California Freight Cleanup → Investigation 6-6
Does health-science uncertainty change which portfolio the CEC should choose?
D_all_in_4B: P(optimal) = 1.000 (8,192/8,192 Sobol draws; binomial 95% lower bound 0.9996), E[regret] = $0.000B • dominance survives all three sensitivity excursions
We sampled 8,192 combinations of the health response coefficient, statistical value of a life, and emissions uncertainty. Across all five candidate portfolios, we measured how much you would regret each choice after seeing which combination turned out to be true. The all-in $4B portfolio wins every draw. Choosing any other portfolio carries between $7.8B and $20.7B in expected regret.
The decision
The standard framing of CRF uncertainty in air-quality analysis is “Di vs. Krewski”: pick one of two hazard-ratio anchors and report the “wrong-decision cost” of having chosen the other. That framing collapses a continuous posterior into two corner labels and confuses information value with model fragility.
Investigation 6-3 produced a continuous hierarchical Bayesian posterior on βPM2.5 across 58 California counties (μ = 0.02439, σ = 0.00447, CI95 = [0.01563, 0.03315]). Investigation 6-6 promotes that bifurcation to a posterior-integrated expected regret surface over the joint posterior (β, VSL, emissions), evaluated on five named portfolios. The decision question: which portfolio minimises expected regret across the 95% credible region — and does CRF fragility change the answer?
Two decision-theoretic objects integrated together: Howard (1966) information value (per-decision EVPI) and posterior-integrated expected regret over the Investigation 6-3 posterior (Bayesian regret — not Savage minimax, which would minimize worst-case regret) — combined to produce an honest answer.
Methodology
Synthesis only — no new simulation environments. Investigation 6-6 reads five upstream
investigations via upstream_value and integrates them into a single
regret surface.
Step 1 — Sampling the uncertainty space
8,192 Sobol quasi-MC draws (Seed 20260429, scrambled) across three axes:
- βPM2.5 ∼ Normal(0.02439, 0.00447) — Investigation 6-3 hierarchical Bayes posterior (58 CA counties)
- VSL ∼ Triangular($7.4M, $10.8M, $13.4M) — EPA 2024 VSL guidance
- emissions_scale ∼ Lognormal(0, 0.20) — EPA NEI 2023 TSD §3.6 (±40% at 95% CI)
Independence copula (3×3 identity). No off-diagonal coupling in the (β, VSL, emissions) sub-block.
Step 2 — Per-portfolio per-draw NPV
For each of 5 portfolios (A_free_lunch, B_transport_2B, C_wildfire_instead, D_all_in_4B, E_smart_2B):
deaths(β, ε) = portfolio_mean_deaths · (β / βref) · ε
NPV($B) = deaths · VSL · annuity(30yr, 3%) − cost_B
Annuity factor = 19.6004 (30-year, 3% discount). F_maximum_impact excluded per plan (the investigation covers the five-portfolio menu; NSGA-II continuous frontier policy space is Investigation M-3’s domain).
Steps 3–5 — Computing regret and ranking portfolios per scenario
Per draw d, regret(p) = maxq NPVd(q) − NPVd(p). Posterior-integrated expected regret = mean over 8,192 draws. Posterior P(optimal) = fraction of draws where portfolio is the per-draw maximiser.
Findings
| Portfolio | Mean NPV ($B) | P5 NPV ($B) | P95 NPV ($B) | P(optimal) | E[regret] ($B) |
|---|---|---|---|---|---|
| A_free_lunch | +11.65 | +6.67 | +17.95 | 0.000 | 20.26 |
| B_transport_2B | +24.10 | +12.94 | +38.21 | 0.000 | 7.82 |
| C_wildfire_instead | +11.24 | +5.73 | +18.21 | 0.000 | 20.67 |
| D_all_in_4B | +31.91 | +16.55 | +51.33 | 1.000 | 0.0000 |
| E_smart_2B | +24.12 | +12.74 | +38.52 | 0.000 | 7.79 |
D_all_in_4B is the per-draw maximiser in every one of 8,192 draws. Its posterior-integrated expected regret is $0.000B — choosing D entails zero regret relative to any other portfolio on this menu, regardless of where within the CRF–VSL–emissions posterior the world turns out to be.
The Di–Krewski extremal slice confirms this result does not depend on which CRF anchor is used: D_all_in_4B wins at β = 0.00770 (Di 2017) and at β = 0.00583 (Krewski 2009). Max regret of the μ-optimal portfolio along the full Di–Krewski β-axis = $0.000B. CRF fragility contributes $0 of work to the decision on this menu.
![Regret surface: D_all_in_4B dominates at E[regret]=0; other portfolios show $7.8–20.7B expected regret](../../assets/plots/44_regret_surface.png)
Sensitivity excursions
Three single-axis perturbations of the canonical assumptions, each holding the other two axes at nominal:
| Excursion | μ-optimal | Regret-min | D E[regret] ($B) | D P(optimal) |
|---|---|---|---|---|
| 7% discount (vs 3%) | D_all_in_4B | D_all_in_4B | 0.0001 | 0.999 |
| 10-year horizon (vs 30) | D_all_in_4B | D_all_in_4B | 0.0030 | 0.987 |
| Cost overrun (εcost ~ LN(0, 0.20)) | D_all_in_4B | D_all_in_4B | 0.0000 | 1.000 |
D_all_in_4B remains the regret-min and μ-optimal portfolio across all three
excursions. At a 10-year horizon D’s P(optimal) slips to 0.987 (a small
fraction of draws go to another portfolio), but remains the dominant choice.
regret_min_stable = True.
Honest framing: menu dominance, not fragility surface
Investigation 6-6 is a menu dominance check, not a fragility surface. The regret-surface tool is the right machinery — but applied to the wrong menu for finding non-trivial fragility. VSL × annuity (≈ $211M per death avoided) makes each marginal death avoided dwarf the $4B cost gap between portfolios. With 170 deaths/yr avoided, D_all_in_4B generates NPV that overwhelms all competitors at any plausible VSL.
The natural home for non-degenerate regret minimisation is Investigation M-3’s continuous Pareto frontier — where the policy space is continuous and NPV gaps between candidates are smaller. On the five-portfolio discrete menu, D always wins. That is an honest finding even if it is not the most informationally rich one.
Caveats
-
Linear deaths-vs-β interpolation.
True health response is loglinear (HR = exp(β · ΔC)) integrated
over the full PM2.5 concentration distribution. The linear approximation
deaths(β) = portfolio_mean · (β/βref) · εis faithful within the Krewski–Di range but understates curvature outside it. Inv 11 and Investigation M-1 use the same approximation internally, so this is a pipeline-consistent choice, not a synthesis-stage error. - Five-portfolio discrete menu. F_maximum_impact ($13.9B) and any continuous Pareto-frontier interior policy are excluded. Investigation M-3 (NSGA-II) is the canonical home for continuous-policy regret.
- 30-year 3% discount is the production assumption. Sensitivity to 7% discount (annuity drops ≈33%) is modelled as a Phase 5c.4 excursion; D’s dominance survives with P(optimal) = 0.999.
-
Cost is treated as deterministic.
Investigation M-1’s MC cost band is available but has no
meanfield; cost uncertainty integration is a recommended follow-up. Effect would inflate per-draw regret but should not flip rankings (cost variance σlog = 0.20 < emissions variance). - 3×3 identity copula. The (β, VSL, emissions) axes are independent in the canonical joint. If future work adds e.g. corr(emissions, VSL) the copula must be re-specified.
- Stale upstream flags at last run. Inv 11, 22, and 15 sha256 hashes had changed since Investigation 6-6 last ran. D_all_in_4B identity is unchanged (diff table: all key fields unchanged), but a fresh re-run is recommended before citing in production reports.
Provenance
| Field | Value |
|---|---|
| Investigation | 44_crf-conditional-decision |
| Tier | Tier 1 |
| Run timestamp | 2026-05-04T07:46:22 |
| results.json sha256 | 5ce9bcd8b87b |
| QMC draws | 8,192 (Sobol, seed 20260429) |
| Upstream: Investigation M-1 | sha256 145dbfd826d0 (portfolio costs & deaths) |
| Upstream: Investigation 6-3 | sha256 3104ba850408 (CRF posterior) |
| Upstream: Investigation 6-5 | sha256 9d0d51e92c1b (meta-EVSI) |
| Methods | Posterior-integrated Bayesian expected regret (Howard 1966 EVPI framework; not Savage minimax) |
| VSL prior | Triangular ($7.4M, $10.8M, $13. This page is generated from
investigations/44_crf-conditional-decision/latest/results.json
(sha256 5ce9bcd8b87b).
|