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Uncertainty-based sensitivity indices for imprecise probability distributions

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  • Hall, Jim W.

Abstract

An uncertainty-based sensitivity index represents the contribution that uncertainty in model input Xi makes to the uncertainty in model output Y. This paper addresses the situation where the uncertainties in the model inputs are expressed as closed convex sets of probability measures, a situation that exists when inputs are expressed as intervals or sets of intervals with no particular distribution specified over the intervals, or as probability distributions with interval-valued parameters. Three different approaches to measuring uncertainty, and hence uncertainty-based sensitivity, are explored. Variance-based sensitivity analysis (VBSA) estimates the contribution that each uncertain input, acting individually or in combination, makes to variance in the model output. The partial expected value of perfect information (partial EVPI), quantifies the (financial) value of learning the true numeric value of an input. For both of these sensitivity indices the generalization to closed convex sets of probability measures yields lower and upper sensitivity indices. Finally, the use of relative entropy as an uncertainty-based sensitivity index is introduced and extended to the imprecise setting, drawing upon recent work on entropy measures for imprecise information.

Suggested Citation

  • Hall, Jim W., 2006. "Uncertainty-based sensitivity indices for imprecise probability distributions," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1443-1451.
    • Handle: RePEc:eee:reensy:v:91:y:2006:i:10:p:1443-1451
    DOI: 10.1016/j.ress.2005.11.042
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    Cited by:

    1. Wang, Lei & Liu, Yaru & Li, Min, 2022. "Time-dependent reliability-based optimization for structural-topological configuration design under convex-bounded uncertain modeling," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    2. Ning-Cong Xiao & Hong-Zhong Huang & Yan-Feng Li & Zhonglai Wang & Xiao-Ling Zhang, 2013. "Non-probabilistic reliability sensitivity analysis of the model of structural systems with interval variables whose state of dependence is determined by constraints," Journal of Risk and Reliability, , vol. 227(5), pages 491-498, October.
    3. Limbourg, Philipp & de Rocquigny, Etienne, 2010. "Uncertainty analysis using evidence theory – confronting level-1 and level-2 approaches with data availability and computational constraints," Reliability Engineering and System Safety, Elsevier, vol. 95(5), pages 550-564.
    4. Rocchetta, Roberto & Patelli, Edoardo, 2020. "A post-contingency power flow emulator for generalized probabilistic risks assessment of power grids," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    5. Tu Duong Le Duy & Laurence Dieulle & Dominique Vasseur & Christophe Bérenguer & Mathieu Couplet, 2013. "An alternative comprehensive framework using belief functions for parameter and model uncertainty analysis in nuclear probabilistic risk assessment applications," Journal of Risk and Reliability, , vol. 227(5), pages 471-490, October.

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