Sequential refined partitioning for probabilistic dependence assessment

Modelling 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 modelling dependence between uncertain variables is lacking, expert judgement might be sought to assess a joint distribution. Key challenges for the use of expert judgement for dependence modelling are over- and under specification. An expert can sometimes provide assessments which are not consistent with any probability distribution (over specification), and on the other hand, without making very restrictive parametric assumptions an expert cannot fully dene a full probability distribution (under specification). The Sequential Refined Partitioning method addresses over- and under specification whilst allowing for flexibility about which part of a joint distribution is assessed and its level of detail. Potential over specification 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. Under specification is addressed by modelling the density of directly and indirectly assessed distribution parts as minimally informative given their constraints. Hence, our method allows for modelling the whole distribution feasibly and in accordance with experts' information. A non-parametric way of assessing and modelling dependence flexibly in such detail has not been presented in the expert judgement literature for probabilistic dependence models so far. We provide an example of assessing terrorism risk in insurance underwriting.