sensitivity (version 1.10.1)

sensitivity-package: Sensitivity Analysis

Description

Methods and functions for global sensitivity analysis.

Model managing

The sensitivity package has been designed to work either models written in Rthan 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).

• Ifmodel = mwheremis a function, it will be invoked once byy <- m(X).
• Ifmodel = mwheremis a predictor, it will be invoked once byy <- 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.

Details

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).
• Poincare constants for Derivative-based Global Sensitivity Measures (DGSM) (Roustant et al., 2014) (PoincareConstant).
• 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),
    • 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).
• 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 Density Modification Based Reliability Sensitivity Indices (DMBRSI) of Lemaitre et al., 2014.

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

References

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. 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.