This paper presents a general model framework for detecting the preferential
sampling of environmental monitors recording an environmental process across
space and/or time. This is achieved by considering 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
between the two processes, the joint model is able to establish whether site
placement was stochastically dependent of the environmental process under
study. The embedding into a spatio--temporal framework also allows for the
modelling of the dynamic site---selection process itself. Real--world factors
affecting both the size and location of the network can be easily modelled and
quantified. Depending upon the choice of population of locations to consider
for selection across space and time under the site--selection process,
different insights about the precise nature of preferential 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 particulate 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 monitoring
network occurred. 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.Comment: 33 pages of main text, 48 including the supplementary materia
