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.

Cascade Sensitivity Measures

“…and Werner et al (2018). Hence, we are concerned with reflecting the impact of the dependence between input factors in sensitivity metrics.…”

“…However, in this stream of literature, sensitivity measures generally do not account explicitly for the impact of the dependence between input factors. This matters, given that the impact of (stochastic) dependencies is a persistent topic in risk modelling; see, for example, Mornet, Opitz, Luzi, and Loisel (2015)), Su, Mahadevan, Xu, and Deng (2015), Wang, Dyer, and Butler (2016), and Werner, Bedford, and Quigley (2018). Hence, we are concerned with reflecting the impact of the dependence between input factors in sensitivity metrics.…”

Risk Assessment of Future Antibiotic Resistance—Eliciting and Modelling Probabilistic Dependencies Between Multivariate Uncertainties of Bug-Drug Combinations

“…[44] and. [45] present modelling and elicitation approaches for minimum information copulas which do not assume a specific parametric copula form. Similarly, [46] introduce an expert judgement method for quantifying Diagonal Band copulas.…”

Probabilistic modeling and analysis of sequential cyber‐attacks

“…In addition, the existing quantitative risk assessment methods mostly focused on the amount or frequency of different and independent system vulnerabilities or hazardous events. In practice, however different hazardous events may take place in a dependent manner, ie, the occurrence of one hazardous event impacts the occurrence of another hazardous event happening to the same system . Dependencies or interactions between different attack events or outcomes have received considerable research attentions from the cybersecurity community in the past several years (see, eg, other works).…”

“…In practice, however different hazardous events may take place in a dependent manner, ie, the occurrence of one hazardous event impacts the occurrence of another hazardous event happening to the same system. 38 Dependencies or interactions between different attack events or outcomes have received considerable research attentions from the cybersecurity community in the past several years (see, eg, other works 28,[39][40][41][42] ). Cyber-attacks have become a major threat to many modern systems and networks.…”