Sensitivity analysis
Sensitivity analysis studies how changes in parameters or inputs change model outputs.
Local sensitivity
For output \(Y(\theta)\), the local sensitivity to parameter \(\theta_j\) is
\[S_j=\frac{\partial Y}{\partial\theta_j}.\]A dimensionless form can compare parameters measured on different scales:
\[S_j^{*}=\frac{\theta_j}{Y}\frac{\partial Y}{\partial\theta_j}.\]Global sensitivity
Global methods vary parameters across ranges or distributions and assess their influence over the wider parameter space, including interactions between parameters.
Key idea. Sensitivity analysis asks which uncertain inputs most strongly influence the outputs that matter.