Back to Bayesics

Bayesian analysis was formulated to permit incorporation of prior information into statistical analysis. It is disconcerting to view the large amount of Bayesian analysis that is focussed on non-informative priors. Less disturbing, but still questionable, is the habit of forcing prior beliefs to be approximated by very restrictive conjugate prior families. More flexible families of conjugate priors are needed to accommodate a broader spectrum of informative (or non-informative) prior beliefs. As a small step in this direction, conditionally specified priors are advocated for use in many standard statistical settings.