Should CEC split its research + monitoring budget — or optimize them jointly?
CEC today runs two parallel procurement tracks: CRF research grants (Inv 24) and ambient-monitor deployments (Inv 27). The RFPs, review cycles, and budget envelopes are separate. But the underlying belief state — our uncertainty about health impact per microgram of PM2.5 — is shared.
This investigation fuses Inv 24 (CRF designs) and Inv 27 (monitor sites) into a single closed-loop Bayesian experimental-design problem. State: (sigma_CRF, sigma_mon_by_region). Action space each year: fund 1 of 5 CRF studies, deploy 1 of 15 monitors, or skip. Policy: greedy EVSI-proxy / cost maximization. Horizon: 10 years. Budget: $50M fungible.
The Inv 21 pooled residual is the value-at-stake
The reward signal inside BED is Delta(sigma^2) x value_at_stake x p_success. The value_at_stake scalar is anchored on the Inv 21 hierarchical-Bayes residual across the CA county-level CRF literature: $0.05B.
Anchor rationale. $0.05B is the Inv 21 hierarchical-Bayes residual across CA county-level CRF fits. Sequential BED acts on this post-pooling residual.
From siloed plans to a closed-loop joint policy
L4 is where the budget is shared and opportunity cost becomes visible: the greedy rule now sees the CRF-vs-monitor tradeoff each year.
What the rule chose
The closed-loop rule bookends the 10-year schedule with 2 CRF studies — a cheap-shrinkage pilot at year 0 (the design with the largest EVSI-proxy / cost), 8 monitor deployments in between (each cutting its target region's sigma by 40-60% for $0.5M/yr), then a confirmation CRF at year 9. By year 9, monitor-network mean sigma had fallen from 1.0 to 0.34. The rule spent $6.5M of the $50M envelope.
| Year | Track | Action | Cost | EVSI-proxy gain | sigma_CRF | sigma_mon_mean |
|---|---|---|---|---|---|---|
| Y0 | CRF | Meta-analysis of existing studies | $0.5M | $23.9M | 0.722 | 1.000 |
| Y1 | Monitor | Monitor sierra_plumas | $0.5M | $13.5M | 0.722 | 0.910 |
| Y2 | Monitor | Monitor sjv_merced | $0.5M | $13.3M | 0.722 | 0.805 |
| Y3 | Monitor | Monitor north_coast_mendocino | $0.5M | $11.8M | 0.722 | 0.727 |
| Y4 | Monitor | Monitor la_basin_E | $0.5M | $10.4M | 0.722 | 0.612 |
| Y5 | Monitor | Monitor sacramento_rancho | $0.5M | $9.4M | 0.722 | 0.531 |
| Y6 | Monitor | Monitor imperial_brawley | $0.5M | $9.3M | 0.722 | 0.447 |
| Y7 | Monitor | Monitor bay_richmond | $0.5M | $7.7M | 0.722 | 0.373 |
| Y8 | Monitor | Monitor shasta_redding | $0.5M | $1.6M | 0.722 | 0.345 |
| Y9 | CRF | Retrospective cohort (UK Biobank / MESA) | $2.0M | $6.3M | 0.629 | 0.345 |
Unified BED beats either single-track strategy
How the headline scales with prior sigma
Variance reduction is proportional to prior variance. Tightening the initial CRF prior 2× (sigma 1.0 → 0.5) quarters the prior variance and quarters the headline EVSI. First-order check — the number is not anchored on assumption-fragile extremes:
| Scenario | Anchor | sigma_CRF0 | EVSI-proxy |
|---|---|---|---|
| Headline | $0.05B | 1.0 | $107.3M |
| Tight prior | $0.05B | 0.5 | $84.0M |
Where the monitors landed
The 8 deployed monitors dropped every region's sigma below the baseline:
| Region | Final sigma | Uncertainty reduction |
|---|---|---|
| rest_ca | 0.174 | 83% |
| la_basin | 0.200 | 80% |
| sjv | 0.270 | 73% |
| imperial | 0.412 | 59% |
| sacramento | 0.432 | 57% |
| north_coast | 0.448 | 55% |
| bay_area | 0.480 | 52% |
Break down the procurement silo
Recommendation: CEC should integrate CRF research budget and monitor deployment budget into a single 10-year envelope. The adaptive rule alternates tracks rather than exhausting one first.
Issue one joint RFP cycle with a single $50M envelope and an EVSI-based scoring rule that can re-weight CRF vs monitor spending year-by-year.
What the closed-loop rule still misses
- EVSI-proxy, not canonical EVSI: uses delta(sigma^2) x value_at_stake x p_success. No outer-y Monte Carlo, no explicit utility u(a,theta). Collapses to true EVSI only under linear-Gaussian utility.
- Greedy one-step-lookahead; by submodularity greedy is (1-1/e)-optimal at best. The reported EVSI is a lower bound on the optimal sequence's EVSI, not the optimum.
- Per-region monitor sigma is independent; cross-region covariance not yet modeled. Joint EVSI may be overstated for correlated regions.
- CRF and monitor belief dimensions are treated as orthogonal (no cross-track covariance). Additive combination overstates joint gain when CRF and monitor information would partially inform the same health-burden estimate.
- CRF shrinkage coefficients are the Inv 24 expected-shrinkage priors (Phase 2), not posterior updates.
- Budget assumed fungible between CRF and monitors; real CEC funding streams are partially siloed.