Precursor-based hierarchical Bayesian approach for rare event frequency estimation

Abstract

Due to a scarcity of data, the estimate of the frequency of a rare event is a consistently challenging problem in probabilistic risk assessment (PRA). However, the use of precursor data has been shown to help in obtaining more accurate estimates. Moreover, the use of hyper-priors to represent prior parameters in the hierarchical Bayesian approach (HBA) generates more consistent results in comparison to the conventional Bayesian method. This study proposes a framework that uses a precursor-based HBA for rare event frequency estimation. The proposed method is demonstrated using the recent BP Deepwater Horizon accident in the Gulf of Mexico. The conventional Bayesian method is also applied to the same case study. The results show that the proposed approach is more effective with regards to the following perspectives: (a) using the HBA in the proposed framework provides an opportunity to take full advantage of the sparse data available and add information from indirect but relevant data; (b) the HBA is more sensitive to changes in precursor data than the conventional Bayesian method; and (c) using hyper-priors to represent prior parameters, the HBA is able to model the variability that can exist among different sources of data.