Sampling of uncertain probabilities at event tree nodes with multiple branches

Philipson, Lloyd L.; Wilde, Paul

doi:10.1016/s0951-8320(00)00061-2

Cited by 4 publications

(3 citation statements)

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“…Several applications, however, entail the creation of models in which parameters are constrained. Examples are event trees (see Philipson & Wilde, 2000), decision trees (see Clemen, 1997), Markov‐chain‐based models (Rief, 1998.) To study the sensitivity of the output to changes in the probabilities, one needs to account for the fact that probabilities of outcomes of the same node (event trees and decision trees) or in the same row (Markov matrices) must sum to unity.…”

Section: Introductionmentioning

confidence: 99%

“…In Section 5, we define a stepwise implementation of the rationale and illustrate its application to a nonbinary event tree. Conclusions are offered in Section 6. tions, as illustrated in Philipson and Wilde (2000) for the case of probabilities summing to unity. The second effect is that deterministic constraints induce correlations among the inputs.…”

Section: Introductionmentioning

confidence: 99%

“…We can briefly summarize some of the features: the first effect is that, in performing the global sensitivity exercise, one needs to generate inputs that not only reflect the analyst uncertainty, but that also match the equation of the constraint. This generates several complications, as illustrated in Philipson and Wilde (2000) for the case of probabilities summing to unity. The second effect is that deterministic constraints induce correlations among the inputs.…”

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

Borgonovo¹

2008

Risk Analysis

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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