##  [Sensitivity Analysis](/sensitivity-analysis-0) 

 Definition

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

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

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

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

Consequence

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

 

 

 

 

## Reversal

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

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

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

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.