Discussion of “Specifying prior distributions in reliability applications”: Towards new formal rules for informative prior elicitation?

Abstract

SummaryThe article by Tian et al. (Appl. Stoch. Models Bus. Ind. 2023) takes an interesting look at the use of non‐informative priors adapted to several censoring processes, which are common in reliability. It proposes a continuum of modelling approaches that go as far as defining weakly informative priors to overcome the well‐known shortcomings of frequentist approaches to problems involving highly censored samples. In this commentary, I make some critical remarks and propose to link this work to a more generic vision of what could be a relevant Bayesian elicitation in reliability, taking advantage of recent theoretical and applied advances. Through tools like approximate posterior priors and prior equivalent sample sizes, and by illustrating them with simple reliability models, I suggest methodological avenues to formalize the elicitation of informative priors in a auditable, defensible way. By allowing a clear modulation of subjective information, this might respond to the authors' primary concern of constructing weakly informative priors and to a more general concern for precaution in Bayesian reliability.