Estimating Sobol sensitivity indices using correlations

Sensitivity analysis is a crucial tool in the development and evaluation of complex mathematical models. Sobol's method is a variance-based global sensitivity analysis technique that has been applied to computational models to assess the relative importance of input parameters on the output. This paper introduces new notation that describes the Sobol indices in terms of the Pearson correlation of outputs from pairs of runs, and introduces correction terms to remove some of the spurious correlation. A variety of estimation techniques are compared for accuracy and precision using the G function as a test case.

► We present Sobol's method in terms of correlation coefficients.
► We derive new error correction terms for the method that remove spurious correlation.
► Multiple estimation methods are compared for precision, accuracy, and efficiency.