What distribution would make a good hyper-prior for a Beta distribution parameterized by mean and sample size? 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?

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)

