Table 1.
Prediction performance for daily PM2.5 concentrations comparing ensemble averaging with a Bayesian hierarchical model (BHM) using satellite-derived aerosol optical depth (AOD) or a BHM using a numerical model (CMAQ) simulation. Ensemble weights were derived from first performing 10-fold CV.
| Evaluation Method | Statistical Model | RMSE | Coverage of 95% PI | Average Posterior SD | R2 |
|---|---|---|---|---|---|
| Ordinary (10-fold) CV | |||||
| PM2.5-AOD BHM | 3.40 | 94.07 | 3.30 | 0.78 | |
| PM2.5-CMAQ BHM | 3.14 | 95.05 | 3.28 | 0.81 | |
| Ensemble | 3.00 | 97.15 | 2.39 | 0.83 | |
| Spatial (Leave-one-monitor-out) CV | |||||
| PM2.5-AOD BHM | 3.45 | 94.25 | 3.39 | 0.77 | |
| PM2.5-CMAQ BHM | 3.33 | 95.32 | 3.45 | 0.78 | |
| Ensemble | 2.99 | 96.81 | 2.38 | 0.83 | |
| Spatially clustered (Leave-one-cluster-out) CV | |||||
| PM2.5-AOD BHM | 3.62 | 94.43 | 3.59 | 0.74 | |
| PM2.5-CMAQ BHM | 3.93 | 93.34 | 3.58 | 0.69 | |
| Ensemble | 3.13 | 95.73 | 3.25 | 0.81 | |
RMSE: root mean squared error (in μg/m3); PI: prediction interval; SD: standard deviation (in μg/m3); CV: cross-validation; PM2.5: particulate matter less than 2.5 μm; AOD: aerosol optical depth; BHM: Bayesian hierarchical model; CMAQ: Community Multiscale Air Quality.