Sensitivity Analysis

Mathematical Modeling · Axiom Academy

LESSON Sensitivity Analysis - Mathematical Modeling Unit 1: Introduction to Modeling - Mathematical Modeling Sensitivity analysis is the study of how changes in model inputs affect model outputs. It answers the critical question: "How much does the output change when we change an input?" Model parameters often have uncertainty Some parameters may be more critical than others We need to know where to focus data collection efforts Understanding model behavior builds confidence in predictions Examines model behavior around a specific point in parameter space. Uses derivatives and small perturbations. Advantages: Computationally cheap, gives precise information at a point Limitations: Only valid near the base point; may miss nonlinear effects Explores model behavior across the entire parameter space. Accounts for parameter interactions and nonlinearities. Advantages: Captures nonlinear effects and parameter interactions Limitations: Computationally expensive; requires many model evaluations One-at-a-Time (OAT) Sensitivity Analysis The simplest approach: vary one parameter while holding all others constant. Set all parameters to their baseline (nominal) values Change that parameter by a fixed percentage (e.g., +/- 10%) Consider with baseline values P_0 = 100 , r = 0.05 , t = 10 . Conclusion: P_0 has the largest influence on output. Partial Derivatives as Sensitivity Measures For differentiable models, partial derivatives provide exact local sensitivity information.

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