Uncertainty-based sensitivity indices for imprecise probability distributions

Jim W. Hall

Reliability Engineering and System Safety, 2006, vol. 91, issue 10, 1443-1451

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.

Keywords: Coherent lower and upper probabilities; Variance-based sensitivity indices; Partial expected value of perfect information; Entropy-based sensitivity indices; Generalized information theory (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:91:y:2006:i:10:p:1443-1451

DOI: 10.1016/j.ress.2005.11.042

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