A nonparametric importance sampling estimator for moment independent importance measures

Pierre Derennes (1, 2) , Jérôme Morio (2) , Florian Simatos (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 DTIS, ONERA, Université de Toulouse [Toulouse]
3 ISAE-SUPAERO - Institut Supérieur de l'Aéronautique et de l'Espace

Moment independent importance measures have been proposed by E. Borgonovo [1] in order to alleviate some of the drawbacks of variance-based sensibility indices. They have gained increasing attention over the last years but their estimation remains a challenging issue. An effective estimation scheme in the case of correlated inputs, referred to as single-loop method, has been proposed by Wei et al. [2]. In this paper we show via simulation that this method may be inaccurate, making for instance 40% error in the simplest possible Gaussian case. We then propose a new estimation scheme which greatly improves the accuracy of the single-loop method, up to a factor 10 in some simple numerical examples. We prove that our estimator is strongly consistent and several simulation results are presented to demonstrate the advantages of the proposed method.

Mots clés: MONTE CARLO SIMULATION; IMPORTANCE SAMPLING; DENSITY-BASED SENSITIVITY ANALYSIS; IMPORTANCE MEASURES

Domaines: Sciences de l'ingénieur [physics]; Physique [physics]; Mathématiques [math]; Informatique [cs]

Pierre Derennes, Jérôme Morio, Florian Simatos. A nonparametric importance sampling estimator for moment independent importance measures. Reliability Engineering and System Safety, 2019, 187, pp.3-16. ⟨10.1016/j.ress.2018.02.009⟩. ⟨hal-02133955⟩