Sequential Refined Partitioning for Probabilistic Dependence Assessment

Abstract

Modeling dependence probabilistically is crucial for many applications in risk assessment and decision making under uncertainty. Neglecting dependence between multivariate uncertainties can distort model output and prevent a proper understanding of the overall risk. Whenever relevant data for quantifying and modeling dependence between uncertain variables are lacking, expert judgment might be sought to assess a joint distribution. Key challenges for the use of expert judgment for dependence modeling are over- and underspecification. An expert can provide assessments that are infeasible, i.e., not consistent with any probability distribution (overspecification), and on the other hand, without making very restrictive parametric assumptions an expert cannot fully define a probability distribution (underspecification). The sequential refined partitioning method addresses over- and underspecification while allowing for flexibility about which part of a joint distribution is assessed and its level of detail. Potential overspecification is avoided by ensuring low cognitive complexity for experts through eliciting single conditioning sets and by offering feasible assessment ranges. The feasible range of any (sequential) assessment can be derived by solving a linear programming problem. Underspecification is addressed by modeling the density of directly and indirectly assessed distribution parts as minimally informative given their constraints. Hence, our method allows for modeling the whole distribution feasibly and in accordance with experts' information. A nonparametric way of assessing and modeling dependence flexibly in such detail has not been presented in the expert judgment literature for probabilistic dependence models so far. We provide an example of assessing terrorism risk in insurance underwriting.

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