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Aug 25, 2014 at 21:51 comment added Rasmus Bååth In Kruschkes "Doing Bayesian Data Analysis" there is indeed a "fully hierarchical" model described on page 330 where he uses a Gamma to model the precisions (inverse variances) of the groups. He does not give any concrete advice regarding the hyperpriors other than that they "must be appropriate for the domain and data at hand".
Aug 19, 2014 at 0:36 comment added Nate Agreed. You can also show that a hierarchical prior on sigma is inverse-gamma distributed, but that might be harder to work with. Also, check "Doing Bayesian Data Analysis" by Kruschke. Great book. Might have the example you're looking for.
Aug 18, 2014 at 11:33 history answered niandra82 CC BY-SA 3.0