Global vs Local Sensitivity
Local sensitivity measures response to small perturbations at one point; global sensitivity apportions output variance across the whole input range.
Two different questions
Local sensitivity analysis asks how the output changes for an infinitesimal change in an input at a nominal point, captured by a partial derivative. Global sensitivity analysis asks how much each input contributes to output variability across its entire uncertainty range, accounting for interactions and nonlinearity. They answer different questions and can disagree sharply.
Local methods
- Partial derivatives and one-at-a-time perturbations
- Adjoint gradients for many inputs at low cost
- Fast but valid only near the chosen point
Global methods
- Variance-based Sobol indices decomposing output variance
- Morris elementary effects for screening
- Derivative-based global measures averaging local gradients over the input space
- Regression and correlation coefficients for monotone responses
When they diverge
For a nonlinear or non-monotone response, a locally flat input can be globally important if the response steepens elsewhere, and a locally steep input can be globally minor if it varies over a narrow range. Interactions are invisible to one-at-a-time local analysis but explicit in Sobol total-effect indices. Relying on local sensitivity alone risks mis-ranking inputs.
Choosing
Use local analysis for optimization, control, and quick diagnostics near an operating point. Use global analysis to prioritize which uncertainties to reduce, to justify fixing an input at a nominal value, or to communicate robustness. In practice, cheap local gradients often screen inputs before a more expensive global study confirms the ranking.