Simple Marginally Noninformative Prior Distributions for Covariance Matrices

A family of prior distributions for covariance matrices is studied. Members of the family possess the attractive property of all standard deviation and correlation parameters being marginally noninformative for particular hyperparameter choices. Moreover, the family is quite simple and, for approximate Bayesian inference techniques such as Markov chain Monte Carlo and mean field variational Bayes, has tractability on par with the Inverse-Wishart conjugate family of prior distributions. A simulation study shows that the new prior distributions can lead to more accurate sparse covariance matrix estimation.