A geostatistical model for combined analysis of point-level and area-level data using INLA and SPDE

In this paper a Bayesian geostatistical model is presented for fusion of data obtained at point and areal resolutions. The model is fitted using the INLA and SPDE approaches. In the SPDE approach, a continuously indexed Gaussian random field is represented as a discretely indexed Gaussian Markov random field (GMRF) by means of a finite basis function defined on a triangulation of the region of study. In order to allow the combination of point and areal data, a new projection matrix for mapping the GMRF from the observation locations to the triangulation nodes is proposed which takes into account the types of data to be combined. The performance of the model is examined and compared with the performance of the method RAMPS via simulation when it is fitted to (i) point, (ii) areal, and (iii) point and areal data to predict several simulated surfaces that can appear in real settings. The model is applied to predict the concentration of fine particulate matter (PM2.5), in Los Angeles and Ventura counties, United States, during 2011.