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EP analytic updates — implement the four planned work packages

Type: feature Target: PyAutoFit Difficulty: large Autonomy: supervised Priority: normal Status: formalised Blocked-by: PyAutoFit#1334, PyAutoFit#1331, PyAutoFit#1332 # WP1 gate (MERGED); WP3/WP4 gates (open) Filed: 2026-07-08 (backfilled from git)

The complete, self-contained implementation plan lives in PyAutoFit#1338 (plan-only issue; nothing implemented). Scoping verdict behind it: PyAutoFit#1337 (EP review Phase 6); umbrella: research/graphical_ep/ep_framework_review.md.

Work packages (sequence; each becomes its own issue/PR at pick-up — do not bulk-issue):

  1. WP1 — exact PriorFactor updates in the declarative path + document the analytic-projection contract (~2–3 days). Start here. Note: rebase over / land after PyAutoFit#1334 (owns README.md). UNBLOCKED 2026-08-09 (draft/ sweep): PyAutoFit#1334 is MERGED — it shipped autofit/graphical/README.md as Phase 2 of the EP framework review on 2026-07-08 ([[ep-framework-review]]). Rebase, don't wait.
  2. WP2 — first-class linear-Gaussian factor; validate against an IC50-shaped integration script (~1 week).
  3. WP3 — Gamma–Poisson / Beta–Bernoulli conjugate factors. Gated: needs the #1331 fix batch (Gamma from_mode) and #1332 F2 (KL direction) merged first.
  4. WP4 — truncated-normal analytic moments (+ optional exact truncated KL, fixing F6). Gated: needs #1331-04 merged first.

Pick-up may be a different session or model (e.g. Opus): read #1338, #1337 and PyAutoFit/autofit/graphical/README.md (PR #1334) — no other context required. Full test_autofit/ + the autofit_workspace_test/scripts/graphical/ scripts must stay green; library unit tests numpy-only; speed-up evidence via the Phase 4 ep_history.csv tooling (#1335).