Comparing methods of randomizing Sobol′ sequences for improving uncertainty of metrics in variance-based global sensitivity estimation

This paper introduces an alternative way of randomizing Sobol′ sequences, called the Column Shift method, for reconstructing replicates to improve estimation of the uncertainty in sensitivity indices. The Column Shift method provides reliable results when applied to variance-based sensitivity analysis of the V-function, with much higher accuracy than commonly used randomization methods in most circumstances. It also addresses the error spikes caused by determinism within the Sobol′ sequence. The Column Shift method is compared with other popular randomization methods for the Sobol′ sequence, and it is shown to be the most consistent of those tested. In addition, the inclusion of standard error in the mean of sensitivity indices in an analysis of replicates provides a good indication of underestimation of errors in simulation results. The relationship between the number of samples and replicates is also discussed.