Methods and functions for global sensitivity analysis
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.
The sensitivity package implements some global sensitivity analysis methods:
Linear regression importance measures: SRC and SRRC (src), PCC, SPCC, PRCC and SPRCC (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) (Lamboni et al., 2013; Roustant et al., 2017) (PoincareConstant) and (PoincareOptimal),
Squared coefficients computation in generalized chaos via Poincare differential operators (Roustant et al., 2019) (PoincareChaosSqCoef),
Distributed Evaluation of Local Sensitivity Analysis (DELSA) (Rakovec et al., 2014) (delsa);
Variance-based sensitivity indices (Sobol' indices) for independent inputs:
Estimation of the Sobol' first order indices with with B-spline Smoothing (Ratto and Pagano, 2010) (sobolSmthSpl),
Monte Carlo estimation of Sobol' indices with independent inputs (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, second order and total indices (sobolSalt),
Saltelli's scheme (Saltelli, 2002) to compute first order and total indices (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 permutations on a single matrix (sobolmara),
Mighty estimator of first-order sensitivity indices based on rank statistics (correlation coefficient of Chatterjee, 2019; Gamboa et al., 2020) (sobolrank),
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),
Replication-based procedures:
Estimation of the Sobol' first order and closed second order indices using replicated orthogonal array-based Latin hypecube sample (Tissot and Prieur, 2015) (sobolroalhs),
Recursive estimation of the Sobol' first order and closed second order indices using replicated orthogonal array-based Latin hypecube sample (Gilquin et al., 2016) (sobolrec),
Estimation of the Sobol' first order, second order and total indices using the generalized method with replicated orthogonal array-based Latin hypecube sample (Tissot and Prieur, 2015) (sobolrep),
Sobol' indices estimation under inequality constraints (Gilquin et al., 2015) by extension of the replication procedure (Tissot and Prieur, 2015) (sobolroauc),
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);
Variance-based sensitivity indices (Shapley effects and Sobol' indices) for independent or dependent inputs:
Exact computation in the linear Gaussian framework (Broto et al., 2019) (shapleyLinearGaussian),
Computation in the Gaussian linear framework with an unknown block-diagonal covariance matrix (Broto et al., 2020) (shapleyBlockEstimation),
Estimation by examining all permutations of inputs (Song et al., 2016) (shapleyPermEx),
Estimation by randomly sampling permutations of inputs (Song et al., 2016) (shapleyPermRand),
Estimation of Shapley effects from data using nearest neighbors method (Broto et al., 2018) (shapleySubsetMc),
Estimation of Shapley effects and all Sobol indices from data using nearest neighbors (Broto et al., 2018) using a fast approximate algorithm, and ranking (Gamboa et al., 2020) (sobolshap_knn);
Support index functions (support) of Fruth et al. (2016);
Sensitivity Indices based on Csiszar f-divergence (sensiFdiv) (particular cases: Borgonovo's indices and mutual-information based indices) and Hilbert-Schmidt Independence Criterion (sensiHSIC) (Da Veiga, 2015; Meynaoui et al., 2019);
Target Sensitivity Analysis via Hilbert-Schmidt Independence Criterion (sensiHSIC) (Spagnol et al., 2019);
Robustness analysis by the Perturbed-Law based Indices (PLI) of Lemaitre et al. (2015), (PLIquantile) of Sueur et al. (2017), and extension as (PLIquantile_multivar) and (PLIsuperquantile) ;
Extensions to multidimensional outputs for:
Sobol' indices (sobolMultOut): Aggregated Sobol' indices (Lamboni et al., 2011; Gamboa et al., 2014) and functional (1D) Sobol' indices,
Shapley effects and Sobol' indices (sobolshap_knn): Functional (1D) indices,
HSIC indices (sensiHSIC) (Da Veiga, 2015): Aggregated HSIC, potentially via a PCA step (Da Veiga, 2015),
Morris method (morrisMultOut).
Moreover, some utilities are provided: standard test-cases (testmodels), weight transformation function of the output sample (weightTSA) to perform Target Sensitivity Analysis, normal and Gumbel truncated distributions (truncateddistrib), squared integral estimate (squaredIntEstim), Addelman and Kempthorne construction of orthogonal arrays of strength two (addelman_const), discrepancy criteria (discrepancyCriteria_cplus), maximin criteria (maximin_cplus) and template file generation (template.replace).
S. Da Veiga, F. Gamboa, B. Iooss and C. Prieur, Basics and trends in sensitivity analysis, Theory and practice in R, Book in preparation
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, 2017, 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 et al., 2008, Global Sensitivity Analysis: The Primer, Wiley