Using prior instead of hyperprior for group level prediction in section 4.6.2 about bookcode_edition1 HOT 3 CLOSED

For the group level prediction, we are using hyper prior - the reason is that, hyper-prior could be considered as the average effect for each specific group/category here. So when you want group level prediction, you can use these hyper-prior directly. You could see in Code block 4.18 where we use a HalfNormal (like what you did in the code) for a new hypothetical group.

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Thanks for the fast response.

What would you do if the hyperprior and the prior had different distributions, not both half-normal like in the book example? Or does this not matter?

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It does not matter as long as you are considering the hyper parameter as the group average, and each group is a small variation on top of the group average. For example, say we are assigning a fix prior sigma_group = yield tfd.Sample(tfd.Normal(10, .01), num_groups), then I usually interpreted the group average being 10, and if I want to generate sample to indicate group average effect i will just use 10 as the standard deviation.
But there is a subtly here: what about other parameterization like

sigma_group = yield tfd.Sample(tfd.HalfNormal(1), num_groups)

or

sigma_group = yield tfd.Sample(tfd.Gamma(a, b), num_groups)

Here, we should be a bit more careful to instead find the expected value of the distribution tfd.HalfNormal(1) and tfd.Gamma(a, b) (a and b is hyper parameters). We didnt do that in the book because the posterior is mostly Gaussian like, but I think this is something we will add a bit more clarity in the 2nd Edition.

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