A general theory for preferential sampling in environamental networks

This paper presents a general model framework for detecting the preferential sampling of environmental monitors recording an envi- ronmental process across space and/or time. This is achieved by con- sidering the joint distribution of an environmental process with a site–selection process that considers where and when sites are placed to measure the process. The environmental process may be spatial, temporal or spatio–temporal in nature. By sharing random effects be- tween the two processes, the joint model is able to establish whether site placement was stochastically dependent of the environmental pro- cess under study. Furthermore, if stochastic dependence is identified between the two processes, then inferences about the probability dis- tribution of the spatio–temporal process will change, as will predic- tions made of the process across space and time. The embedding into a spatio–temporal framework also allows for the modelling of the dynamic site—selection process itself. Real–world factors affect- ing both the size and location of the network can be easily modelled and quantified. Depending upon the choice of population of loca- tions to consider for selection across space and time under the site– selection process, different insights about the precise nature of pref- erential sampling can be obtained. The general framework developed in the paper is designed to be easily and quickly fit using the R-INLA package. We apply this framework to a case study involving partic- ulate air pollution over the UK where a major reduction in the size of a monitoring network through time occurred. It is demonstrated that a significant response–biased reduction in the air quality moni- toring network occurred, namely the relocation of monitoring sites to locations with the highest pollution levels, and the routine removal of sites at locations with the lowest. We also show that the network was consistently unrepresentative of the levels of particulate matter seen across much of GB throughout the operating life of the network. Finally we show that this may have led to a severe over-reporting of the population–average exposure levels experienced across GB. This could have great impacts on estimates of the health effects of black smoke levels.