Estimation of global sensitivity indices for models with dependent variables
A novel approach to estimate variance based sensitivity indices for the case of correlated variables is presented. Both the first order and total sensitivity indices are derived as generalizations of Sobol’ sensitivity indices. Formulas and Monte Carlo numerical estimates similar to Sobol’ formulas are derived. A Gaussian copula based approach to sampling from multivariate probability distributions is proposed. The method is shown to quickly reach convergence and to be faster than the so-called brute force method. A good agreement between analytical and numerical values of the first order and total indices for two test cases is obtained. A third test case, including both correlation and interaction among input variables, shows that the behaviour of sensitivity indices depends on the relative predominance of interaction and correlation.
KUCHERENKO Sergei;
TARANTOLA Stefano;
ANNONI Paola;
2012-02-03
ELSEVIER SCIENCE BV
JRC64266
0010-4655,
http://www.sciencedirect.com/science/article/pii/S0010465511004085,
https://publications.jrc.ec.europa.eu/repository/handle/JRC64266,
10.1016/j.cpc.2011.12.020,
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