Elicitation of Weibull priors

TL;DR

This paper introduces a new method for eliciting Weibull priors based on expert predictive lifetime information, simplifying prior calibration and improving Bayesian reliability modeling.

Contribution

It proposes a novel approach to prior elicitation using expert predictive data and a virtual sample size, enhancing tractability and interpretability.

Findings

The method allows straightforward prior calibration from expert opinions.

It maintains full tractability despite Weibull conjugation challenges.

The approach facilitates sensitivity analysis and balanced posterior inference.

Abstract

Based on expert opinions, informative prior elicitation for the common Weibull lifetime distribution usually presents some difficulties since it requires to elicit a two-dimensional joint prior. We consider here a reliability framework where the available expert information states directly in terms of prior predictive values (lifetimes) and not parameter values, which are less intuitive. The novelty of our procedure is to weigh the expert information by the size m of a virtual sample yielding a similar information, the prior being seen as a reference posterior. Thus, the prior calibration by the Bayesian analyst, who has to moderate the subjective information with respect to the data information, is made simple. A main result is the full tractability of the prior under mild conditions, despite the conjugation issues encountered with the Weibull distribution. Besides, m is a practical focus point for discussion between analysts and experts, and a helpful parameter for leading sensitivity studies and reducing the potential imbalance in posterior selection between Bayesian Weibull models, which can be due to favoring arbitrarily a prior. The calibration of m is discussed and a real example is treated along the paper.