Name: Prior distributions for variance parameters in hierarchical models
Author: Andrew Gelman
Bayesian Analysis (2006) 1, Number 3, pp. 515–533
Brief Intro: Various noninformative prior distributions have been suggested for
scale parameters in hierarchical models. We construct a new folded-noncentral-t
family of conditionally conjugate priors for hierarchical standard deviation pa-
rameters, 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 instead to use a uni-
form prior on the hierarchical standard deviation, using the half-t family when the
number of groups is small and in other settings where a weakly informative prior
is desired. We also illustrate the use of the half-t family for hierarchical modeling
of multiple variance parameters such as arise in the analysis of variance.