Bayesian perspective in BEPU licensing analysis

Highlights: • Bayesian methods are much less used than frequentist methods in Forward Uncertainty Quantification for BEPU Methodologies. • Bayesian methods are the most used in Inverse Uncertainty Quantification for BEPU methodologies. A major reason is the fact that they produce well-posed solutions for the inverse problem. • In Forward Uncertainty Quantification, Bayesian methods based on estimation of the probability of exceeding regulatory limits can be considered as a Bayesian counterpart to Wilks' method. • A major problem of the licensing of Bayesian methods for BEPU analysis is that the choice of priors must be justified. - Abstract: The main objective of this paper is giving insights about the Bayesian formulation of Best-Estimate-Plus-Uncertainty (BEPU) methodologies of Nuclear Safety. It is written from a regulatory standpoint, focusing on the assessment and licensing process of this type of methodologies. The current use of Bayesian methods in Uncertainty Quantification (UQ) is summarized, distinguishing Forward and Inverse UQ. In Forward UQ, the most popular methods are frequentist and nonparametric. They are based on a minimum of assumptions, and this fact makes them simple to use and may expedite their assessment and licensing process, compared to other methods. Bayesian formulations, on the other hand, need to adequately justify the choice of prior distributions, to make sure that uncertainties are not estimated in an anticonservative fashion. Concerning Forward UQ, methods based on calculation of probabilities of exceeding regulatory limits (P-methods) are an alternative to standard methods based on quantile estimation (Q-methods). A frequentist P-method, the Clopper-Pearson interval, is basically equivalent to the noted Wilks' method, and so it is extensively used in the BEPU realm. Bayesian framework has been typically overlooked in the realm of P-methods for licensing purposes. The possibility of using such formulation to implement prior information about previous BEPU analysis of similar plant designs, operational conditions and accident scenarios should be explored. Bayesian methodologies of this type are used in Reliability, and they combine specific data with generic data (in the form of priors) of component or system failures. In inverse UQ, the situation is opposite to forward UQ: Bayesian methodologies are preferred to frequentist ones. One of the main reasons may be that Bayesian formulation produce regularized (well-posed) solutions to inverse problems.