Tracking: Statistical & Bayesian rigor in Nous (3 children — power analysis, principle posteriors, sub-arm sweeps)

[sriumcp]

Three integrations surfaced by auditing 29 campaigns in inference-sim/.nous (May 2026). Each is opt-in / schema-additive, adds zero LLM tokens at the design seam, and ships behind a constructor injection point so tests run without live calls (per CLAUDE.md test policy).

Why now

• Most arms hard-code 10 seeds with no statistical rationale. Campaigns mech-design-kvtime (acc 25%/0%) and reviewer-gauntlet (acc 0%/0%/66%) may be underpowered rather than scientifically refuted.
• The principles.json lifecycle (INSERT/UPDATE/PRUNE) is heuristic over a "low"/"medium"/"high" confidence string. The data-model already carries evidence (citing-arm list) — enough to ground a calibrated posterior.
• composite-sensitivity-boundary (5 iters, ~65 sim runs each) and capacity-probe (rate × seed grids) hand-roll search grids that adaptive sampling would cut 30–60%.

Children

• feat: power analysis at design time — right-size seeds per arm #163 — Power analysis at design time (scipy.stats.power)
• feat: Bayesian posterior over principles via PyMC (opt-in, scipy default) #164 — Bayesian posterior over principles (PyMC, opt-in)
• feat: Optuna-backed adaptive sub-arm sweeps (opt-in via arms[].sweep) #165 — Optuna-backed adaptive sub-arm sweeps

Single-PR landing

One branch off upstream/reflective, three feat commits (one per child, each Closes #<child>), tracking PR title:
Tracking #<this>: Statistical & Bayesian rigor (3 children). Mirrors #153/#161.

/goal predicate (for the tracking issue)

A PR exists with base upstream/reflective, head sriumcp:<branch>, AND the working tree of that PR satisfies ALL of:

• orchestrator/power.py exists and exports required_seeds
• orchestrator/principles_posterior.py exists and exports posterior accepting a posterior_fn= injection arg
• orchestrator/arm_sweep.py exists and exports run_sweep accepting a sampler= injection arg
• tests/test_power.py, tests/test_principles_posterior.py, tests/test_arm_sweep.py all exist and pytest -q passes
• tests/conftest.py blocks live PyMC NUTS sampling and live Optuna trial execution alongside its existing live-LLM block
• pytest -q exit code is 0
• the PR body references Closes #163, Closes #164, Closes #165 and Refs #<this>

[sriumcp]

All three children landed in #171 (merged into reflective):

• feat: power analysis at design time — right-size seeds per arm #163 — power analysis (commit 78c05c1)
• feat: Bayesian posterior over principles via PyMC (opt-in, scipy default) #164 — Beta-Binomial principles posterior (commit d3f64e2)
• feat: Optuna-backed adaptive sub-arm sweeps (opt-in via arms[].sweep) #165 — Optuna-backed sub-arm sweeps (commit f2092c2)
• fix(deps): scipy added to runtime deps (commit 1111f68)

Final: 662 passed, 2 skipped, both Python 3.11 + 3.12 CI green.