Risk surface mapping through multivariate geographical dependences by hierarchical Bayesian models

This work compares several hierarchical Bayesian techniques for modelling risk surfaces by multivariate areal data. Spatial (random) effects are generally incorporated to capture areal clustering. Moreover, they are typically given a CAR model as hierarchical prior. Nevertheless, such specification may reveal too simple/rigid when the correlation structure is complex. Especially when large geographical areas are involved, different subareas can be more or less smooth. Moreover, predictors can have modified effects at different areal aggregation levels. In addition, their spatial distribution can be characterized by a smoothing different from that imposed by the spatial effects model. Then, we develope various alternatives to the common CAR model: (i) a multilevel convolution prior or (ii) a proper multilevel CAR model; lastly a CAR model for modified spatial effects of predictors is proposed.