Introduction to Sensitivity Analysis

Introduction to Sensitivity Analysis

2008 | A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M. Saisana and S. Tarantola
Sensitivity analysis studies how uncertainty in a model's output can be attributed to uncertainty in its inputs. It is closely related to uncertainty analysis, which quantifies uncertainty in model output. Both should be used together, with uncertainty analysis preceding sensitivity analysis. A model is a representation of a system, and its inputs and outputs are key elements. Models can be diagnostic or prognostic, data-driven or law-driven. Uncertainty is inherent in modeling and scientific inquiry, and models are part of the scientific method, subject to epistemological debate. Post-Normal Science (PNS) addresses the challenges of uncertainty and high stakes in scientific modeling. Models may have different structures that are compatible with the same data, leading to equifinality. Sensitivity analysis helps determine which inputs are most important in influencing model output. The quality of a model depends on its fitness for purpose, and sensitivity analysis can help assess model robustness. Sensitivity analysis can be local or global. Local methods, such as derivatives, are efficient but limited to the point of evaluation. Global methods explore the input space and are more effective in capturing the overall impact of inputs. A test model with linear relationships shows that scatterplots can reveal the influence of inputs, while derivatives may not. Normalized derivatives and standardized regression coefficients provide more reliable sensitivity measures. These measures can be used to rank inputs by their contribution to model output variance. For linear models, the first-order sensitivity index matches the squared standardized regression coefficients. For nonadditive models, the first-order indices may not sum to one. Sensitivity analysis requires a clear definition of what constitutes importance, and settings such as factor prioritization help define the purpose of the analysis. Nonadditive models complicate the interpretation of sensitivity measures, as the effects of inputs may not be separable. Sensitivity analysis is essential for understanding model behavior, identifying critical inputs, and improving model accuracy and reliability.Sensitivity analysis studies how uncertainty in a model's output can be attributed to uncertainty in its inputs. It is closely related to uncertainty analysis, which quantifies uncertainty in model output. Both should be used together, with uncertainty analysis preceding sensitivity analysis. A model is a representation of a system, and its inputs and outputs are key elements. Models can be diagnostic or prognostic, data-driven or law-driven. Uncertainty is inherent in modeling and scientific inquiry, and models are part of the scientific method, subject to epistemological debate. Post-Normal Science (PNS) addresses the challenges of uncertainty and high stakes in scientific modeling. Models may have different structures that are compatible with the same data, leading to equifinality. Sensitivity analysis helps determine which inputs are most important in influencing model output. The quality of a model depends on its fitness for purpose, and sensitivity analysis can help assess model robustness. Sensitivity analysis can be local or global. Local methods, such as derivatives, are efficient but limited to the point of evaluation. Global methods explore the input space and are more effective in capturing the overall impact of inputs. A test model with linear relationships shows that scatterplots can reveal the influence of inputs, while derivatives may not. Normalized derivatives and standardized regression coefficients provide more reliable sensitivity measures. These measures can be used to rank inputs by their contribution to model output variance. For linear models, the first-order sensitivity index matches the squared standardized regression coefficients. For nonadditive models, the first-order indices may not sum to one. Sensitivity analysis requires a clear definition of what constitutes importance, and settings such as factor prioritization help define the purpose of the analysis. Nonadditive models complicate the interpretation of sensitivity measures, as the effects of inputs may not be separable. Sensitivity analysis is essential for understanding model behavior, identifying critical inputs, and improving model accuracy and reliability.
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