Variance components and generalized Sobol' indices

TL;DR

This paper develops generalized Sobol' indices for variance component analysis, compares estimation strategies, introduces new efficient estimators, and extends bias correction methods with numerical validation.

Contribution

It introduces a systematic framework for generalized Sobol' indices, proposes new estimators, and extends bias correction techniques for variance-based sensitivity analysis.

Findings

Efficient estimators for variance components are identified.

Bias correction methods are extended and validated.

Numerical comparisons demonstrate estimator performance.

Abstract

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 (2002) and Mauntz (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.\,(2012) and extends the bias correction to generalized Sobol' indices. Some numerical comparisons are given.