A comprehensive comparison of total-order estimators for global sensitivity analysis

Arnald Puy*, William Becker, Samuele Lo Piano, Andrea Saltelli

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
32 Downloads (Pure)


Sensitivity analysis helps identify which model inputs convey the most uncertainty to the model output. One of the most authoritative measures in global sensitivity analysis is the Sobol’ total-order index, which can be computed with several different estimators. Although previous comparisons exist, it is hard to know which estimator performs best since the results are contingent on the benchmark setting defined by the analyst (the sampling method, the distribution of the model inputs, the number of model runs, the test function or model and its dimensionality, the weight of higher order effects, or the performance measure selected). Here we compare several total-order estimators in an eight-dimension hypercube, where these benchmark parameters are treated as random parameters. This arrangement significantly relaxes the dependency of the results on the benchmark design. We observe that the most accurate estimators are from Razavi and Gupta, Jansen, or Janon/Monod for factor prioritization, and from Jansen, Janon/Monod, or Azzini and Rosati for approaching the “true” total-order indices. The rest lag considerably behind. Our work helps analysts navigate myriad total-order formulae by reducing the uncertainty in the selection of the most appropriate estimator.

Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalInternational Journal for Uncertainty Quantification
Issue number2
Publication statusPublished - 30 Apr 2022

Bibliographical note

Funding Information:
We thank Saman Razavi for his insights on the Razavi and Gupta estimator. This work has been funded by the European Commission (Marie Skłodowska-Curie Global Fellowship, Grant No. 792178 to A.P.).

Publisher Copyright:
© 2022 by Begell House.


  • benchmarking analysis
  • modeling
  • sensitivity analysis
  • Sobol’ indices
  • uncertainty analysis
  • variance decomposition

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Discrete Mathematics and Combinatorics
  • Control and Optimization


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