Global sensitivity analysis

Definition

Global sensitivity analysis is a statistical method used to determine how variations in model inputs influence the outputs of a mathematical model across its entire parameter space. It helps in identifying which input variables are most influential on the output, allowing for better understanding of model behavior and uncertainty. This approach contrasts with local sensitivity analysis, focusing on small perturbations around a nominal point, and is crucial for robust uncertainty quantification.

5 Must Know Facts For Your Next Test

1. Global sensitivity analysis considers the entire input space and evaluates the effect of all input variables simultaneously, providing a more comprehensive view of model behavior.
2. This method can help identify critical parameters that need tighter control or better measurement due to their significant impact on output variability.
3. Techniques like Sobol' indices and FAST (Fourier Amplitude Sensitivity Test) are common methods used in global sensitivity analysis.
4. Incorporating global sensitivity analysis into model development can enhance model reliability and decision-making processes by prioritizing areas that require further investigation.
5. Global sensitivity analysis is especially important in complex systems where many variables interact, making it difficult to assess their individual effects through local methods.

Review Questions

• How does global sensitivity analysis differ from local sensitivity analysis, and why is this distinction important?
  • Global sensitivity analysis differs from local sensitivity analysis in that it examines the effects of input variations across the entire parameter space rather than just near a specific point. This distinction is crucial because it allows for a more comprehensive understanding of how different inputs collectively influence model outputs. Local analysis might miss interactions between variables or fail to capture non-linear relationships that global sensitivity analysis can reveal, making it essential for accurately assessing uncertainty in complex models.
• Discuss the significance of global sensitivity analysis in the context of uncertainty quantification and its impact on model validation.
  • Global sensitivity analysis plays a key role in uncertainty quantification as it helps identify which input parameters contribute most to output variability. By understanding these sensitivities, modelers can prioritize efforts to improve measurements or controls on those critical inputs. This process enhances model validation by ensuring that the most influential factors are accurately represented and assessed, leading to more reliable predictions and informed decision-making based on the model results.
• Evaluate the effectiveness of different methods used in global sensitivity analysis, such as Sobol' indices and Monte Carlo simulations, in capturing the complexities of real-world models.
  • The effectiveness of methods like Sobol' indices and Monte Carlo simulations in global sensitivity analysis lies in their ability to handle complex interactions and non-linearities present in real-world models. Sobol' indices provide a detailed breakdown of how much each input contributes to output variance, revealing interactions among parameters. On the other hand, Monte Carlo simulations allow for comprehensive sampling across the input space, providing insights into uncertainty propagation. Both methods complement each other, with Sobol' indices offering precise insights while Monte Carlo simulations capture broader uncertainties, together facilitating a deeper understanding of model behavior.

Related terms

Local Sensitivity Analysis: A technique that examines how small changes in input parameters affect the output of a model, typically around a specific point.

Monte Carlo Simulation:

A computational algorithm that relies on repeated random sampling to obtain numerical results, often used in uncertainty quantification.

Variance-Based Sensitivity Analysis: A method that decomposes the variance of model outputs to assess the contribution of each input variable to the overall uncertainty.