  Spatially misaligned data can be fused by using a Bayesian melding model that
assumes that underlying all observations there is a spatially continuous
Gaussian random field process. This model can be used, for example, to predict
air pollution levels by combining point data from monitoring stations and areal
data from satellite imagery.
  However, if the data presents preferential sampling, that is, if the observed
point locations are not independent of the underlying spatial process, the
inference obtained from models that ignore such a dependence structure might
not be valid.
  In this paper, we present a Bayesian spatial model for the fusion of point
and areal data that takes into account preferential sampling. The model
combines the Bayesian melding specification and a model for the stochastically
dependent sampling and underlying spatial processes.
  Fast Bayesian inference is performed using the integrated nested Laplace
approximation (INLA) and the stochastic partial differential equation (SPDE)
approaches. The performance of the model is assessed using simulated data in a
range of scenarios and sampling strategies that can appear in real settings.
The model is also applied to predict air pollution in the USA.
