Thomas comments on The Joys of Conjugate Priors - Less Wrong Discussion
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Well ... what bothers me? That the alpha and beta should have their own probability distribution each. And so on and on.
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.64.5680&rep=rep1&type=pdf
EDIT: They don't extend the hierarchy infinitely upward in the paper, but there is no reason not to, as far as I can see.
Like so: Infinite hierarchies and prior distributions.
Thanks for the link! Should make good reading. It sounds like you know a fair amount of ML, are you doing research in the field?
I taught myself Bayesian statistics for use in my engineering Ph.D. (My advisor didn't care how I got good answers -- he cared that I got good answers.) Until recently I was a postdoc in a statistics lab, but the research did not focus on what I would consider cutting-edge Bayesian stats.