The lay abstract featured today (for Specifying prior distributions in reliability applications by Qinglong Tian, Colin Lewis-Beck, Jarad B. Niemi and William Q. Meeker) is from Applied Stochastic Models in Business and Industry with the full article (Open Access) now available to read here.
Bayesian inference methods require the specification of a joint prior distribution to describe available knowledge about the model parameters. There are strong motivations for using Bayesian inference methods in reliability applications including the option to use information from physics-of-failure or previous experience with a failure mode in a particular material to specify an informative prior distribution. Often there is prior information for one parameter but not the other(s) and thus a noninformative prior may be needed for one or more parameters. Much work has been done to find noninformative prior distributions that will provide inference methods with good (and in some cases exact) frequentist coverage properties. This paper reviews some of this work and provides, evaluates, and illustrates principled extensions and adaptations of these methods to the practical realities of reliability data (e.g., non-trivial censoring) when using a log-location-scale distribution. The paper has been discussed by twenty experts in reliability, Bayesian inference, or both. The discussions and the authors’ rejoinder nicely complement the main paper, providing additional information on topics such as default priors, user-friendly Bayesian software, alternatives to the methods presented in the paper, and prior specifications for more complicated models.
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