Kriging vs Decision-Theoretic Placement
Kriging-optimal placement minimizes spatial prediction variance. It asks: “where is the PM2.5 field most uncertain?” The answer is always the location farthest from existing monitors — typically remote, unpopulated terrain.
Decision-theoretic placement maximizes the Monitoring Value Index (MVI) — a score for how much a new sensor would sharpen the health-burden estimate at that location. It asks: “where would a new sensor reduce the most uncertainty in health burden estimates?” MVI combines PM2.5 variance with mortality burden:
MVI = (mortality_burden × β)² × PM2.5_variance · Gap score = MVI_norm × log(1 + distance_km)
The gap score weights MVI by distance to the nearest monitor, balancing health decision value with spatial coverage. A high-population cell with high PM2.5 and moderate distance outranks a zero-population cell at maximum distance.
Same Network, Different Answers
With 520 monitors and a 10.3 km mean spacing, the remaining spatial gaps sit in unpopulated terrain; the decision value is concentrated where exposed population density is highest.
Where the Value Is
| Rank | Region | Gap Score | MVI | Dist (km) | Population | PM2.5 |
|---|---|---|---|---|---|---|
| 1 | LA Basin | 1.000 | 1.000 | 9.2 | 13,747 | 14 |
| 2 | SJV | 0.833 | 0.534 | 32.7 | 9,371 | 16 |
| 3 | SJV | 0.788 | 1.000 | 4.9 | 8,420 | 16 |
| 4 | LA Basin | 0.651 | 0.606 | 10.2 | 11,414 | 14 |
| 5 | Rest CA | 0.605 | 0.388 | 32.6 | 5,241 | 8 |
The top 10 candidates are dominated by LA Basin and San Joaquin Valley — the two regions with the highest PM2.5 and population density. No DAC communities appear in the top 10 because DACs are not systematically undermonitored: DAC mean distance is 9.4 km vs non-DAC 10.6 km.
What Is a New Sensor Worth?
Expected Value of Sample Information (EVSI) quantifies the annual dollar value of each potential sensor location — the reduction in expected wrong-decision costs from having one more measurement point.
| Region | Pop. Covered | Deaths σ Reduction | EVSI ($/yr) | ROI |
|---|---|---|---|---|
| LA Basin (13655) | 2,215,187 | 0.360 | $41,779 | 1.7× |
| SJV (6697) | 458,774 | 0.106 | $12,302 | 0.5× |
| SJV (8681) | 625,181 | 0.102 | $11,885 | 0.5× |
| LA Basin (16640) | 561,775 | 0.090 | $10,486 | 0.4× |
| Rest CA (6909) | 5,241 | 0.003 | $316 | 0.0× |
EVSI computed as reduction in health-burden uncertainty × VSL. Monitor cost: $25,000/yr. ROI = EVSI / cost. The kriging-optimal remote cell (pop=0) has EVSI near zero — perfect spatial coverage of unpopulated terrain has no decision value.
Amortization disclosure: The $25K/yr figure amortizes a $125K 5-year BAM-equivalent capital expense plus assumed site lease & telemetry. It is a planning assumption, not a CARB price list. If the true all-in cost is 2× higher, the top-ROI cell (LA Basin, 1.7×) drops to break-even; cells 2–4 already round to <1.0× and would become net-negative. The ordinal ranking (LA Basin > SJV > Rest CA) is robust to cost misspecification; the absolute ROI numbers are not.
The implication. The same monitoring network serves different purposes depending on the question. CARB network design should explicitly state which objective function it optimizes: spatial prediction, health burden accuracy, or environmental justice coverage.
520 AQS monitors · 21,164 grid cells · Ordinary kriging for spatial variance · MVI = (mortality × β)² × PM2.5_var · Gap = MVI_norm × log(1 + dist) · β = 0.00545 (Krewski ≥30 CRF slope) · Monitor cost $25K/yr · Influence radius 20 km