Dynamic multiscale spatiotemporal models for Gaussian areal data

Summary.  We introduce a new class of dynamic multiscale models for spatiotemporal processes arising from Gaussian areal data. Specifically, we use nested geographical structures to decompose the original process into multiscale coefficients which evolve through time following state space equations. Our approach naturally accommodates data that are observed on irregular grids as well as heteroscedasticity. Moreover, we propose a multiscale spatiotemporal clustering algorithm that facilitates estimation of the nested geographical multiscale structure. In addition, we present a singular forward filter backward sampler for efficient Bayesian estimation. Our multiscale spatiotemporal methodology decomposes large data analysis problems into many smaller components and thus leads to scalable and highly efficient computational procedures. Finally, we illustrate the utility and flexibility of our dynamic multiscale framework through two spatiotemporal applications. The first example considers mortality ratios in the state of Missouri whereas the second example examines agricultural production in Espírito Santo State, Brazil.