Spatial data fusion adjusting for preferential sampling using integrated nested Laplace approximation and stochastic partial differential equation

Abstract

Abstract 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. This model can be employed, for instance, to forecast air pollution levels through the integration of point data from monitoring stations and areal data derived from satellite imagery. However, if the data present 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 may 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. Fast Bayesian inference is performed using the integrated nested Laplace approximation and the stochastic partial differential equation 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.