Sensitivity Analysis


Methods and functions for global sensitivity analysis.


The sensitivity package implements some global sensitivity analysis methods:

  • Linear regression coefficients: SRC and SRRC (src), PCC and PRCC (pcc);

  • Bettonvil's sequential bifurcations (Bettonvil and Kleijnen, 1996) (sb);

  • Morris's "OAT" elementary effects screening method (morris);

  • Derivative-based Global Sensitivity Measures:

    • Poincare constants for Derivative-based Global Sensitivity Measures (DGSM) (Roustant et al., 2014) (PoincareConstant),

    • Distributed Evaluation of Local Sensitivity Analysis (DELSA) (Rakovec et al., 2014) (delsa);

  • Variance-based sensitivity indices (Sobol' indices):

    • Monte Carlo estimation of Sobol' indices (also called pick-freeze method):

      • Sobol' scheme (Sobol, 1993) to compute the indices given by the variance decomposition up to a specified order (sobol),

      • Saltelli's scheme (Saltelli, 2002) to compute first order and total indices with a reduced cost (sobol2002),

      • Mauntz-Kucherenko's scheme (Sobol et al., 2007) to compute first order and total indices using improved formulas for small indices (sobol2007),

      • Jansen-Sobol's scheme (Jansen, 1999) to compute first order and total indices using improved formulas (soboljansen),

      • Martinez's scheme using correlation coefficient-based formulas (Martinez, 2011; touati, 2016) to compute first order and total indices, associated with theoretical confidence intervals (sobolmartinez and soboltouati),

      • Janon-Monod's scheme (Monod et al., 2006; Janon et al., 2013) to compute first order indices with optimal asymptotic variance (sobolEff),

      • Mara's scheme (Mara and Joseph, 2008) to compute first order indices with a cost independent of the dimension, via a unique-matrix permutations (sobolmara),

      • Owen's scheme (Owen, 2013) to compute first order and total indices using improved formulas (via 3 input independent matrices) for small indices (sobolowen),

      • Total Interaction Indices using Liu-Owen's scheme (Liu and Owen, 2006) (sobolTIIlo) and pick-freeze scheme (Fruth et al., 2014) (sobolTIIpf),

    • Estimation of the Sobol' first order and closed second order indices using replicated orthogonal array-based Latin hypecube sample (Tissot and Prieur, 2012) (sobolroalhs),

    • Estimation of the Sobol' first order and total indices with Saltelli's so-called "extended-FAST" method (Saltelli et al., 1999) (fast99),

    • Estimation of the Sobol' first order and total indices with kriging-based global sensitivity analysis (Le Gratiet et al., 2014) (sobolGP);

    Support index functions (support) of Fruth et al. (2015);

    Sensitivity Indices based on Csiszar f-divergence (sensiFdiv) (particular cases: Borgonovo's indices and mutual-information based indices) and Hilbert-Schmidt Independence Criterion (sensiHSIC) of Da Veiga et al. (2014);

    Reliability sensitivity analysis by the Perturbed-Law based Indices (PLI) of Lemaitre et al. (2015);

    Sobol' indices for multidimensional outputs (sobolMultOut): Aggregated Sobol' indices (Lamboni et al., 2011; Gamboa et al., 2014) and functional (1D) Sobol' indices.

    Moreover, some utilities are provided: standard test-cases (testmodels) and template file generation (template.replace).

Model managing

The sensitivity package has been designed to work either models written in R than external models such as heavy computational codes. This is achieved with the input argument model present in all functions of this package.

The argument model is expected to be either a funtion or a predictor (i.e. an object with a predict function such as lm).

  • If model = m where m is a function, it will be invoked once by y <- m(X).

  • If model = m where m is a predictor, it will be invoked once by y <- predict(m, X).

X is the design of experiments, i.e. a data.frame with p columns (the input factors) and n lines (each, an experiment), and y is the vector of length n of the model responses.

The model in invoked once for the whole design of experiment.

The argument model can be left to NULL. This is refered to as the decoupled approach and used with external computational codes that rarely run on the statistician's computer. See decoupling.


Gilles Pujol, Bertrand Iooss, Alexandre Janon with contributions from Paul Lemaitre for the PLI function, Laurent Gilquin for the sobolroalhs function, Loic le Gratiet for the sobolGP function, Khalid Boumhaout, Taieb Touati and Bernardo Ramos for the sobolowen and soboltouati functions, Jana Fruth for the PoincareConstant and support functions, sobolTIIlo and sobolTIIpf functions, Sebastien Da veiga for the sensiFdiv and sensiHSIC functions, Joseph Guillaume for the delsa and parameterSets functions, Frank Weber.

(maintainer: Bertrand Iooss


R. Faivre, B. Iooss, S. Mahevas, D. Makowski, H. Monod, editors, 2013, Analyse de sensibilite et exploration de modeles. Applications aux modeles environnementaux, Editions Quae.

B. Iooss and A. Saltelli (in press). Introduction: Sensitivity analysis. In: Springer Handbook on Uncertainty Quantification, R. Ghanem, D. Higdon and H. Owhadi (Eds), Springer.

B. Iooss and P. Lemaitre, 2015, A review on global sensitivity analysis methods. In Uncertainty management in Simulation-Optimization of Complex Systems: Algorithms and Applications, C. Meloni and G. Dellino (eds), Springer.

A. Saltelli, K. Chan and E. M. Scott eds, 2000, Sensitivity Analysis, Wiley.

A. Saltelli, P. Annoni, I. Azzini, F. Campolongo, M. Ratto and S. Tarantola, 2010, Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index, Computer Physics Communications 181, 259–270.

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