Sequential Refined Partitioning for Probabilistic Dependence Assessment

Area of Science:

• Decision Analysis
• Probability Theory
• Risk Management

Background:

• Probabilistic modeling of dependence is vital for risk assessment and decision-making under uncertainty.
• Ignoring dependence can lead to distorted model outputs and misinterpretations of overall risk.
• Expert judgment is often necessary when data for dependence modeling is scarce.

Purpose of the Study:

• To present a novel method, sequential refined partitioning, for expert-based probabilistic dependence modeling.
• To address and overcome the challenges of over- and underspecification inherent in expert judgment.
• To enable flexible and feasible assessment of joint distributions in the absence of complete data.

Main Methods:

• The sequential refined partitioning method elicits single conditioning sets and feasible assessment ranges to minimize cognitive complexity for experts.
• Linear programming is used to derive feasible ranges for sequential assessments.
• Minimally informative distributions are modeled for assessed parts, balancing expert input with distributional constraints.

Main Results:

• The method successfully addresses over- and underspecification issues in expert judgment for dependence modeling.
• It allows for flexible, nonparametric assessment and modeling of dependence in joint distributions.
• The approach enables the feasible modeling of entire distributions based on expert information.

Conclusions:

• The sequential refined partitioning method offers a robust framework for expert-based probabilistic dependence modeling.
• This nonparametric approach enhances the accuracy and feasibility of risk assessment and decision-making under uncertainty.
• The method is applicable to complex scenarios, such as terrorism risk assessment in insurance underwriting.