On the nature and practical handling of the Bayesian aggregation anomaly

This paper addresses the issue, arising in probabilistic parameter estimation, which is sometimes referred to as the “Bayesian anomaly,” or also as the problem of “imperfect aggregation in Bayesian estimation.” The issue is clarified here from a generalized and theoretical point of view, but also in terms of a practical and mathematically consistent solution for probabilistic parameter estimation cases arising in actual reliability analysis and probabilistic risk assessment applications. More specifically, both theoretical and practical technical arguments are presented to show the reasons that make the purported anomaly manifest itself, and how the situations where it could in theory lead to serious estimation errors can be correctly handled. Interpretations and conclusions previously drawn with respect to the anomaly are also examined and re-evaluated in light of the new information and developments presented by the paper.