How do local and global sensitivity analysis differ?

Local sensitivity analysis

In a local sensitivity analysis, the influence of the model input parameters $\mathbf{X}$ on the model output is assessed around a specific point $\mathbf{x}_0$. The point $\mathbf{x}_0$ is often selected as the mean value or, in the context of reliability analysis, as the most likely failure point. It is typically computationally cheap to evaluate local sensitivity measures since only a small number of model calls is required.

Local sensitivity analysis is typically based on derivatives evaluated around $\mathbf{x}_0$. For nonlinear models, the interpretation of the obtained sensitivities is only valid around $\mathbf{x}_0$.

Global sensitivity analysis

In a global sensitivity analysis, the influence of the uncertainty about the model input parameters $\mathbf{X}$ on the model output is assessed over the entire range of the input parameters. Global sensitivity analysis is often preferable, but it typically comes at a higher computational cost [Straub, 2019].

Variance-based sensitivity analysis and input/output scatterplots are global sensitivity approaches.

References

[Straub, 2019]  Straub, Daniel: Lecture Notes in Engineering Risk Analysis. Technische Universität München, 2019.