🤖 AI Summary
This study addresses the challenge of dependency uncertainty in risk and decision models where marginal distributions are sparse and dependence structures are partially unknown, rendering traditional probability bounds analysis ineffective. The authors propose a black-box risk decision framework that integrates p-boxes, precise cumulative distribution functions, and fixed quantities as mixed inputs. Known dependencies are characterized using copulas, while unknown dependencies are propagated through Fréchet-type admissible coupling sets. For the first time, dependence sensitivity is incorporated into probability bounds analysis, enabling cross-dependence modeling between imprecise and precise variables and substantially enhancing the transparency and reasonableness of uncertainty propagation. Case studies demonstrate that neglecting dependence structure can severely underestimate tail risk, leading to overly optimistic decision assessments.
📝 Abstract
Risk and decision models often combine sparse marginal information, precisely specified probability distributions, and dependence assumptions that are only partly justified. Probability bound analysis (PBA) represents epistemic uncertainty through probability boxes, but many applications assume independence or require dependence structures to be fully specified. We develop a dependence-sensitive PBA framework for black-box risk and decision models in which both marginal information and dependence information may be incomplete. The framework combines p-box parameters, precise-CDF parameters, and fixed quantities; incorporates specified dependence through copulas; and propagates unknown dependence through Fréchet-style admissible coupling sets. We also extend the construction to cross-dependence between imprecisely specified and precisely specified inputs. In an illustrative risk decision model, dependence assumptions materially affected output bounds and tail-risk summaries; analyses that ignored or simplified dependence produced narrower characterizations of plausible outcomes. The framework supports transparent uncertainty propagation when evidence is insufficient to justify either precise marginal distributions or a single dependence model.