Sobol’ main effect index: an Innovative Algorithm (IA) using Dynamic Adaptive Variances

Abstract

The Innovative Algorithm (IA) allows Sobol’ main effect index estimation at reduced model runs • The new formula is based on dynamic adaptive variances. • Tests with random samples show impressive results. • The new formula can be applied to a wide range of domains being model independent. • The new IA estimator consistently reduces the number of model run required. • The new iAzz-function has been proposed. Variance-based methods are very popular techniques to carry out global sensitivity analysis of model responses. In particular, Monte Carlo-based estimators related to Sobol’ sensitivity indices are often preferred due to their versatility, easiness of interpretation, and straightforward implementation. However, the number of model evaluations required to achieve an appropriate level of convergence, which strictly depends on the number of input factors, is an issue. The use of quasi-Monte Carlo sequences and/or the study of groups of inputs are ways to increase the efficiency of the sensitivity analysis, but the size of the needed sample is still a crucial challenge. This paper proposes an Innovative Algorithm (named IA estimator) to estimate the Sobol’ main effect indices, based on dynamic adaptive variances. The new estimator is tested on a broad set of test functions. The results are compared with benchmark estimations and the new algorithm proves to outperform in most cases, reducing significantly the required model evaluations. IA performances using quasi-Monte Carlo sequences and random numbers are often very similar. The case of the atmospheric dispersion module of the Accident Damage Analysis Module (ADAM) tool for consequence assessment is illustrated.