Global Reliability‐oriented Sensitivity Analysis under Distribution Parameter Uncertainty

Chabridon, Vincent; Balesdent, Mathieu; Perrin, Guillaume; Mitard, J.; Bourinet, Jean‐Marc; Gayton, Nicolas

doi:10.1002/9781119817635.ch7

Cited by 9 publications

(19 citation statements)

References 29 publications

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“…As noticed in the previous section, both S u 2,W2 = S u 2,U niv (T a , P ⊗2 ) with T a defined in (17) and (21), are particular cases of indices of the form (12).…”

Section: Estimation Proceduresmentioning

confidence: 64%

“…• In Section 4.2, we use the notion of Fréchet means on Wasserstein spaces (see Section 3.2) and the index defined in (12) with appropriate choices of a, T a , and Q.…”

Section: 3mentioning

confidence: 99%

“…The paper [44] is devoted to second level uncertainty which corresponds to the uncertainty on the type of the input distributions and/or on the parameters of the input distributions. As mentioned by the authors, such uncertainties can be handled in two different manners: (1) aggregating them with no distinction [13,12] or (2) separating them [44]. In [13], e.g., the uncertainty concerns the parameters of the input distributions.…”

Section: State Of the Artmentioning

confidence: 99%

“…The authors study the expectation with respect to the distribution of the parameters of the conditional output. In [12], the second level uncertainties are transformed into first level uncertainties considering the aggregated vector containing the input random variables vector together with the vector of uncertain parameters. Alternatively, in [44], the uncertainty brought by the lack of knowledge of the input distributions and the uncertainty of the random inputs are treated separately.…”

Section: State Of the Artmentioning

confidence: 99%

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Global sensitivity analysis and Wasserstein spaces

Fort¹,

Klein²,

Lagnoux³

2020

Preprint

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Sensitivity indices are commonly used to quantity the relative influence of any specific group of input variables on the output of a computer code. In this paper, we focus both on computer codes the output of which is a cumulative distribution function and on stochastic computer codes. We propose a way to perform a global sensitivity analysis for these kinds of computer codes. In the first setting, we define two indices: the first one is based on Wasserstein Fréchet means while the second one is based on the Hoeffding decomposition of the indicators of Wasserstein balls. Further, when dealing with the stochastic computer codes, we define an "ideal version" of the stochastic computer code thats fits into the frame of the first setting. Finally, we deduce a procedure to realize a second level global sensitivity analysis, namely when one is interested in the sensitivity related to the input distributions rather than in the sensitivity related to the inputs themselves. Several numerical studies are proposed as illustrations in the different settings.

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“…As noticed in the previous section, both S u 2,W2 = S u 2,U niv (T a , P ⊗2 ) with T a defined in (17) and (21), are particular cases of indices of the form (12).…”

Section: Estimation Proceduresmentioning

confidence: 64%

“…• In Section 4.2, we use the notion of Fréchet means on Wasserstein spaces (see Section 3.2) and the index defined in (12) with appropriate choices of a, T a , and Q.…”

Section: 3mentioning

confidence: 99%

Section: State Of the Artmentioning

confidence: 99%

Section: State Of the Artmentioning

confidence: 99%

See 2 more Smart Citations

Global sensitivity analysis and Wasserstein spaces

Fort¹,

Klein²,

Lagnoux³

2020

Preprint

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show abstract

“…Performing sensitivity analysis in such a context requires to use dedicated tools which have been gathered by various authors under the denomination of "reliability-oriented sensitivity analysis" (ROSA) (see, e.g., [15,46,20]). A large panel of ROSA methods have been proposed in the structural reliability community such as, for example, several variance-based approaches (see, e.g., [47,13,15,48]) and moment-independent approaches (see, e.g., [49,19,46]). From the GSA community, several extensions have also been proposed as extensions to handle risk or reliability measures.…”

Section: A Brief Overview Of Reliability-oriented Sensitivity Analysismentioning

confidence: 99%

Developments and applications of Shapley effects to reliability-oriented sensitivity analysis with correlated inputs

Idrissi,

Chabridon,

Iooss

2021

Preprint

Self Cite

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Reliability-oriented sensitivity analysis methods have been developed for understanding the influence of model inputs relatively to events characterizing the failure of a system (e.g., a threshold exceedance of the model output). In this field, the target sensitivity analysis focuses primarily on capturing the influence of the inputs on the occurrence of such a critical event. This paper proposes new target sensitivity indices, based on the Shapley values and called "target Shapley effects", allowing for interpretable influence measures of each input in the case of dependence between the inputs. Two algorithms (a Monte Carlo sampling one, and a given-data algorithm) are proposed for the estimation of these target Shapley effects based on the ℓ 2 norm. Additionally, the behavior of these target Shapley effects are theoretically and empirically studied through various toy-cases. Finally, applications on two realistic use-cases (a river flood model and a COVID-19 epidemiological model) are discussed.

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Global sensitivity analysis of failure probability of structures with uncertainties of random variable and their distribution parameters

Wang

Liu

et al. 2021

Engineering with Computers

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Global Reliability‐oriented Sensitivity Analysis under Distribution Parameter Uncertainty

Cited by 9 publications

References 29 publications

Global sensitivity analysis and Wasserstein spaces

Global sensitivity analysis and Wasserstein spaces

Developments and applications of Shapley effects to reliability-oriented sensitivity analysis with correlated inputs

Global sensitivity analysis of failure probability of structures with uncertainties of random variable and their distribution parameters

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