Nonparametric adaptive estimation of order 1 Sobol indices in stochastic models, with an application to Epidemiology

TL;DR

This paper introduces a new non-parametric, adaptive method using warped wavelets for estimating first-order Sobol indices in stochastic models, avoiding the need for metamodels, with applications demonstrated in epidemiology.

Contribution

It proposes a novel non-parametric estimator for Sobol indices that adapts to model regularity without requiring metamodels, applicable to stochastic models.

Findings

Estimator converges in mean square as simulations increase

Shows an elbow effect depending on model regularity

Effective in epidemiological applications

Abstract

Global sensitivity analysis is a set of methods aiming at quantifying the contribution of an uncertain input parameter of the model (or combination of parameters) on the variability of the response. We consider here the estimation of the Sobol indices of order 1 which are commonly-used indicators based on a decomposition of the output's variance. In a deterministic framework, when the same inputs always give the same outputs, these indices are usually estimated by replicated simulations of the model. In a stochastic framework, when the response given a set of input parameters is not unique due to randomness in the model, metamodels are often used to approximate the mean and dispersion of the response by deterministic functions. We propose a new non-parametric estimator without the need of defining a metamodel to estimate the Sobol indices of order 1. The estimator is based on warped wavelets and is adaptive in the regularity of the model. The convergence of the mean square error to zero, when the number of simulations of the model tend to infinity, is computed and an elbow effect is shown, depending on the regularity of the model. Applications in Epidemiology are carried to illustrate the use of non-parametric estimators.