Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper)

Various noninformative prior distributions have been suggested for scale parameters in hierarchical models. We construct a new folded-noncentral-tfamily of conditionally conjugate priors for hierarchical standard deviation parameters, and then consider noninformative and weakly informative priors in this family. We use an example to illustrate serious problems with the inverse-gamma family of "noninformative" prior distributions. We suggest...