I'm estimating several inverse covariance matrices of a set of measurements across different subpopulations using an wishart prior in jags/rjags/R.
Instead of specifying a scale matrix and degrees of freedom on the inverse covariance matrix prior (the wishart distribution), I would like to use a hyperprior on the scale matrix and degrees of freedom, so they can be estimated from the variation across subpopulations.
I haven't found much literature on hyperpriors for the scale matrix and degrees of freedom. Most of the literature seems to stop the hierarchy at the choice of the prior to the covariance/inverse covariance and/or are focused on estimating a single covariance matrix rather than several covariance matrices across different populations.
Any suggestions as to how to go about this - what are the recommended hyperprior distributions to use for the scale matrix and degrees of freedom of the wishart distribution? Is there some literature on this that I'm missing?