Summary

When a Prior with non-empty dims has another Prior (also with non-empty dims) as a parameter, create_variable(..., xdist=True) builds a model where sample_prior_predictive succeeds but model.compile_logp() raises because inner RV nodes remain in the logp graph. The bug affects the centered parameterization only; centered=False and xdist=False both sidestep it.

Reproducer

import pymc as pm
from pymc_extras.prior import Prior
prior = Prior(
    "Normal",
    mu=Prior("Normal", mu=0.0, sigma=0.1, dims=("brand",)),
    sigma=Prior("HalfNormal", sigma=0.1, dims=("brand",)),
    dims=("brand", "customer"),
)
with pm.Model(coords={"brand": ["a", "b"], "customer": ["x", "y"]}) as model:
    prior.create_variable("beta", xdist=True)
model.compile_logp()

ValueError: Random variables detected in the logp graph:
  {halfnormal_rv{"(),()->()"}.out, normal_rv{"(),()->()"}.out}.

Necessary conditions (from a sweep of 10 nesting variants)

All four must hold to trigger the failure:

1. xdist=True
2. Outer Prior has non-empty dims
3. At least one parameter is a nested Prior whose dims is non-empty (dims=() or dims=None on the inner doesn't trigger it)
4. Outer Prior.centered is True (the default)

What I verified

• model.free_RVs contains beta_mu, beta_sigma, beta — inner RVs are registered.
• Inner RVs are reachable from the outer RV's graph (pytensor.graph.traversal.ancestors([beta]) contains the registered objects).
• sample_prior_predictive succeeds.
• prior.create_variable("beta", xdist=False) on the same Prior produces a compile_logp-able model.
• Flipping the outer Prior.centered=False (still xdist=True) also produces a compile_logp-able model.
• The failing path is _create_centered_variable with xdist=True. _create_non_centered_variable has the analogous xdist=True branch but does not fail on the sweep.

Where this surfaces

pymc_marketing.mmm.fourier.FourierBase.apply hard-codes xdist=True:

beta = self.prior.create_variable(self.variable_name, xdist=True)

so a fourier component whose outer Prior is centered and has nested Prior parameters with dims will hit this (e.g. hierarchical seasonality with brand-level deviations on mu/sigma). Flat priors, non-centered outer priors, and nested priors with scalar (dims=()) inner priors are unaffected.

Environment

pymc-extras 0.10.0, pymc 5.28.2, pytensor 2.38.2, Python 3.12.