Cross-classified hierarchical Bayesian models for risk-based analysis of complex systems under sparse data

Decisionmaking problems in risk analysis often involve extreme events, where empirical data are usually either sparse or lacking. With sparse data, important parameters and quantities for risk and safety analyses may not be estimated and tested within an acceptable level of significance. This paper applies Hierarchical Bayesian Models (HBMs) to reduce the estimation variance and thus build relatively robust models for extreme event data through borrowing strength from different but related systems or subsystems. Based on this application, this paper further applied HBMs with cross-classified random effects (CHBMs) to address the multi-dimensional property of complex systems and borrow strength from the multiple dimensions of such systems. Case studies with both simulated and real data demonstrate the effectiveness of HBMs and CHBMs in risk-based systems analysis.