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I have a model which includes a Beta distribution and I am looking for guidance on how to parameterize a hyper-prior for it. For example, this post uses a Beta parameterized with a mean and concentration and takes the concentration kappa ~ Pareto(1, 1.5).

What are some recommended distributions that I should consider for my kappa? And what principles might I use to select the right one for my setting?

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I ended up using a uniform distribution with a lower bound selected to be not-too-low through trial and error:

kappa_s = numpyro.sample("kappa_s", dist.Uniform(5, 500))  # Model converges to unacceptable values when kappa_s is smaller (e.g. 1)
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  • $\begingroup$ I won't accept this, but I though it might inspire someone to offer a more acceptable answer. $\endgroup$
    – Abraham D Flaxman
    Commented Dec 22, 2021 at 0:18

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