Variance Components and Generalized Sobol' Indices

This paper introduces generalized Sobol' indices, compares strategies for their estimation, and makes a systematic search for efficient estimators. Of particular interest are contrasts, sums of squares, and indices of bilinear form which allow a reduced number of function evaluations compared to alternatives. The bilinear framework includes some efficient estimators from Saltelli [Comput. Phys. Comm., 145 (2002), pp. 280--297] and Mauntz [Global Sensitivity Analysis of General Nonlinear Systems, Master's thesis, Imperial College, London, 2002] as well as some new estimators for specific variance components and mean dimensions. This paper also provides a bias corrected version of the estimator of Janon et al. [Asymptotic Normality and Efficiency of Two Sobol' Index Estimators, technical report, INRIA, Rocquencourt, France] and extends the bias correction to generalized Sobol' indices. Some numerical comparisons are given.