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I have a hierarchical model that includes a normal distribution and a beta distribution.

For the normal distribution, it has two parameters: $\mu$ and $\tau^2$. However, I want to implement hierarchy such that the $\mu$ and $\tau^2$ parameters are sampled from group-level distributions. What are good distributions to use for each of these two parameters? I am assuming the $\mu$ parameter could be sampled from another normal distribution, and the $\tau^2$ parameter could be sampled from an inverse gamma distribution. Is this along the right lines?

For the beta distribution, it has two parameters: $\alpha$ and $\beta$. I want to also implement this hierarchically in the same manner, so I have the same question. What is a good distribution to use which would then sample values for $\alpha$ and $\beta$?

I am sorry if these are simple questions but I have been having a very difficult time finding answers online.

kjetil b halvorsen
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Paul Scotti
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  • Have you had a look at https://github.com/stan-dev/stan/wiki/Prior-Choice-Recommendations ? – Björn Feb 07 '19 at 20:38
  • Yes, I looked over that wiki already but came away confused. For instance, I couldn't find anywhere what a suitable distribution might be to yield the shape parameter of distribution (in this case a beta distribution). – Paul Scotti Feb 07 '19 at 21:05
  • This answer might be useful: https://stats.stackexchange.com/a/94310/18539 – Robin Ryder Feb 07 '19 at 21:36

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