A set of methods for quantifying how variations in model inputs, parameters, or assumptions influence model outputs, with the goal of identifying influential factors and characterizing input–output relationships.

Principle

Organize input perturbations or distributions and measure resultant changes in outputs using derivatives, variance decompositions, or input–output mappings; distinguish local (infinitesimal) from global (distributional) effects and account for interactions and nonlinearity.

Demonstration

Compute Sobol indices for a hydrological model to rank rainfall, soil permeability and evapotranspiration contributions to streamflow variance; or evaluate local partial derivatives of an aerodynamic lift model to find which angle-of-attack range most affects lift.

Misapplication

Treat correlated inputs as independent when using variance-based indices, or rely exclusively on one-at-a-time perturbations for systems with strong interactions, producing misleading importance rankings.

Consequence

Correct application identifies high-impact parameters for calibration, model reduction, targeted data collection, and robust decision-making under input uncertainty.

Reversal

Focusing on robustness rather than sensitivity — identifying inputs or designs where outputs remain stable under perturbations — inverts the aim from finding influential factors to finding insensitive regions.

Boundary

Applies to models where inputs and outputs are well-defined; does not by itself establish causation from statistical associations and may be invalid if the analysis domain lies outside the model’s trained or physically meaningful input range.

Semantic Tension

Overlaps with uncertainty quantification (which measures output uncertainty magnitude) and parameter estimation (which fits parameters): sensitivity assesses influence structure rather than predictive uncertainty or parameter plausibility.

Synthesis

Sensitivity analysis systematically probes how input variability maps to output variability, using local derivatives or global variance/entropy-based measures to reveal influential factors, guide experiments, and prioritize modeling effort while noting limitations from input dependence and domain extrapolation.