A Bayesian approach to forecasting daily air-pollutant levels

Forecasting air-pollutant levels is an important issue, due to their adverse effects on public health, and often a legislative necessity. The advantage of Bayesian methods is their ability to provide density predictions which can easily be transformed into ordinal or binary predictions given a set of thresholds. We develop a Bayesian approach to forecasting PM$$_{10}$$10 and O$$_3$$3 levels that efficiently deals with extensive amounts of input parameters, and test whether it outperforms classical models and experts. The new approach is used to fit models for PM$$_{10}$$10 and O$$_3$$3 level forecasting that can be used in daily practice. We also introduce a novel approach for comparing models to experts based on estimated cost matrices. The results for diverse air quality monitoring sites across Slovenia show that Bayesian models outperform classical models in both PM$$_{10}$$10 and O$$_3$$3 predictions. The proposed models perform better than experts in PM$$_{10}$$10 and are on par with experts in O$$_3$$3 predictions--where experts already base their predictions on predictions from a statistical model. A Bayesian approach--especially using Gaussian processes--offers several advantages: superior performance, robustness to overfitting, more information, and the ability to efficiently adapt to different cost matrices.