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Sensitivity
Sobol' Sensitivity Indices - Variance-based global sensitivity decomposition
Global sensitivity - variance-based ANOVA decomposition
Sobol', I.M.1993
Overview
ST_i > S_i indicates interactions. Fix factors with ST_i < 0.01 to reduce model complexity. Ensure N(k+2) evaluations are feasible. Use quasi-random Sobol' sequences for faster convergence.
- Output
- sensitivity index, higher is better
- Data
- Crisp, complete numeric matrix
- Size
- 2+ alternatives, 3-10 criteria works best
- Used for
- Sensitivity analysis, uncertainty quantification, MCDM robustness
Fits when / Look elsewhere when
Fits when
- •Rigorous variance decomposition
- •Quantifies interactions (ST_i − S_i)
- •Model-free
Look elsewhere when
- •k > 20 without prior Morris screening
- •Budget < N(k+2) evaluations
Assumptions to verify
- Input factors are independent
- Distributions are specified for all factors
Limitations
- •N(k+2) evaluations required - expensive for large k
- •Requires specification of input distributions
Edge cases and pitfalls
Using N too small (N<500) → unstable S_i estimates.
Ignoring that ΣS_i < 1 when interactions exist - do not normalise S_i to sum to 1.
Applying Sobol' to ordinal outputs (rank) directly - use expected rank or RAI instead.
Works with
Its derived weights can feed
How to cite
Sobol', I.M. (1993). Sensitivity estimates for nonlinear mathematical models. Mathematical Modelling and Computational Experiment.
System ID, as it appears in reports and the API
SENSITIVITY-SOBOL