Sensitivity analysis

Sensitivity analysis measures how changes in model inputs are reflected in outputs. An input may be a parameter, boundary condition, dataset, or structural assumption, while an output may be a prediction, risk estimate, or decision metric. The analysis is distinct from uncertainty analysis: uncertainty analysis asks how uncertain the output is, whereas sensitivity analysis investigates which inputs contribute to that uncertainty or to output variation.¹ Results can support model calibration, experimental design, quality assurance, and communication of assumptions. They do not by themselves establish causation in the real-world system; they describe dependence within the specified model.

Local analysis changes one input near a reference point, often using derivatives or small perturbations. Global analysis varies several inputs across defined ranges or probability distributions, making it better suited to nonlinear models, wide uncertainty intervals, and interactions.² The choice of ranges and distributions is therefore part of the analysis rather than a neutral technical detail.

Method selection depends on model cost, dimensionality, and the question being asked. One-at-a-time perturbations and derivative-based measures are inexpensive, but they can miss curvature and interactions. Morris screening uses structured sampling to identify potentially influential factors before a more expensive global analysis.⁵ Regression, rank-correlation, and variance-based methods offer different compromises between computational demand and interpretability.

Variance-based global sensitivity analysis decomposes output variance into contributions from individual inputs and their interactions. Sobol indices commonly report a first-order index for an input’s main effect and a total-order index including interactions; the difference can indicate interaction or nonlinear contribution.⁴ Monte Carlo, quasi-Monte Carlo, polynomial chaos, surrogate models, and emulators can reduce the number of full model evaluations, but approximation error must be checked rather than treated as sensitivity evidence.

Sensitivity results are useful only when their ranking, scale, and conditioning are interpreted against the model’s purpose. A highly sensitive parameter may deserve better measurement, tighter calibration, or explicit monitoring; a weakly influential parameter may be simplified without materially changing the selected output. In environmental modeling, systematic reviews describe uses ranging from parameter prioritization and model reduction to identifying data needs and comparing alternative models.²

Dependence among inputs requires special care. Standard variance decompositions often assume independent inputs, yet physical quantities, socioeconomic variables, and fitted parameters may be correlated. Ignoring that dependence can distort rankings. Analysts should report the output, input distributions or ranges, sampling design, model version, treatment of correlations, convergence checks, and whether conclusions change under alternative plausible assumptions. Sensitivity is also output-specific: the ranking for a mean prediction may differ from the ranking for an extreme quantile or threshold decision.

Sensitivity analysis can expose structural uncertainty, not merely uncertain numerical parameters. Comparing model formulations, data-processing choices, boundary conditions, or alternative causal assumptions may reveal that the largest source of variation is how the model is built rather than any single coefficient.¹ This broader use is sometimes called scenario, structural, or robustness analysis, although terminology varies across disciplines.

Screening can produce counterintuitive results: an input with a small average effect may matter greatly in a rare region, near a decision threshold, or through interaction with another input. Conversely, a high global index over a broad range may be irrelevant in the narrower regime used for a particular decision. Finite samples also create estimation noise, especially for tail-focused outputs. Repeated sampling, confidence intervals, and convergence diagnostics help distinguish genuine rankings from Monte Carlo variation.³ Sensitivity analysis can therefore guide model refinement, but it cannot compensate for biased data or an inappropriate model structure.

Local sensitivity analysis

Analysis of output response to small input changes around a specified reference point.

Global sensitivity analysis

Analysis that explores inputs across prescribed ranges or distributions, often including nonlinearities and interactions.

First-order Sobol index

The fraction of output variance attributed to an input’s main effect under the chosen probabilistic setup.

Total-order Sobol index

The fraction of output variance attributable to an input’s main effect plus all interactions involving that input.