Sensitivity analysis of model output with input constraints: a generalized rationale for local methods.

Area of Science:

• Risk Analysis
• Computational Modeling
• Statistical Methods

Background:

• Sensitivity analysis (SA) methods are crucial for understanding model behavior.
• Existing SA approaches often struggle with input parameter constraints in risk analysis.
• Current handling of constraints in SA is largely heuristic and lacks a systematic foundation.

Purpose of the Study:

• To develop a generalized rationale for local sensitivity analysis (SA) methods that accommodates input constraints.
• To systematically analyze and explain the effects of constraints on SA.
• To extend existing SA measures and introduce an efficient procedure for constrained SA.

Main Methods:

• Systematic analysis of the effects of input parameter constraints on SA.
• Extension of the local SA rationale (Helton, 1993) to incorporate constraints.
• Adaptation of Birnbaum, criticality, and differential importance measures for constrained environments.
• Development of a cost-efficient procedure for obtaining constrained SA results.

Main Results:

• Identified three key effects of constraints: impossibility of independent parameter variation, output insensitivity when a parameter is solved by a constraint, and dependency of SA results on the choice of dependent parameter.
• Provided a theoretical explanation for these effects by extending existing SA frameworks.
• Successfully extended established SA measures to the constrained case.
• Demonstrated a procedure for efficient constrained SA.

Conclusions:

• The proposed generalized rationale provides a robust framework for local SA under input constraints.
• The extended SA measures offer more accurate insights into model behavior in constrained systems.
• The developed procedure allows for efficient and cost-effective constrained SA, applicable to fields like risk analysis.
• The findings are numerically illustrated using a nonbinary event tree model.