A Bayesian Monte Carlo-based method for efficient computation of global sensitivity indices

Global sensitivity analysis, such as Sobol' indices, plays an important role for quantifying the relative importance of random inputs to the response of complex model, and the estimation of Sobol' indices is a challenging problem. In this paper, Bayesian Monte Carlo method is employed for developing a new technique to estimate the Sobol' indices with low computational cost. In the developing technique, the output response is expanded as the sum of different order components accurately, then the posterior predictors of all order components are analytically derived by use of the Bayesian inference, on which an analytical predictor of Sobol' index can be derived conveniently for input following any arbitrary distributions. In all analytical derivations, only the hyperparameters which are used to obtain a posterior predictor of output need to be estimated by the input-output samples, and the number of the hyperparameters grows linearly with the dimension of the input, thus the efficiency of the newly developing method is very high. The advantages of the proposed method are demonstrated through applications to several examples. The results show that the newly developing technique is comparable to the sparse polynomial chaos expansion and Quasi-Monte Carlo method.