Global Sensitivity Analysis with Mixtures: A Generalized Functional ANOVA Approach.

Area of Science:

• Computational mathematics
• Risk analysis
• Uncertainty quantification

Background:

• Global sensitivity analysis (GSA) typically assumes a unique distribution for model inputs.
• Analysts may use alternative or mixture distributions, complicating sensitivity measure interpretation.
• Existing variance-based GSA methods may lose theoretical grounding or independence assumptions under these conditions.

Purpose of the Study:

• To investigate the impact of alternative and mixture input distributions on GSA.
• To develop theoretically sound methods for variance-based sensitivity analysis with mixture distributions.
• To provide practical recommendations for risk analysts dealing with input distribution uncertainty.

Main Methods:

• Analysis of mathematical properties affected by non-unique input distributions in GSA.
• Application of generalized functional ANOVA expansion for theoretically grounded analysis.
• Numerical implementation using diffeomorphic modulation and homotopy regression for effect estimation.

Main Results:

• The uniqueness assumption in GSA is challenged by alternative or mixture input distributions.
• Generalized functional ANOVA expansion provides a robust framework for GSA with mixture distributions.
• Variance-based sensitivity measures can be calculated for models like Nordhaus' DICE under mixture distributions.

Conclusions:

• Analysts must carefully consider the implications of input distribution choices on GSA results.
• The proposed generalized functional ANOVA approach offers a theoretically sound method for mixture distributions.
• Recommendations are provided to guide risk analysts in applying GSA with complex input scenarios.