Dynamic Multi-Resolution Spatial Models

The material presented in this talk is the result of joint research by Gardar Johannesson (Lawrence Livermore), Noel Cressie (Ohio State) and Hsin-Cheng Huang (Academia Sinica). We consider the problem of spatial-temporal prediction of global processes using a model that recognizes multiple resolutions in the spatial domain. Here, optimal spatial-prediction procedures can be shown to be extremely fast. Similar ideas can be used in the spatial-temporal domain; a vector autoregressive model is assumed at the coarsest resolution and, at each time-point, a multi-resolution spatial strucure is modeled. Then the idea is to use Bayesian updating to make the prior distribution of the coarse-resolution process more informative as time proceeds. Our spatial-temporal methodology will be compared to the spatial-only methodology on data from the Total Ozone Mapping Spectrometer (TOMS) instrument, on the Nimbus-7 satellite.