test: property-based correctness sweep over every Prior subclass

[Jammy2211]

Overview

Phase 3 of the priors/messages cleanup (census: PyAutoMind/draft/research/autofit/priors_and_messages_math_audit.md, finding C3; prompt bug/priors/09; hub #1331). All nine confirmed bugs from the audit are fixed and merged (#1345, #1348), each locked by a pointwise regression test. This task adds the general property-based sweep over every Prior subclass — the tests that would have caught the original LogUniform sign bug (#1266), the with_limits crash, the Gamma from_mode inversion and the TruncatedNormal normalisation gap in one stroke — so the next latent math bug of this shape cannot survive. It also folds in the remaining small half of bug/priors/11: the LinearShiftTransform class docstring (the reversal-convention half shipped via #1334).

Plan

• Add a parametrised property-test module sweeping every concrete Prior subclass (Uniform, LogUniform, Gaussian, LogGaussian, TruncatedGaussian; ≥2 parameterisations each).
• Five properties: inverse-CDF round-trip; normalised pdf integrates to 1 (locking the Priors & messages: 9 confirmed bugs — guidance wanted on 5 decisions #1331 Option A drop-constants + log_normalisation() contract, and extending check_dist_norm-style coverage to TruncatedNormalMessage and transformed priors — the exact gap that hid the log-partition bug); log-prior gradient matches the message-density gradient by finite differences (constants cancel — the sign-convention canary); with_limits round-trip for every family; from_mode(m, V) mean/variance invariants for NormalMessage and GammaMessage with V≠1 discriminating points.
• NumPy-only at the library level (house rule; EP-level integration coverage was Phase 3 of the EP framework review and complements this).
• Add the LinearShiftTransform docstring: shift/scale are physical-space parameters, the stored parent Jacobian is 1/scale because the transform runs physical → base, and the log_det sign follows.
• Expect all tests to PASS on current main; any failure is a new finding to file separately, not to bundle here.

Detailed implementation plan

Affected Repositories

• PyAutoFit (primary)

Branch Survey

Repository	Current Branch	Dirty?
/workspace/pyautofit	main @ 7d4d931 (shallow clone, cloud session)	clean

PyAutoFit is also claimed by two in-flight tasks (stored-sample-reconstruction-guard → autofit/non_linear/samples/; version-stamp-sync-guards → autofit/__init__.py) — file-disjoint from this task's surface (test_autofit/mapper/prior/, autofit/messages/transform.py), proceeding under the documented disjoint-override convention.

Suggested branch: feature/prior-property-tests

Implementation Steps

1. New test_autofit/mapper/prior/test_prior_properties.py:
   • all_priors() fixture list: UniformPrior(0,1), UniformPrior(-3,7.5), GaussianPrior(0,1), GaussianPrior(2.5,0.3), LogUniformPrior(1e-2,1e2), LogGaussianPrior(0,1), LogGaussianPrior(1,0.5), TruncatedGaussianPrior(0,1,-2,2), TruncatedGaussianPrior(1,0.5,0,3). Skip containers/point-masses (TuplePrior, Constant, DeferredArgument).
   • P1 — inverse CDF: prior.cdf(prior.value_for(u)) ≈ u for u ∈ {0.01, 0.1, 0.3, 0.5, 0.7, 0.9, 0.99}, abs=1e-6.
   • P2 — normalisation: ∫ exp(log_prior_from_value(x) + log_normalisation()) dx ≈ 1 over the support (infinite limits truncated via value_for(1e-9) / value_for(1-1e-9); scipy.integrate.quad, abs=1e-3). Also ∫ message.pdf ≈ 1 where the generic exponential-family path exists — extends check_dist_norm to TruncatedNormalMessage and TransformedMessage-wrapped priors (the Priors & messages: 9 confirmed bugs — guidance wanted on 5 decisions #1331-04 gap).
   • P3 — gradient consistency: central finite difference of log_prior_from_value matches central finite difference of message.logpdf at x = value_for(u), u ∈ {0.3, 0.5, 0.7} (rtol=1e-2, atol=1e-3); constants cancel, so this catches exactly the sign/convention drift class of fix: log_prior_from_value sign-convention bug across Prior subclasses #1266.
   • P4 — with_limits: constructs for every family (regression breadth for Priors & messages: 9 confirmed bugs — guidance wanted on 5 decisions #1331-01); for limit-respecting families value_for(1e-6)/value_for(1-1e-6) lie within [lower, upper]; LogGaussianPrior.with_limits asserts construction + positive support only (the shipped fix drops the kwargs by design).
   • P5 — from_mode: NormalMessage.from_mode(m, V) and GammaMessage.from_mode(m, V) reproduce .mean ≈ m, .variance ≈ V at V≠1 discriminating points (e.g. (2, 0.25), (2, 4.0)) — locks the Priors & messages: 9 confirmed bugs — guidance wanted on 5 decisions #1331-D3 mean+variance invariant.
2. autofit/messages/transform.py — LinearShiftTransform class docstring (bug/priors/11 §2): kwargs describe physical space; stored parent Jacobian is DiagonalMatrix(1/scale) because transform() maps physical → base; log_det = -log(scale) accordingly.
3. Run: pytest test_autofit/mapper/prior/ test_autofit/messages/ test_autofit/graphical/functionality/test_messages.py.

Key Files

• test_autofit/mapper/prior/test_prior_properties.py — new property sweep
• autofit/messages/transform.py — LinearShiftTransform docstring
• test_autofit/graphical/functionality/test_messages.py — pattern source (check_dist_norm, tolerance precedents); unchanged
• autofit/mapper/prior/abstract.py — log_normalisation() contract (P2's anchor)

Original Prompt

Click to expand starting prompt (bug/priors/09_prior_property_tests.md)

@PyAutoFit Add property-based correctness tests for every Prior subclass

Type: bug
Target: priors
Difficulty: large
Autonomy: supervised
Priority: normal
Status: formalised

Found during the priors/messages audit (see
PyAutoPrompt/autofit/priors_and_messages_math_audit.md, finding C3).

Prerequisite: Prompts 01-08 should be acked (and ideally merged)
first. The point of these tests is to lock in the fixes — adding them
before the fixes would just produce a long list of red tests with no
clear action.

Problem

The audit found three real bugs (LogGaussianPrior.with_limits crash,
GammaMessage.from_mode wrong formula, TruncatedNormalMessage pdf
not normalised) that would each have been caught by a single
property-based test. None of them were caught because the existing
test suite is hand-rolled per-class and covers each method in
isolation.

The original LogUniformPrior sign-convention bug (e95295b83) is
in the same category — it would have been caught by a single test:
"for every prior, the analytic gradient of log_prior_from_value
matches a finite-difference gradient".

Wider context — what exists already

@PyAutoFit/test_autofit/graphical/functionality/test_messages.py:

• check_dist_norm(dist) — uses scipy.integrate.quad to verify
  pdf integrates to 1. Run on NormalMessage, BetaMessage,
  GammaMessage, LogNormalMessage only. Not run on
  TruncatedNormalMessage, LogGaussianPrior, any Prior subclass,
  or any TransformedMessage-wrapped distribution. That's why
  prompt 04's bug survived.

• check_log_normalisation(ms) — verifies the product-of-messages
  log normalisation matches numerical integration.

• check_numerical_gradient_hessians(message, x=None) — verifies
  analytic gradient and Hessian match finite differences. Same limited
  coverage as above.

So the patterns are there; they just don't sweep every prior.

Proposed scope

Add test_autofit/mapper/prior/test_prior_properties.py (and/or
test_autofit/messages/test_message_properties.py) with the five
properties above. Parametrise over every concrete subclass.

For each property, pick the tolerance carefully:

• Integrals: abs=1e-3 is enough to catch all the audit findings;
  tighter would slow CI.
• Inverse-CDF round-trip: abs=1e-6 works for double precision.
• Gradient finite-difference: rtol=1e-2, atol=1e-3 (existing
  check_numerical_gradient_hessians uses these).

Fable verdict (2026-07-08, PyAutoFit main @ 0f26ff2; PyAutoFit#1330)

Verdict: still wanted, unchanged — schedule after 01–08 land.
Coverage gap re-verified: check_dist_norm-style sweeps in
test_autofit/graphical/functionality/test_messages.py still exclude
TruncatedNormalMessage, LogGaussianPrior, prior subclasses and
transformed messages — which is why 04 survived. Keep library-level property
tests numpy-only (house rule); EP-level integration coverage is Phase 3 of
research/graphical_ep/ep_framework_review.md and complements, not
replaces, this.

(Full prompt with the test-sketch code block: PyAutoMind/active/09_prior_property_tests.md. Folded-in second half: PyAutoMind/draft/bug/priors/11_transformed_message_semantics_doc.md §2 only — the LinearShiftTransform docstring.)