Global Sensitivity Analysis with Dependent Inputs

Abstract

Sobol' indices are a well established measure for global sensitivity analysis on models with independent input variables. However, several alternative sensitivity measures have been proposed to deal with dependent (correlated) inputs. Among others, Kucherenko (2012) and Caniou (2012) have proposed two different generalisations of the Sobol' indices. The first uses a direct decomposition of variance, evaluatable with a double loop Monte Carlo estimation, while the latter uses a High Dimensional Model Representation as structural substitute of the actual model. The two approaches lead to different indices whose interpretation differs and is sometimes not trivial. In the context of this thesis, the two methods are implemented and applied onto models with increasing complexity to assess how the indices change for different dependence structures. The resulting indices are interpreted and discussed in order to understand the evolution of the values for varying correlation. Dependence is modeled by a Gaussian copula. For expensive-to-evaluate models the double loop Monte Carlo estimation of Kucherenko indices might in general not be feasible. Instead of the actual model, a cheap-to-evaluate surrogate, built using polynomial chaos expansion, is applied.

Keywords

Sensitivity analysis, Dependence, Surrogate modelling

BibTeX cite

MSCTHESIS{PWiederkehrThesis,
author = {Wiederkehr, Philippe},
title = {Global Sensitivity Analysis with Dependent Inputs},
school = {ETH Zurich, Zurich, Switzerland},
year = {2018}
}