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Global Sensitivity Analysis with Mixtures: A Generalized Functional ANOVA Approach
Author(s) -
Borgonovo Emanuele,
Li Genyuan,
Barr John,
Plischke Elmar,
Rabitz Herschel
Publication year - 2022
Publication title -
risk analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.972
H-Index - 130
eISSN - 1539-6924
pISSN - 0272-4332
DOI - 10.1111/risa.13763
Subject(s) - sensitivity (control systems) , variance based sensitivity analysis , variance (accounting) , econometrics , mathematics , aggregate (composite) , independence (probability theory) , computer science , statistics , analysis of variance , one way analysis of variance , engineering , materials science , accounting , electronic engineering , business , composite material
This work investigates aspects of the global sensitivity analysis of computer codes when alternative plausible distributions for the model inputs are available to the analyst. Analysts may decide to explore results under each distribution or to aggregate the distributions, assigning, for instance, a mixture. In the first case, we lose uniqueness of the sensitivity measures, and in the second case, we lose independence even if the model inputs are independent under each of the assigned distributions. Removing the unique distribution assumption impacts the mathematical properties at the basis of variance‐based sensitivity analysis and has consequences on result interpretation as well. We analyze in detail the technical aspects. From this investigation, we derive corresponding recommendations for the risk analyst. We show that an approach based on the generalized functional ANOVA expansion remains theoretically grounded in the presence of a mixture distribution. Numerically, we base the construction of the generalized function ANOVA effects on the diffeomorphic modulation under observable response preserving homotopy regression. Our application addresses the calculation of variance‐based sensitivity measures for the well‐known Nordhaus' DICE model, when its inputs are assigned a mixture distribution. A discussion of implications for the risk analyst and future research perspectives closes the work.