New sensitivity analysis subordinated to a contrast

Abstract

In a model of the form Y = h(X1, . . . , X d ) where the goal is to estimate a parameter of the probability distribution of Y , we define new sensitivity indices which quantify the importance of each variable Xi with respect to this parameter of interest. The aim of this paper is to define goal oriented sensitivity indices and we will show that Sobol indices are sensitivity indices associated to a particular characteristic of the distribution Y . We name the framework we present as Goal Oriented Sensitivity Analysis (GOSA).

Estimation of quantile oriented sensitivity indices

“…In order to validate our estimation procedure, we illustrate the asymptotic results of Proposition 4.2 in the following example that is considered in [7]. Example 1.…”

“…In what follows, we introduce some concepts about contrast functions and contrast index. The reader is referred for instance to [7]. We assume that the output Y = f (X) is a continuous random variable.…”

“…The construction of these indices is based on contrast functions. Roughly speaking, given ψ a contrast function and X, Y two random variables, the ψ-X contrast index on Y is given by (see [7]):…”

“…It is a statistical measure of the relative impact of X on the variability of Y ; the most sensitive parameters can be identified and ranked as the parameters with the largest Sobol indices. Introduced in [7], contrast indices named "Goal Oriented Sensitivity Analysis" generalize the Sobol ones. The construction of these indices is based on contrast functions.…”

Estimation of the Derivative-Based Global Sensitivity Measures Using a Gaussian Process Metamodel

“…[16]). Recently, [12] introduced the Goal Oriented Sensitivity Analysis, providing an unified framework for several sensitivity analyses based on the mean output value, on a specific output quantile for excess probability considerations, and so on. With the same idea to go further than the Sobol' indices, [6] proposes new sensitivity measures considering the whole distribution of the output respect to those of the input parameters, either comparing characteristic functions [48], or measuring the covariance between input and output parameters in some reproducing kernel Hilbert spaces [14].…”