Proceedings of the Eighth International Conference on Probabilistic Safety Assessment & Management (PSAM)
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The process of Bayesian updating for parameter estimation in risk assessment has become commonplace to the point where it has often been proceduralized. In order to avoid numerical integration, the update procedures often involve use of a conjugate prior: gamma distributions for Poisson or exponential events, beta distributions for binomial events. However, much of the generic information used for prior distributions is still expressed in terms of a lognormal distribution, so the procedures provide a recipe for finding a conjugate prior to replace the nonconjugate lognormal distribution in the generic database. This almost always involves matching the mean and variance of the two distributions. In many instances, the lognormal prior is quite diffuse, leading to a reverse J-shaped conjugate prior that weights small parameter values much more heavily than does the original lognormal prior. When the update procedure combines this conjugate prior with zero observed occurrences, the result is excess shrinkage of the posterior mean, leading to unreasonably small values for the parameter being estimated. Propagating these values through the risk model can lead to skewed importance rankings, etc. This problem is illustrated with two examples taken from the utility industry.