Sensitivity analysis via Karhunen–Loève expansion of a random field model: Estimation of Sobol' indices and experimental design. (July 2019) - Pronzato, Luc
Highlights: A method to estimate Sobol' indices for sensitivity analysis is proposed. It relies on a tensorised Bayesian linear model built from Kahrunen–Loève expansions. Posterior distributions of indices are derived and used to design adapted experiments. Abstract: We use the Karhunen–Loève expansion of a random-field model to construct a tensorised Bayesian linear model from which Sobol' sensitivity indices can be estimated straightforwardly. The method combines the advantages of models built from families of orthonormal functions, which facilitate computations, and Gaussian-process models, which offer a lot of flexibility. The posterior distribution of the indices can be derived, and its normal approximation can be used to design experiments especially adapted to their estimation. Implementation details are provided, and values of tuning parameters are indicated that yield precise estimation from a small number of function evaluations. Several illustrative examples are included that show the good performance of the method, in particular in comparison with estimation based on polynomial chaos expansion.