertainty," Risk Analysis, John Wiley & Sons, vol. 38(11), pages 2459-2477, November.
    2. S. Cucurachi & E. Borgonovo & R. Heijungs, 2016. "A Protocol for the Global Sensitivity Analysis of Impact Assessment Models in Life Cycle Assessment," Risk Analysis, John Wiley & Sons, vol. 36(2), pages 357-377, February.
    3. Aliee, Hananeh & Borgonovo, Emanuele & Glaß, Michael & Teich, Jürgen, 2017. "On the Boolean extension of the Birnbaum importance to non-coherent systems," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 191-200.
    4. Andreas Tsanakas & Pietro Millossovich, 2016. "Sensitivity Analysis Using Risk Measures," Risk Analysis, John Wiley & Sons, vol. 36(1), pages 30-48, January.
    5. Mikko V. Pohjola & Pasi Pohjola & Marko Tainio & Jouni T. Tuomisto, 2013. "Perspectives to Performance of Environment and Health Assessments and Models—From Outputs to Outcomes?," IJERPH, MDPI, vol. 10(7), pages 1-22, June.

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