Sensitivity Analysis

Sensitivity analysis is a technique used in statistics and modeling to assess the impact of changes in input variables on the output variable of a model. It involves exploring how much the model’s results vary when the input parameters are varied.

Purpose:

• To understand the relative importance of different input variables.
• To assess the robustness of the model against changes in input data.
• To guide model optimization and improve its accuracy.

Methods:

There are different methods for conducting sensitivity analysis, including:

• First-Order Sensitivity Analysis: Computes the partial derivatives of the output variable with respect to each input variable.
• Second-Order Sensitivity Analysis: Measures the curvature of the output variable’s surface with respect to each input variable.
• Latin Hypercube Sampling: Randomly samples input variables within their respective ranges to assess the impact on the output variable.
• ** Morris Method:** Uses a series of experimental runs to explore the input space and evaluate the model’s sensitivity.

Steps:

1. Define the model: A mathematical model that relates input variables to the output variable.
2. Specify input ranges: Define the possible ranges for each input variable.
3. Run the model: Evaluate the model for different combinations of input values.
4. Analyze results: Evaluate the impact of changes in input variables on the output variable.

Applications:

Sensitivity analysis is widely used in various fields, including:

• Engineering: Design optimization, system analysis
• Finance: Risk assessment, model validation
• Science: Model interpretation, hypothesis testing
• Social sciences: Policy evaluation, data analysis

Benefits:

• Improved understanding: Provides insights into the relationships between input and output variables.
• Enhanced model robustness: Helps identify inputs that are most sensitive and mitigate their impact on results.
• Guided model optimization: Can be used to find optimal parameter settings for improved accuracy.

Conclusion:

Sensitivity analysis is a valuable technique for understanding and assessing the sensitivity of models. It is an important tool for model calibration, optimization, and robustness evaluation.