Re‐examining informative prior elicitation through the lens of Markov chain Monte Carlo methods

Summary.  In recent years, advances in Markov chain Monte Carlo techniques have had a major influence on the practice of Bayesian statistics. An interesting but hitherto largely underexplored corollary of this fact is that Markov chain Monte Carlo techniques make it practical to consider broader classes of informative priors than have been used previously. Conjugate priors, long the workhorse of classic methods for eliciting informative priors, have their roots in a time when modern computational methods were unavailable. In the current environment more attractive alternatives are practicable. A reappraisal of these classic approaches is undertaken, and principles for generating modern elicitation methods are described. A new prior elicitation methodology in accord with these principles is then presented.