Sensitivity analysis in general metric spaces

Gamboa, Fabrice; Klein, Thierry; Lagnoux, Agnès; Moreno, Leonardo

doi:10.1016/j.ress.2021.107611

Cited by 8 publications

(20 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By doing so, the symmetry of the estimator is lost. Interestingly, Lamboni [12] also derived unbiased estimators with minimum variance of the non-normalized Sobol' indices by leaning on the theory of U -statistics (see [6,5]). His construction led to estimators exactly equal to the numerators of Eqs.…”

Section: New Estimatorsmentioning

confidence: 99%

Comparison of two sets of Monte Carlo estimators of Sobol’ indices

Azzini

Mara

Rosati

2021

Environmental Modelling & Software

View full text Add to dashboard Cite

This study compares the performances of two sampling-based strategies for the simultaneous estimation of the first-and total-order variance-based sensitivity indices (a.k.a. Sobol' indices). The first strategy corresponds to the current approach employed by practitioners and recommended in the literature. The second one was only recently introduced by the first and last authors of the present article. Both strategies rely on different estimators of first-and total-order Sobol' indices. The asymptotic normal variances of the two sets of estimators are established and their accuracies are compared theoretically and numerically. The results show that the new strategy outperforms the current one. The global sensitivity analysis of the radiative forcing model of sulfur aerosols is performed with the new strategy. The results confirm that in this model interactions are important and only one input variable is irrelevant.

show abstract

Section: New Estimatorsmentioning

confidence: 99%

Comparison of two sets of Monte Carlo estimators of Sobol’ indices

Azzini

Mara

Rosati

2021

Environmental Modelling & Software

View full text Add to dashboard Cite

show abstract

“…In this section, we consider a computer code valued in a general metric space X as presented in [15]. In this context, the authors of [15] consider a family of test functions parametrized by m elements of X (m ∈ N * ). For any a = (a i ) i=1,...,m ∈ X m , the test functions…”

Section: Sensitivity Indices In General Metric Spacesmentioning

confidence: 99%

“…Estimation procedure based on U-statistics In [15], the authors propose a more efficient estimation procedure based on U-statistics (see [15, Equation (13)]). More precisely, for any 1 i m + 2, we let y i = (y i , y 1 i ) and we define Φ 1 (y 1 , .…”

Section: Sensitivity Indices In General Metric Spacesmentioning

confidence: 99%

“…They use the Pick-Freeze scheme to provide a consistent estimator requiring 4N evaluations of the output code. The authors of [15] extend the previous indices to general metric spaces and propose U-statistics-based estimators improving the classical Pick-Freeze procedure. We emphasize that the Pick-Freeze estimation procedure allows the estimation of several sensitivity indices: the classical Sobol indices for real-valued outputs, as well as their generalization for vectorial valued codes, but also the indices based on higher moments [26] and the Cramér-von-Mises indices which take into account on the whole distribution [14,11].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Global Sensitivity Analysis: a new generation of mighty estimators based on rank statistics

Gamboa¹,

Gremaud²,

Klein³

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

We propose a new statistical estimation framework for a large family of global sensitivity analysis methods. Our approach is based on rank statistics and uses an empirical correlation coefficient recently introduced by Sourav Chatterjee. We show how to apply this approach to compute not only the Cramér-von-Mises indices, which are directly related to Chatterjee's notion of correlation, but also Sobol indices at any order, higher-order moment indices, and Shapley effects. We establish consistency of the resulting estimators and demonstrate their numerical efficiency, especially for small sample sizes.

show abstract

“…In [5], the stochastic model is seen as a mapping that goes from the input space to a space of probability measures equipped with the Wasserstein distance. Following [8,9], the Wasserstein space is mapped to the real line R with some family of test functions, thus allowing for a standard Sobol-Hoeffding decomposition which is then averaged over all possible test functions. In more specific contexts, global sensitivity analysis methods also have been proposed.…”

mentioning

confidence: 99%

A Trade-Off Between Explorations and Repetitions for Estimators of Two Global Sensitivity Indices in Stochastic Models Induced by Probability Measures

Mazo¹

2021

SIAM/ASA J. Uncertainty Quantification

View full text Add to dashboard Cite

Sobol sensitivity indices assess how the output of a given mathematical model is sensitive to its inputs. If the model is stochastic then it cannot be represented as a function of the inputs, thus raising questions as how to do a sensitivity analysis in those models. Practitioners have been using a method that exploits the availability of softwares for deterministic models. For each input, the stochastic model is repeated and the outputs are averaged. These averages are seen as if they came from a deterministic model and hence Sobol's method can be used. However, in the context of limited computational resources, one must ensure that the number of repetitions of the stochastic model multiplied by the number of explorations of the input space is less than a fixed threshold. The problem of finding an optimal tradeoff between the repetitions and the explorations is addressed. A bound on an error criterion that penalizes bad rankings of the inputs' sensitivities is minimized. The estimator induced by the empirical method described above is shown to be asymptotically biased if the number of repetitions goes to infinity too slowly. A functional relationship between the output, the input and some random noise is derived from minimal distributional assumptions, which leads to a new sensitivity index with better statistical properties. The theory is illustrated on numerical experiments.

show abstract

Sensitivity analysis in general metric spaces

Cited by 8 publications

References 30 publications

Comparison of two sets of Monte Carlo estimators of Sobol’ indices

Comparison of two sets of Monte Carlo estimators of Sobol’ indices

Global Sensitivity Analysis: a new generation of mighty estimators based on rank statistics

A Trade-Off Between Explorations and Repetitions for Estimators of Two Global Sensitivity Indices in Stochastic Models Induced by Probability Measures

Contact Info

Product

Resources

About