The underlying event model for approximating probabilistic dependence among binary events

This paper presents a model for approximating positive probabilistic dependence among binary (success/failure) events in decision, economic evaluation, and risk analysis problems. It is not always feasible to obtain the probabilities needed to completely specify the joint probability structure among the binary events in real-world problems, so simplifying assumptions such as independence that require only the marginal probabilities are frequently employed. The proposed model requires the assessment of only one conditional probability in addition to the marginal probabilities. Extensive numerical studies show that it produces more accurate joint outcome probabilities, expected values, and certainty equivalents than commonly used approximations. Binary events are important in a variety of practical problems, such as exploring geologically related petroleum exploration prospects, conducting related R&D projects, or pursuing related lawsuits. The proposed model addresses a practical need for better modeling of dependence in such problems, and it is operational.