Multi-factor dependence modelling with specified marginals and structured association in large-scale project risk assessment

This paper examines the high-dimensional dependence modelling problem in the context of project risk assessment. As the dimension of uncertain performance units (i.e., itemized costs and activity times) in a project increases, specifying a feasible correlation matrix and eliciting relevant pair-wise information, either from historical data or with expert judgement, becomes practically unattainable or simply not economical. This paper presents a factor-driven dependence elicitation and modelling framework with scalability to large-scale project risks. The multi-factor association model (MFAM) accounts for hierarchical relationships of multiple association factors and provides a closed-form solution to a complete and mathematically consistent correlation matrix. Augmented with the structured association (SA) technique for systematic identification of hierarchical association factors, the MFAM offers additional flexibility of utilizing the minimum information available in standardized, ubiquitous project plans (e.g., work breakdown structure, resource allocation, or risk register), while preserving the computational efficiency and the scalability to high dimensional project risks. Numerical applications and simulation experiments show that the MFAM, further combined with extended analytics (i.e., parameter calibration and optimization), provides credible risk assessments (with accuracy comparable to full-scale simulation) and further enhances the realism of dealing with high-dimensional project risks utilizing all relevant information.