Performance of Empirical Bayes Estimation Techniques Used in Probabilistic Risk Assessment

Abstract This paper analyzes, validates, compares, and contrasts parameter estimation techniques used in probabilistic risk assessment. The analysis and validation are performed using computer-simulated as well as real-world component reliability data collected in nuclear industry. The analysis is focused on parametric and nonparametric empirical Bayes as well as frequentists methods. Different techniques are analyzed in terms of total squared error risk. A recently published nonparametric Bayes method based on the solution of an integral equation is described and its performance is contrasted with parametric and hierarchical Bayes. The results show that the nonparametric Bayes can achieve a smaller squared error risk than other Bayesian methods and maximum likelihood estimators when applied to the data collected at different nuclear power plants. However, the improvement produced by empirical Bayes techniques is not uniform and cannot be guaranteed for each and every plant. The paper shows strengths and limitations of different estimations techniques and concludes with practical recommendations.