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ABSTRACT
Physical phenomena are commonly modelled by time consuming numerical simulators, function of many uncertain parameters whose influences can be measured via a global sensitivity analysis. The usual variance-based indices require too many simulations, especially as the inputs are numerous. To address this limitation, we consider recent advances in dependence measures, focusing on the distance correlation and the Hilbert–Schmidt independence criterion. We study and use these indices for a screening purpose. Numerical tests reveal differences between variance-based indices and dependence measures. Then, two approaches are proposed to use the latter for a screening purpose. The first approach uses independence tests, with existing asymptotic versions and spectral extensions; bootstrap versions are also proposed. The second considers a linear model with dependence measures, coupled to a bootstrap selection method or a Lasso penalization. Numerical experiments show their potential in the presence of many non-influential inputs and give successful results for a nuclear reliability application.
Acknowledgments
We are grateful to Béatrice Laurent and Sébastien Da Veiga for helpful discussions. We thank Simon Nanty for his technical help in the nuclear application.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1. The significance level of a statistical hypothesis test is the rate of the type I error which corresponds to the rejection of the null hypothesis when it is true.
2. The type I error occurs when the test concludes that a non-significant input is significant. The power of the test is the probability to conclude that a significant input is significant.
3. Matlab implementation of the LARS algorithm: http://www.stat.berkeley.edu/∼yugroup/downloads/.