Making best use of model evaluations to compute sensitivity indices

By Andrea Saltelli. 2002

2,041 citations recorded by the source corpus.

This paper deals with computations of sensitivity indices in sensitivity analysis. Given a mathematical or computational model y=f(x1,x2,…,xk), where the input factors xi's are uncorrelated with one another, one can see y as the realization of a stochastic process obtained by sampling each of the xi from its marginal distribution. The sensitivity indices are related to the decomposition of the variance of y into terms either due to each xi taken singularly (first order indices), as well as into terms due to the cooperative effects of more than one xi. In this paper we assume that one has computed the full set of first order sensitivity indices as well as the full set of total-order sensitivity indices (a fairly common strategy in sensitivity analysis), and show that in this case the same set of model evaluations can be used to compute double estimates of: • the total effect of two factors taken together, for all such k2 couples, where k is the dimensionality of the model; • the total effect of k−2 factors taken together, for all k2 such (k−2) ples. We further introduce a new strategy for the computation of the full sets of first plus total order sensitivity indices that is about 50% cheaper in terms of model evaluations with respect to previously published works. We discuss separately the case where the input factors xi's are not independent from each other.

Subfields: Civil and Structural Engineering, Mechanics of Materials, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c74795df4a8a11545977d259d82bb14378c7bfed

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Citations in the corpus

Variance-based sensitivity analysis of a forest growth model (2012, methodology): “To compute Si and STi simultaneously, a scheme suggested by Saltelli (2002) was used which reduced the model runs to N(k + 2).”
A methodology for performing global uncertainty and sensitivity analysis in systems biology. (2008, methodology): “Examples of these methods are the Sobol method and its extended version based on (quasi) random numbers and an ad hoc design (see Saltelli, 2002 for details), the Fourier amplitude sensitivity test (FAST) and its extended version (eFAST).”
Creating composite indicators with DEA and robustness analysis: the case of the Technology Achievement Index (2008, positive): “the interaction between the input factors falls beyond the scope of the current study; we refer the interested reader to Saltelli et al (2000). We confine ourselves to indicating those additional properties of model-free variance-based techniques that render them suitable for the present analysis:”
A simple and efficient method for global sensitivity analysis based on cumulative distribution functions (2015, positive): “(1), and still easy to implement because, once the sample < yj > j¼1;…;N of output evaluations has been generated, the sensitivity indices can be approximated by simply applying a closed form, algebraic equation over the output samples (Saltelli, 2002a).”
Uncertainty and sensitivity analysis techniques as tools for the quality assessment of composite indicators (2005, methodology): “Here the method of Sobol’ (1993), in its improved version due to Saltelli (2002), is used.”
Convergence and uncertainty analyses in Monte-Carlo based sensitivity analysis (2011, neutral): “, it requires a large number of model runs: for a base sample sizem, it takes at leastm * (nþ 2)model runs to calculate the (Si, STi) forn factors (Saltelli, 2002).”
Sobol' sensitivity analysis of a complex environmental model (2011, methodology): “Saltelli (2002) introduced a method to almost halve the number of model runs required to n$(p þ 2).”
Quantifying parameter sensitivity, interaction, and transferability in hydrologically enhanced versions of the Noah land surface model over transition zones during the warm season (2010, methodology): “The method of Sobol0 is more robust (it employs a representative sample of the parameter space) and efficient than factorial analysis [Saltelli, 2002], and it bypasses the perceived complexities (e.g., the design of the calculation matrix) often associated with factorial analysis.”
A comprehensive evaluation of various sensitivity analysis methods: A case study with a hydrological model (2014, methodology): “Some DOEbased SA methods, such as Morris One-At-a-Time (MOAT) (Morris, 1991), Fourier Amplitude Sensitivity Test (FAST) (Cukier et al., 1973), and extended Sobol' method (Saltelli, 2002), require special sampling techniques.”
Sensitivity Analysis for Hydraulic Models (2009, neutral): “Finally, any other interaction term between the third and the (cid:1) k −3 (cid:2) -th can be estimated at the further additional cost of m model runs each (cid:1) Saltelli 2002 (cid:2) .”
Measuring firm performance using financial ratios: A decision tree approach (2013, background): “More details about this formulation can be studied in Saltelli (2002). w i : normalized weight values for each model.”