fix(loo): derive the refit path's observed-variable name instead of hard-coding y_post

[frankbuckley]

Note

Drafted by an LLM-based AI tool (Claude Code/Opus 5).

What and why

The exact-refit (reloo) repair added in #439 read idata.log_likelihood["y_post"] in its alignment guards and in the held-out density evaluation. That name is a property of the likelihood, not a constant. The Beta-Binomial mechanism models register their observed node as y_post, but the floor-rule likelihood registers y_offfloor (factories.py). Registering an off-floor mechanism model — which is the primary estimand proposed in #433 — would have turned all three sites into a KeyError raised at comparison time, after the reporting fits had already run.

The point of the change is when the failure happens, not whether one can happen. Before: sample for an hour, then crash with KeyError: 'y_post' in the comparison step. After: either it works, or it says "this model is not supported" before any sampling starts.

The change

_observed_variable_name(model, idata_orig, model_id) derives the name from the built model's single observed RV and verifies it against the stored trace, replacing the hard-coded string at all three call sites. It refuses two cases explicitly rather than guessing:

• ≠ 1 observed variable. A joint model carries one obs_id axis per outcome, so there is no well-defined single row for reloo to hold out. Better to refuse than to splice against whichever outcome happens to sort first.
• A stored log_likelihood group that does not match the rebuilt model — either naming something else (construction drift) or holding more than one variable (no way to tell which the Pareto-k indices refer to).

This follows the module's existing posture: every guard in build_mechanism_wrapper fails closed with a reason, because a spliced exact elpd is only meaningful if the refit is provably the same model as the fit.

Verification

• 1093 tests pass, including 4 new ones in tests/statistical_models/test_loo_refit.py. One of them closes the loop by asserting log_likelihood__i actually reads the derived name rather than merely recording it — the guard and its consumer can drift apart, and a test on the guard alone would not have caught the original defect either.
• ruff check src/, npm run format:check, npm run spellcheck all clean.
• No behaviour change for the models that exist today. Rebuilding the wrapper against the stored --config reporting traces for lrp-rli-mech-063 and lrp-rli-mech-104 still resolves obs_var='y_post' and passes every alignment guard unchanged.

Note on scope

This is one of two prerequisites for the #433 off-floor mechanism model, and the smaller one. build_mechanism_model has no likelihood parameter at all today, so the mechanism family is Beta-Binomial-only and off-floor support still needs plumbing into the factory before the refit path becomes reachable. That is left to #433 itself rather than built speculatively here.

Branched off main after #440 (d2b57c0) landed, which rewrites this same file's refit gate; the two changes are orthogonal and the full suite was re-run against the updated base.

Refs #433, #438

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