Bayesian Hierarchical Models for the Combination of Spatially Misaligned Data: A Comparison of Melding and Downscaler Approaches Using INLA and SPDE

The spatially misaligned data problem occurs when data at different spatial scales need to be combined. Bayesian hierarchical models such as melding and downscaler approaches are suitable to solve this problem but their application is limited when MCMC is used for inference due to the high computational cost. The use of INLA and SPDE represents an alternative to MCMC for Bayesian inference that enables faster inference for latent Gaussian models. In this paper, we describe how INLA and SPDE can be adapted to fit Bayesian melding and downscaler models to combine spatially misaligned data. We assess the performance of the models using simulated and real data in a range of scenarios and sampling strategies and compare the suitability of the models in each situation. We also show how to obtain fine particulate matter (PM $$_{2.5}$$ 2.5 ) predictions in the UK at a continuous surface and at policy-relevant spatial scales by combining spatially misaligned monitoring station data, satellite-derived indicators, road information, and environmental factors.