Generalized Hoeffding-Sobol Decomposition for Dependent Variables -Application to Sensitivity Analysis
Ga\"elle Chastaing (M\'ethodes d'Analyse Stochastique des Codes et, Traitements Num\'eriques, INRIA Grenoble Rh\^one-Alpes / LJK Laboratoire Jean, Kuntzmann), Fabrice Gamboa (M\'ethodes d'Analyse Stochastique des Codes et, Traitements Num\'eriques, IMT)
TL;DR
This paper extends the Hoeffding-Sobol decomposition to dependent variables in regression models, enabling new sensitivity indices and discussing their estimation under boundedness assumptions.
Contribution
It introduces a generalized Hoeffding-Sobol decomposition for dependent variables and develops new sensitivity indices with estimation methods.
Findings
Existence of a generalized Hoeffding-Sobol decomposition under boundedness
Introduction of new sensitivity indices for dependent variables
Discussion on estimation procedures for these indices
Abstract
In this paper, we consider a regression model built on dependent variables. This regression modelizes an input output relationship. Under boundedness assumptions on the joint distribution function of the input variables, we show that a generalized Hoeffding-Sobol decomposition is available. This leads to new indices measuring the sensitivity of the output with respect to the input variables. We also study and discuss the estimation of these new indices.
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