Chapter X of The Handbook of Applied Bayesian Analysis

We analyze annual per county agricultural production in Esṕırito Santo State, Brazil, from 1990 to 2005 using a novel Bayesian multiscale spatio-temporal model. The model uses the natural geopolitical division of Esṕırito Santo State to define three scales of resolution: macrore-gions, microregions, and counties. The county-level data are aggregated to obtain the data at the other scales of resolution. Then, at each time point, the observed data are decomposed into empirical multiscale coefficients that represent weighted differences between each subregion and its descendants. We assume that these empirical multiscale coefficients correspond to latent multiscale coefficients that evolve through time following singular random walks and estimate these latent multiscale coefficients using an efficient Markov chain Monte Carlo scheme. More-over, the analysis of the estimated multiscale coefficients that we propose sheds light on the similarities and differences in agricultural production between regions within each scale of res-olution. In addition, the temporal change in relative agricultural importance of those regions is explicitly described by the evolution of the estimated multiscale coefficients. Finally, analogous to wavelet analysis, we re-aggregate the estimated multiscale coefficients to obtain an estimate of the underlying spatio-temporal agricultural production process at each level of resolution