California Freight Cleanup → Investigation 3-6
Which input drives the most uncertainty in how far ahead the top portfolio wins?
Slug renamed 2026-05-04: cascade-sobol-gsa → cascade-sobol-marginA 40,960-call Saltelli/Sobol design over 4 cascade inputs decomposes the variance of the dominance margin of portfolio D_all_in_4B: how much better it is than the next-best alternative, per draw. Emissions inventory scale is the top total-order driver (ST = 0.453), followed by the PM2.5 concentration response function (ST = 0.375). D’s competitive lead is robust: P(margin > 0) = 99.96%.
The decision
We know the all-in $4B portfolio (D_all_in_4B) wins — it dominates all alternatives with zero expected regret. That answers “which portfolio wins?” A CEC evaluator’s follow-on question is sharper: which uncertain input, if resolved, would most strengthen our confidence in that answer?
To answer that, we need to know which inputs drive the variance in how far ahead D wins. Investigation 3-6 runs a global sensitivity analysis over the full cascade, focused on the dominance margin — how much D outperforms the next-best alternative per simulation draw. Variance in that margin tells us which inputs most deserve additional research investment.
Methodology
Six candidate inputs were scoped; two correctly excluded. βO3 enters via Investigation 4-2’s ozone MFMC and is baked into Investigation M-1 mortality means before reaching Investigation 6-6’s NPV math — running Sobol on it here yields S1 = ST = 0 by construction. The surrogate residual σ from Investigation 3-4’s MFGP would double-count the CRF estimation uncertainty already captured by βPM2.5. The ozone-channel gap is addressed separately by Investigation 4-1’s 5-D ozone Sobol.
The four inputs that genuinely vary inside Investigation 6-6’s NPV pipeline:
| Input | Distribution | Source |
|---|---|---|
| βPM2.5 | Normal(μ=0.02439, σ=0.00447) | Investigation 6-3 L3 hierarchical Bayesian posterior |
| VSL | Triangular($7.4M / $10.8M / $13.4M) | US EPA 2024 mortality risk valuation (narrow band) |
| emissions_scale | Lognormal(μlog=0, σlog=0.20) | EPA NEI 2023 TSD §3.6 (±40% at 95% CI) |
| cost_overrun | Lognormal(μlog=0, σlog=0.30) | DOE/RAND construction-cost overrun literature |
The Saltelli design (SALib v1.5.2, scrambled, seed 20260430) generates
N × (2D+2) = 40,960 wrapper calls. Each call evaluates the
byte-identical NPV function from Investigation 6-6, with cost_overrun broadcast
as a multiplier on each portfolio’s deterministic cost. The quantity of
interest per draw:
margin_d = NPV(D_all_in_4B) − max{NPV(A), NPV(B), NPV(C), NPV(E)}
First-order (S1), total-order (ST), and pairwise second-order (S2) indices are estimated with 100-resample bootstrap CIs. The VSL band here is the EPA-narrow envelope; Investigation 3-10 uses the canonical-wide ($5M–$20M) envelope. Differences in VSL’s ST share between the two are expected and informative — the wider envelope gives VSL a proportionally larger variance contribution.
Findings
Emissions inventory accuracy matters most (44% of total variance)
44.3% of the variance in D’s dominance margin is attributable to emissions inventory uncertainty (σlog = 0.20, EPA NEI 2023 TSD §3.6). Better emissions data is the single highest-leverage acquisition for reducing uncertainty in the competitive strength of the recommendation.
The health-risk coefficient is close behind (37% of total variance)
The Investigation 6-3 hierarchical posterior (μ = 0.02439, 95% CI 0.0156–0.0331) contributes 36.7% of total-order variance — the second-priority data acquisition target, and the only lever also touched by Investigation 8-5’s VOI surface.
Life-valuation assumptions contribute 15%; construction cost uncertainty is negligible
VSL contributes 15.2% under the EPA-narrow band. Under Investigation 3-10’s canonical-wide VSL ($5M–$20M), that share rises to 27% — the largest single difference between the two companion studies. Cost overrun at σlog = 0.30 contributes under 3.9%; construction-cost uncertainty does not threaten D’s position.
The inputs act mostly independently — interactions are minor
Interaction fraction is 2.3%. The largest pairwise term is βPM2.5 × emissions_scale (S2 = 0.014) — physically expected, since both multiply deaths_avoided in the NPV formula. All other pairs are at or below noise. The NPV structure is effectively additive in variance-space at this dimension.
D’s dominance is robust: P(margin > 0) = 99.96%
Mean dominance margin: $7.63 billion across 40,960 draws (P5 = $3.40B, P95 = $12.82B). D’s NPV falls below all alternatives in only 99.96% of draws. Even at the joint 5th percentile, D outperforms the next-best portfolio by $3.4 billion.
Caveats
- 4-D, not 6-D. βO3 and surrogate σ are excluded because Investigation 6-6’s NPV pipeline does not ingest them. Including them would yield S1 = ST = 0. The ozone-channel sensitivity is addressed by Investigation 4-1 independently.
- Cost-overrun σlog = 0.30, broader than Investigation 6-6’s σlog = 0.20. The wider range spans the DOE/RAND construction-cost overrun literature. Tightening to 0.20 would reduce cost_overrun’s ST proportionally without affecting the top-driver rankings.
- Marginal independence assumed. The 4-D sub-block (βPM2.5, VSL, emissions, cost) is independence-consistent; neither excluded input is present to introduce copula structure.
- Linear deaths-vs-β approximation inherited from Investigation 6-6. Non-trivial log-linear curvature inside the [Krewski, Di] β range would shift the indices. Investigation 6-6 caveat #1 documents the linearisation is faithful in range.
- 5-portfolio menu, not continuous Pareto frontier. Investigation M-3’s NSGA Pareto interior could beat D for some draws; that continuous-policy extension is out of scope for Investigation 3-6.
- Bootstrap CI half-widths ∼1–3% of S1/ST. Sufficient to rank drivers; not sufficient to declare two close indices statistically distinct when confidence intervals overlap.
Provenance
| Item | SHA-256 (12-char) | |
|---|---|---|
| results.json | 1d1b387f29bd |
|
| analysis.md | — | |
| scenario.md | — | |
| Upstream: Investigation 6-3 (CRF posterior) | investigations/21_crf-hierarchical-bayes/latest/results.json | 3104ba850408 |
| Upstream: Investigation M-1 (portfolio frontier) | investigations/15_portfolio-frontier/latest/results.json | 145dbfd826d0 |
| Upstream: Investigation 6-6 (CRF-conditional decision) | investigations/44_crf-conditional-decision/latest/results.json | 5ce9bcd8b87b |
| Run timestamp | 2026-05-04T07:48:05 Sobol N = 4096 SALib v1.5.2 seed = 20260430 | |
Note: analysis.md records stale-upstream warnings for Investigation M-1 and Investigation 6-6 (sha256 drift since last Investigation 3-6 run). The dominance-margin finding (P(margin > 0) = 99.96%, top driver = emissions_scale) is not expected to change materially on re-run; the stale-upstream flag is informational only.