Geostatistical integration and uncertainty in pollutant concentration surface under preferential sampling

In this paper the focus is on environmental statistics, with the aim of estimating the concentration surface and related uncertainty of an air pollutant. We used air quality data recorded by a network of monitoring stations within a Bayesian framework to overcome difficulties in accounting for prediction uncertainty and to integrate information provided by deterministic models based on emissions meteorology and chemico-physical characteristics of the atmosphere. Several authors have proposed such integration, but all the proposed approaches rely on representativeness and completeness of existing air pollution monitoring networks. We considered the situation in which the spatial process of interest and the sampling locations are not independent. This is known in the literature as the preferential sampling problem, which if ignored in the analysis, can bias geostatistical inferences. We developed a Bayesian geostatistical model to account for preferential sampling with the main interest in statistical integration and uncertainty. We used PM10 data arising from the air quality network of the Environmental Protection Agency of Lombardy Region (Italy) and numerical outputs from the deterministic model. We specified an inhomogeneous Poisson process for the sampling locations intensities and a shared spatial random component model for the dependence between the spatial location of monitors and the pollution surface. We found greater predicted standard deviation differences in areas not properly covered by the air quality network. In conclusion, in this context inferences on prediction uncertainty may be misleading when geostatistical modelling does not take into account preferential sampling.