Global sensitivity analysis is used to quantify the influence of input variables on a numerical model output. Sobol’ indices are now classical sensitivity measures. However their estimation requires a large number of model evaluations, especially when interaction effects are of interest. Derivative-based global sensitivity measures (DGSM) have recently shown their efficiency for the identificat...

We prove in a constructive way that multivariate integration in appropriate weighted Sobolev classes is strongly tractable and the e-exponent of strong tractability is 1 (which is the best-possible value) under a stronger assumption than Sloan and Wo! zniakowski’s assumption. We show that quasi-Monte Carlo algorithms based on the Sobol sequence and Halton sequence achieve the convergence order ...

Sensitivity analysis is a crucial tool in the development and evaluation of complex mathematical models. Sobol’s method is a variance-based global sensitivity analysis technique that has been applied to computational models to assess the relative importance of input parameters on the output. This paper introduces new notation that describes the Sobol indices in terms of the Pearson correlation ...

We define and study a generalization of Sobol sensitivity indices for the case of a vector output. To cite this article: F. Gamboa, A. Janon, T. Klein, A. Lagnoux, C. R. Acad. Sci. Paris, Ser. xx xxx (2013).

A new method for approximate solution of mechanics problems is presented that uses a classifier to identify regions in a random heterogeneous material where stress is likely to be highly concentrated under a prescribed set of boundary conditions. The example problem studied is an aggregate of hexagonal grains, each modeled as orthotropic and linear elastic, and subject to uniaxial extension. It...

This paper compares different types of simulated draws over a range of number of draws in generating Bayesian efficient designs for stated choice studies. The paper examines how closely pseudo Monte Carlo, quasi Monte Carlo and polynomial cubature methods are able to replicate the true levels of Bayesian efficiency for SC designs of various dimensions. The authors conclude that the predominantl...

Quasi-Monte Carlo methods are based on the idea that random Monte Carlo techniques can often be improved by replacing the underlying source of random numbers with a more uniformly distributed deterministic sequence. Quasi-Monte Carlo methods often include standard approaches of variance reduction, although such techniques do not necessarily directly translate. In this paper we present a quasi-M...

This paper compares different types of simulated draws over a range of number of draws in generating Bayesian efficient designs for stated choice (SC) studies. The paper examines how closely pseudo Monte Carlo, quasi Monte Carlo and Gaussian quadrature methods are able to replicate the true levels of Bayesian efficiency for SC designs of various dimensions. The authors conclude that the predomi...