Modeling Correlated Discrete Uncertainties in Event Trees with Copulas

Area of Science:

• Decision Analysis
• Risk Analysis
• Probability Theory

Background:

• Accurate modeling of uncertainty dependence is crucial for effective decision and risk analyses.
• Existing methods often struggle with correlated discrete uncertainties, requiring extensive probability assessments.
• Copula-based approaches have shown promise for continuous uncertainties.

Purpose of the Study:

• To extend the copula-based approach for modeling correlated continuous uncertainties to discrete uncertainties.
• To reduce the number of probability assessments needed in risk analysis.
• To provide a flexible framework for incorporating various dependence measures and copula families.

Main Methods:

• Adaptation of the copula-based framework to handle discrete random variables.
• Utilizing parametric families of copulas (e.g., normal, t, Archimedean) to model dependence structures.
• Incorporation of multiple dependence measures (e.g., correlation, tail dependence).

Main Results:

• Significant reduction in the number of required probability assessments compared to traditional methods.
• Successful representation of dependence structures between discrete uncertainties.
• Demonstration of the approach's flexibility with different dependence measures and copula types.

Conclusions:

• The extended copula-based approach offers an efficient and flexible method for modeling discrete uncertainty dependence in decision and risk analyses.
• This methodology simplifies problem structuring and enhances the accuracy of risk assessments.
• The approach is extensible to mixed discrete and continuous uncertainty scenarios.