Feature Request: Nested priors for common terms

Hi,

I’m trying to play around with sparse models and would like to place NormalMixture prior with Dirichlet weights as the prior for the common terms. The code would be like

model = bmb.Model("response~1+d", data)
w_prior = bmb.Prior("Dirichlet", a=[1.0, 1.0])
subject_prior = bmb.Prior("NormalMixture", w=w_prior, mu=[0, 0], sigma=[0.1, 4.5])
p = {"d": subject_prior}
model.set_priors(p)
model.build()

It crashes with aesara saying NotImplementedError: Cannot convert Dirichlet(a: [1.0 1.0]) to a tensor variable. I think it should be fairly simple fix to build the priors recursively also for CommonTerm😒 like already done for GroupSpecificTerm😒. (Apologies for this not being a pull request.)

[kpalin]

That seems to work, also with formula like response ~ 0+d0+d1+d2+d3+d4+d5+d6+d7+d8+d9 (I’ve never before seen the c(d0,d1...) syntax.)

I don’t have proper references for this apart from the blog post https://betanalpha.github.io/assets/case_studies/modeling_sparsity.html I already linked. I guess sparsity is not a thing with Bayes, when you can just sum over probability zero events.

[tomicapretto]

I’m leaving it open because I don’t have time now to finish off this PR (and understand how it works too!). But it is definitely very interesting.

Edit

For the record. c(d0, d1, ..., d9) is not the same than d0 + d1 + ... + d9. The first creates a single model term which is ten-dimensional, and the second creates ten model terms where each one is one-dimensional.