PR draft — ClosedFormStrategy: fail clearly on non-constant base measure (fixes issue-01)

[docxology]

Problem

ClosedFormStrategy.compute_gradient! only defines logbasemeasure_correction for ConstantBaseMeasure. For variational families with a non-constant base measure (Poisson, Chisq, Binomial, Rayleigh, Weibull, NegativeBinomial) the call throws an opaque MethodError deep inside the solver.

Change

Add an explicit, informative guard in the extension's compute_gradient! before the base-measure correction, and document the limitation.

Patch

File: ext/ClosedFormExpectationsExt/ClosedFormExpectationsExt.jl (in ExponentialFamilyProjection.compute_gradient!)

     # Compute ∇_η E[log p̃ * (T - μ)]
     grad_target = mean(ClosedWilliamsProduct(strategy.backend), target_fn, q_dist)
+    base_measure_type = ExponentialFamily.isbasemeasureconstant(q_dist)
+    if base_measure_type === ExponentialFamily.NonConstantBaseMeasure()
+        error(
+            "`ClosedFormStrategy` supports only variational families with a constant base measure, " *
+            "but got `$(base_measure_type)` for the variational family. The analytic " *
+            "-E_q[log h_q (T - μ)] base-measure correction is not implemented. " *
+            "Use `ControlVariateStrategy` instead.",
+        )
+    end
     grad_eta = logbasemeasure_correction(
         strategy,
-        ExponentialFamily.isbasemeasureconstant(q_dist),
+        base_measure_type,
         q_dist,
         grad_target,
     )

File: src/strategies/closed_form.jl — add to the docstring:

-This strategy provides a "Zero-Variance" gradient estimator, avoiding the noise associated
-with Monte Carlo sampling (like in `ControlVariateStrategy`).
+This strategy provides a "Zero-Variance" gradient estimator, avoiding the noise associated
+with Monte Carlo sampling (like in `ControlVariateStrategy`).
+
+!!! note
+    Currently only target–variational pairs where the variational distribution has a **constant
+    base measure** are supported (e.g. Normal, LogNormal, Beta, Gamma). For variational families
+    with a non-constant base measure (Poisson, Chisq, Binomial, Rayleigh, Weibull,
+    NegativeBinomial) the strategy errors; use `ControlVariateStrategy` for those.

Verification

• Added regression test: ClosedFormStrategy on a non-constant-base-measure target errors with the new message (not a MethodError).
• Full suite still green.