Global vs Local Sensitivity
Local sensitivity is a derivative at one point; global sensitivity explores the whole input space and captures interactions.
Two Views of Sensitivity
Sensitivity analysis comes in local and global flavors, and confusing them causes real errors. Local sensitivity measures how the output responds to a small change in an input around a fixed nominal point, essentially a partial derivative. Global sensitivity measures how the output responds as all inputs vary across their full uncertainty ranges at once.
Local Sensitivity
- Cheap to compute, often from a few perturbed runs or from adjoint methods.
- Exact at the nominal point, useful for gradient-based optimization and small-uncertainty problems.
- Blind to nonlinearity and interactions away from the nominal point.
Global Sensitivity
Global methods sample the whole input space, capturing nonlinear effects and interactions between inputs that local methods miss. They can tell you not just that an input matters near the nominal point, but that it matters across its whole range, and how much of its effect comes from acting alone versus in combination with others. Variance-based Sobol indices are the standard global measure; Morris screening is a cheaper global method for ranking.
Choosing Between Them
The right choice depends on the input uncertainty. When uncertainties are small and the response is roughly linear over them, local sensitivity is accurate and cheap. When uncertainties are large, the response is nonlinear, or interactions are suspected, local sensitivity can be badly misleading, ranking inputs incorrectly or missing an interaction entirely, and global methods are required despite their cost.
A common and dangerous mistake is to compute a local sensitivity, cheap and easy, and report it as if it were global, extrapolating a derivative at one point across a wide uncertainty range. The safe practice is to state which kind was computed and, when uncertainties are large, to prefer or at least spot-check with a global method.