Eliciting vague but proper maximal entropy priors in Bayesian experiments

Priors elicited according to maximal entropy rules have been used for years in objective and subjective Bayesian analysis. However, when the prior knowledge remains fuzzy or dubious, they often suffer from impropriety which can make them uncomfortable to use. In this article we suggest the formal elicitation of an encompassing family for the standard maximal entropy (ME) priors and the maximal data information (MDI) priors, which can lead to obtain proper families. An interpretation is given in the objective framework of channel coding. In a subjective framework, the performance of the method is shown in a reliability context when flat but proper priors are elicited for the Weibull lifetime distributions. Such priors appear as practical tools for sensitivity studies.