Adaptive use of replicated Latin Hypercube Designs for computing Sobol' sensitivity indices

TL;DR

This paper enhances Sobol' sensitivity analysis by adaptively using replicated Latin Hypercube Designs with Oracle 1 estimators, improving accuracy for small and moderate indices while reducing computational costs.

Contribution

It introduces an adaptive strategy combining Oracle 2 and Oracle 1 estimators with rLHDs for more efficient and accurate Sobol' index estimation.

Findings

Oracle 1 estimators outperform Oracle 2 for small/moderate indices.

Averaged Oracle 1 estimator achieves high accuracy in numerical tests.

Adaptive rLHD-based approach reduces computational costs while maintaining accuracy.

Abstract

As recently pointed out in the field of Global Sensitivity Analysis (GSA) of computer simulations, the use of replicated Latin Hypercube Designs (rLHDs) is a cost-saving alternative to regular Monte Carlo sampling to estimate first-order Sobol' indices. Indeed, two rLHDs are sufficient to compute the whole set of those indices regardless of the number of input variables. This relies on a permutation trick which, however, only works within the class of estimators called Oracle 2. In the present paper, we show that rLHDs are still beneficial to another class of estimators, called Oracle 1, which often outperforms Oracle 2 for estimating small and moderate indices. Even though unlike Oracle 2 the computation cost of Oracle 1 depends on the input dimension, the permutation trick can be applied to construct an averaged (triple) Oracle 1 estimator whose great accuracy is presented on a numerical example. Thus, we promote an adaptive rLHDs-based Sobol' sensitivity analysis where the first stage is to compute the whole set of first-order indices by Oracle 2. If needed, the accuracy of small and moderate indices can then be reevaluated by the averaged Oracle 1 estimators. This strategy, cost-saving and guaranteeing the accuracy of estimates, is applied to a computer model from the nuclear field.