Discussion of specifying prior distributions in reliability applications

Abstract

AbstractTian et al. have reviewed and discussed various noninformative or weakly informative priors when reliability data are modeled using the log‐location‐scale family of distributions. They have compared these priors to partially informative priors, which are also called modified Jeffreys' priors in the literature. The authors recommend adaptations to Bayesian methods when analyzing reliability data with a small number of failures. Does a chosen Bayesian computation method play a role in the inference? Can a Bayesian model, without an informative prior, really solve the inference problem which is due to a lack of information provided by the data? How should a practitioner describe formal decisions based on the chosen Bayesian model (a likelihood as well as a prior)? Can one translate available information into an appropriate parameter space and a prior distribution on it, independent of the type of censoring? In this commentary, we put forward such questions and concerns that deserve a discussion, from a practitioner's point of view.