Enforcing monotonic constraints on effect size parameters

You can translate and multiply to get results in any range. For example, if the range of values you want is (L, U), you can sample

\theta \sim \text{Dirichlet}(\alpha)

and set

\phi = (U - L) \cdot \theta + L.

You can look at the marginals in a Dirichlet, which are beta distributions, but they’re not uniform. There’s also correlation because of the sum-to-one constraint on the simplex \theta.

If you want to get more detailed here, you can parameterize on an unconstrained scale with an isometric log ratio (ILR) transform—I think @aseyboldt was discussing the ILR here, but I can’t find the post. It’s also under discussion for inclusion directly: Implement `Ordered` distribution factory · Issue #7297 · pymc-devs/pymc · GitHub

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