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Spatio-temporal areal data can be seen as a collection of time series whichare spatially correlated according to a specific neighboring structure.Incorporating the temporal and spatial dimension into a statistical model poseschallenges regarding the underlying theoretical framework as well as theimplementation of efficient computational methods. We propose to includespatio-temporal random effects using a conditional autoregressive prior, wherethe temporal correlation is modeled through an autoregressive meandecomposition and the spatial correlation by the precision matrix inheritingthe neighboring structure. Their joint distribution constitutes a GaussianMarkov random field, whose sparse precision matrix enables the usage ofefficient sampling algorithms. We cluster the areal units using a nonparametricprior, thereby learning latent partitions of the areal units. The performanceof the model is assessed via an application to study regional unemploymentpatterns in Italy. When compared to other spatial and spatio-temporalcompetitors, the proposed model shows more precise estimates and the additionalinformation obtained from the clustering allows for an extended economicinterpretation of the unemployment rates of the Italian provinces.

Bayesian modeling and clustering for spatio-temporal areal data: An application to Italian unemployment