In decision and risk analysis problems, modelling uncertainty probabilistically provides key insights and information for decision makers. A common challenge is that uncertainties are typically not isolated but interlinked which introduces complex (and often unexpected) effects on the model output. Therefore, dependence needs to be taken into account and modelled appropriately if simplifying assumptions, such as independence, are not sensible. Similar to the case of univariate uncertainty, which is described elsewhere in this book, relevant historical data to quantify a (dependence) model are often lacking or too costly to obtain. This may be true even when data on a model’s univariate quantities, such as marginal probabilities, are available. Then, specifying dependence between the uncertain variables through expert judgement is the only sensible option. A structured and formal process to the elicitation is essential for ensuring methodological robustness. This chapter addresses the main elements of structured expert judgement processes for dependence elicitation. We introduce the processes’ common elements, typically used for eliciting univariate quantities, and present the differences that need to be considered at each of the process’ steps for multivariate uncertainty. Further, we review findings from the behavioural judgement and decision making literature on potential cognitive fallacies that can occur when assessing dependence as mitigating biases is a main objective of formal expert judgement processes. Given a practical focus, we reflect on case studies in addition to theoretical findings. Thus, this chapter serves as guidance for facilitators and analysts using expert judgement.@en

Many applications in decision making under uncertainty and probabilistic risk assessment require the assessment of multiple, dependent uncertain quantities, so that in addition to marginal distributions, interdependence needs to be modelled in order to properly understand the overall risk. Nevertheless, relevant historical data on dependence information are often not available or simply too costly to obtain. In this case, the only sensible option is to elicit this uncertainty through the use of expert judgements. In expert judgement studies, a structured approach to eliciting variables of interest is desirable so that their assessment is methodologically robust. One of the key decisions during the elicitation process is the form in which the uncertainties are elicited. This choice is subject to various, potentially conflicting, desiderata related to e.g. modelling convenience, coherence between elicitation parameters and the model, combining judgements, and the assessment burden for the experts. While extensive and systematic guidance to address these considerations exists for single variable uncertainty elicitation, for higher dimensions very little such guidance is available. Therefore, this paper offers a systematic review of the current literature on eliciting dependence. The literature on the elicitation of dependence parameters such as correlations is presented alongside commonly used dependence models and experience from case studies. From this, guidance about the strategy for dependence assessment is given and gaps in the existing research are identified to determine future directions for structured methods to elicit dependence.@en

Many applications in decision making under uncertainty and probabilistic risk assessment require the assessment of multiple, dependent uncertain quantities, so that in addition to marginal distributions, interdependence needs to be modelled in order to properly understand the overall risk. Nevertheless, relevant historical data on dependence information are often not available or simply too costly to obtain. In this case, the only sensible option is to elicit this uncertainty through the use of expert judgements. In expert judgement studies, a structured approach to eliciting variables of interest is desirable so that their assessment is methodologically robust. One of the key decisions during the elicitation process is the form in which the uncertainties are elicited. This choice is subject to various, potentially conflicting, desiderata related to e.g. modelling convenience, coherence between elicitation parameters and the model, combining judgements, and the assessment burden for the experts. While extensive and systematic guidance to address these considerations exists for single variable uncertainty elicitation, for higher dimensions very little such guidance is available. Therefore, this paper offers a systematic review of the current literature on eliciting dependence. The literature on the elicitation of dependence parameters such as correlations is presented alongside commonly used dependence models and experience from case studies. From this, guidance about the strategy for dependence assessment is given and gaps in the existing research are identified to determine future directions for structured methods to elicit dependence.@en

Many applications in decision making under uncertainty and probabilistic risk assessment require the assessment of multiple, dependent uncertain quantities, so that in addition to marginal distributions, interdependence needs to be modelled in order to properly understand the overall risk. Nevertheless, relevant historical data on dependence information are often not available or simply too costly to obtain. In this case, the only sensible option is to elicit this uncertainty through the use of expert judgements. In expert judgement studies, a structured approach to eliciting variables of interest is desirable so that their assessment is methodologically robust. One of the key decisions during the elicitation process is the form in which the uncertainties are elicited. This choice is subject to various, potentially conflicting, desiderata related to e.g. modelling convenience, coherence between elicitation parameters and the model, combining judgements, and the assessment burden for the experts. While extensive and systematic guidance to address these considerations exists for single variable uncertainty elicitation, for higher dimensions very little such guidance is available. Therefore, this paper offers a systematic review of the current literature on eliciting dependence. The literature on the elicitation of dependence parameters such as correlations is presented alongside commonly used dependence models and experience from case studies. From this, guidance about the strategy for dependence assessment is given and gaps in the existing research are identified to determine future directions for structured methods to elicit dependence.@en