Discussion of specifying prior distributions in reliability applications

Abstract

This is a thorough review of approaches to prior elicitation in reliability and includes some extensive illustrations of the approaches. For me, this article is both a very useful reference document and can act as a good primer for new students in the reliability field who would like to understand better how prior elicitation can be undertaken in reliability applications.

The focus is largely on uninformative priors and the various approaches in which the idea of lack of background information about a parameter can be realised. Since statistical reliability largely uses probability models with few (2 or 3 is typical) parameters that are common across many fields of application, it is not surprising that these are the approaches that we see generally in the Bayesian literature when trying to specify a lack of background information.

The various problems with non-informative priors are well known. For the case of a ‘random sample’ of data to be analysed, the noninformative prior methods of this paper will tend to work well and more specifically in the small data case that is emphasised. However, it should be noted that they can start to work in misleading ways in more complex data situations which one can see in reliability settings. For example, in hierarchical models, non-informative parameters on scale parameters can lead to inferences that describe the data as entirely noise.¹ Model comparison, for example using Bayes factors, can also be problematic.² In these cases, as the authors point out, priors that avoid assigning belief to implausible values become important.

No doubt a separate paper can be written on prior specification under these more complex models, and the pitfalls therein. I thank the authors for bringing together a comprehensive study of prior elicitation in reliability applications.