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Title: Data fusion in a two-stage spatio-temporal model using the INLA-SPDE approach Authors:  Janine Illian - University of Glasgow (United Kingdom)
Stephen Jun Villejo - University of Glasgow (United Kingdom) [presenting]
Ben Swallow - University of Glasgow (United Kingdom)
Abstract: A two-stage model is proposed, motivated by an epidemiological problem which involves data with different spatial supports. The response is areal, while the predictor data are measurements from a geostatistical process and high-resolution outputs either from satellites or numerical models. The first stage assumes a common latent field for the geostatistical and the high-resolution data, whereby both are error-prone realizations of the field. The spatial effect of the latent field is assumed to evolve in time, inducing spatiotemporal dependence and is modelled using a stochastic partial differential equation approach. This provides a Markov structure on the random field, speeding up computation and spatial interpolation. The second stage fits a GLMM using spatial averages of the estimated latent field, and additional spatial and temporal random effects. The latent Gaussian models are estimated using the integrated nested Laplace approximation, a deterministic Bayesian inference approach. Uncertainty from the first stage is accounted for by simulating several times from the posterior predictive distribution of the latent field. A simulation study was done to assess the impact of the sparsity of the data, length of time, and priors specification on the model fit. The method was also applied to actual data in England.