Sensitivity Analysis
Which inputs actually move the answer? Sensitivity analysis ranks them, focusing measurement and modeling effort where it matters.
Ranking the Inputs
A model may have dozens of uncertain inputs, but usually only a few control the output. Sensitivity analysis identifies and ranks them. This ranking guides where to spend effort: an input that dominates the output deserves careful measurement and modeling, while one the output barely responds to can be fixed at a nominal value.
Local Sensitivity
Local methods measure the response to a small change around a nominal point, essentially a partial derivative of the output with respect to each input. They are cheap and informative near the operating point, but they miss nonlinear effects and interactions, and they can mislead when the input uncertainty is large.
Global Sensitivity
Global methods vary all inputs across their full ranges simultaneously and apportion the output variance among them. Variance-based measures such as Sobol indices quantify both the direct effect of each input and the effect of its interactions with others. Screening methods such as the Morris method cheaply separate the influential inputs from the negligible ones before a full analysis.
- Use screening first when there are many inputs, to discard the negligible ones.
- Use variance-based indices when interactions matter and the budget allows.
- Report first-order and total-effect measures; a large gap between them signals strong interactions.
Why It Pays Off
Sensitivity analysis and UQ are complementary. UQ tells you how uncertain the output is; sensitivity analysis tells you why, and therefore what to fix. It also serves verification indirectly: an input the physics says should matter but the model ignores, or an input the model responds to that should be inert, both point to modeling or coding errors. For design, the sensitivity ranking becomes a priority list for the experiments and measurements that will most tighten the prediction.