A Bayesian kriged Kalman model for short-term forecasting of air pollution levels

Short-term forecasts of air pollution levels in big cities are now reported in newspapers and other media outlets. Studies indicate that even short-term exposure to high levels of an air pollutant called atmospheric particulate matter can lead to long-term health effects. Data are typically observed at fixed monitoring stations throughout a study region of interest at different time points. Statistical spatiotemporal models are appropriate for modelling these data. We consider short-term forecasting of these spatiotemporal processes by using a Bayesian kriged Kalman filtering model. The spatial prediction surface of the model is built by using the well-known method of kriging for optimum spatial prediction and the temporal effects are analysed by using the models underlying the Kalman filtering method. The full Bayesian model is implemented by using Markov chain Monte Carlo techniques which enable us to obtain the optimal Bayesian forecasts in time and space. A new cross-validation method based on the Mahalanobis distance between the forecasts and observed data is also developed to assess the forecasting performance of the model implemented.