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Title: Combined analysis of misaligned data using Gaussian fields and the stochastic partial differential equation approach Authors:  Paula Moraga - Lancaster University (United Kingdom) [presenting]
Abstract: Spatially misaligned data are becoming increasingly common. To optimize the use of these data, methods to combine data at different spatial scales and enable better predictions are needed. Current approaches present some limitations in terms of convergence and computational time. We present a geostatistical model for fusion of data obtained at point and areal resolutions using INLA and SPDE. This new approach is fast and flexible. The model presented assumes that underlying all observations there is a spatially continuous variable that can be modeled using a Gaussian random field process. In the SPDE approach, the continuously indexed Gaussian random field is represented as a discretely indexed Gaussian Markov random field (GMRF). To allow the combination of data, we propose a new projection matrix for mapping the GMRF from the observation locations to the triangulation nodes. The performance of the model is compared with the method RAMPS via simulation. The model is also applied to predict the concentration of fine particulate matter. The results show that the combination of point and areal data provides better predictions than if the method is applied to just one type of data, and this is consistent over both simulated and real data. The approach presented is a helpful advance in the area of spatial statistics that provides a useful tool that is applicable in a wide range of situations.