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.
