A multivariate non-parametric kernel estimator for global sensitivity analysis

Lamia Djerroud (1) , Tristan Senga Kiessé (2) , Smail Adjabi (1)

1 Unité de recherche LaMOS = Research unit LaMOS - Unité de recherche Laboratoire de Modélisation et Optimisation des Systèmes [Université de Béjaïa]
2 SAS - Sol Agro et hydrosystème Spatialisation

To estimate how a model output is influenced by the variations of inputs has become an important problematic in reliability and sensitivity analyses. This paper is interested in estimating sensitivity indices useful to quantify the contribution of inputs to the variance of model output. A multivariate mixed kernel estimator is investigated since, until now, discrete and continuous inputs have been separately considered in kernel estimation of sensitivity indices. To illustrate the differences between the influence of mixed, discrete and continuous inputs, analytical expressions of Sobol sensitivity indices are expressed in these three cases for the Ishigami test function. Besides, the performance of mixed kernel estimator is illustrated through simulations in which the Bayesian procedure is applied for bandwidth parameter choice. An application is also realized on a real example. Finally, to use an appropriate kernel estimator according to the type of inputs is found to be influential on the accuracy of sensitivity indice estimates.

Mots clés: Sensitivity in-dices; Nonparametric regression; Associated kernel; Analysis of variance

Domaines: Statistiques [math.ST]

Lamia Djerroud, Tristan Senga Kiessé, Smail Adjabi. A multivariate non-parametric kernel estimator for global sensitivity analysis. Communications in Statistics - Simulation and Computation, 2017, 47 (6), pp.1606-1622. ⟨10.1080/03610918.2017.1309430⟩. ⟨hal-02058869⟩