# Hyperprior Noninformative Beta Binomial Model [closed]

I've been working through Gelman's Bayesian Data Analysis 3 text and have been trying to understand one of the hierarchical models revolving around rat tumors (Chapter 5). He uses a binomial model with p assigned a beta distribution. The Beta distribution has parameters $\alpha$ and $\beta$ which need a distribution for the fully Bayesian hierarchical model.

In order to create a noninformative distribution he parametrizes the model in terms of $\frac{\alpha}{\alpha+\beta}$ (prior mean) and an approximation of the standard deviation of the beta distribution $(\alpha+\beta)^{-1/2}$ . (described here too http://andrewgelman.com/2009/10/21/some_practical/) On his blog, he mentions not favoring this approach anymore and preferring weakly informative models, but I'd still like to understand the thinking that supports this model.

• Bonus: What connection, if any, does this have to a Pareto distribution? I tried parametrizing this model with a Pareto(1.5,1) distribution for $\alpha+\beta$ and a uniform distribution on $\alpha/(\alpha+\beta)$ and ended up with $p(\alpha,\beta)\propto (\alpha+\beta)^{-3/2}$ but Gelman's approach seems to yield $p(\alpha,\beta)\propto (\alpha+\beta)^{-5/2}$ which disagrees with the gentleman writing into Gelman's blog in the link above.