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Multivariate sensitivity analysis and derivative-based global sensitivity measures with dependent variables
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Abstract In this paper, we propose a new methodology for better assessing the single, overall and interactions contributions of dependent and/or correlated variables over the whole model outputs. Our methodology relies on our ability to extract a model that characterizes the dependency structures of any random vector. Such dependency model is then coupled with the initial model to perform uncertainty quantification, variance-based sensitivity analysis and derivative-based global sensitivity measures. Our methodology allows for defining the main-effect and total sensitivity indices of input(s) with the former index less than the latter. We provide derivative-based upper bounds of total indices, which can be used for screening dependent variables. We also extend Morris’ methods to cope with dependent variables. For proposing such indices, we distinguish the case of the multivariate and/or functional outputs.
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“An alternative lens on proxy discrimination draws on the fact that the protected covariate 𝐷 , given its dependence on 𝑿 , can be written as 𝐷 = ℎ ( 𝑿 , 𝑈 ) , where 𝑈 is a random variable independent of 𝑿 .”
From Sensitivity-based measures of discrimination in insurance pricing (2026) · cites this paper as Lamboni & Kucherenko, 2021
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Metadata
- Authors
- Lamboni, M., & Kucherenko, S.
- Affiliations
- Université de Montpellier (FR)
- Imperial College London (GB)
- Corresponding author
- Lamboni, Matieyendou
- Venue
- Reliability Engineering & System Safety
- Publisher
- Elsevier BV
- Published
- 2021-08
- Volume
- 212
- Pages
- 107519
- ISSN
- 0951-8320 (ISSN-L)
- OpenAlex
- W3134200530
- Cited by
- 44
- References
- 52
- Citations by year
- 2026: 6 · 2025: 11 · 2024: 11 · 2023: 9 · 2022: 4 · 2021: 3
- FWCI
- 3.91
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- www.elsevier.com/tdm/userlicense/1.0/ (tdm)
- www.elsevier.com/legal/tdmrep-license (tdm)
- www.elsevier.com/open-access/userlicense/1.0/ (am, 579 d)
- doi.org/10.15223/policy-017 (stm-asf)
- doi.org/10.15223/policy-037 (stm-asf)
- doi.org/10.15223/policy-012 (stm-asf)
- doi.org/10.15223/policy-029 (stm-asf)
- doi.org/10.15223/policy-004 (stm-asf)
- Locations
- Reliability Engineering & System Safety (acceptedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Topics
- Physical Sciences › Engineering › Computational Mechanics › Probabilistic and Robust Engineering Design
- Physical Sciences › Computer Science › Artificial Intelligence › Gaussian Processes and Bayesian Inference
- Social Sciences › Decision Sciences › Management Science and Operations Research › Simulation Techniques and Applications
- Keywords
- correlated variables, uncertainty quantification, variance-based sensitivity analysis, variable screening, Morris method, functional outputs
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