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I am studying hierarchical models, and trying to understand a point in the book where they try to decide on a non-informative hyperprior distribution.

The hyperparameters is $\alpha$ and $\beta$ for a beta distribution. So we are interested in the density $p(\alpha, \beta)$. In the book however they start looking at a reparameterize version instead, $p(log(\alpha/\beta), log(\alpha + \beta))$

It is not clear why this is done in the book. Could anybody explain?

Also, when we have a density such as $p(log(\alpha/\beta), log(\alpha + \beta))$, whats the steps using change of variable formula to get back to $p(\alpha, \beta)$?

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