Winding Stairs: A sampling tool to compute sensitivity indices

Sensitivity analysis aims to ascertain how each model input factor influences the variation in the model output. In performing global sensitivity analysis, we often encounter the problem of selecting the required number of runs in order to estimate the first order and/or the total indices accurately at a reasonable computational cost. The Winding Stairs sampling scheme (Jansen M.J.W., Rossing W.A.H., and Daamen R.A. 1994. In: Gasman J. and van Straten G. (Eds.), Predictability and Nonlinear Modelling in Natural Sciences and Economics. pp. 334-343.) is designed to provide an economic way to compute these indices. The main advantage of it is the multiple use of model evaluations, hence reducing the total number of model evaluations by more than half. The scheme is used in three simulation studies to compare its performance with the classic Sobol' LPtau. Results suggest that the Jansen Winding Stairs method provides better estimates of the Total Sensitivity Indices at small sample sizes.