Marco A. R. Ferreira
University of Missouri

Dynamic Multiscale Spatio-Temporal Models for Gaussian Areal Data

We introduce a new class of dynamic multiscale models for spatio-temporal 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 observed on irregular grids as well as heteroscedasticity. Moreover, we propose a multiscale spatio-temporal 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 spatio-temporal 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 spatio-temporal applications. The first example considers mortality ratios in the state of Missouri whereas the second example examines agricultural production in Espirito Santo State Brazil. This is joint work S. Holan and A. Bertolde.