Dynamic Models for Spatio-Temporal Models

Jonathan R. Stroud, Peter Müller, Bruno Sansó

University of Chicago, MD Anderson Cancer Center, and UC-Santa Cruz

We propose a model for nonstationary spatio-temporal data. To account for spatial variability, we model the mean function at each time period as a locally-weighted mixture of linear regressions. To incorporate temporal variation, we allow the regression coefficients to change through time. Kriging-based variogram models can also be incorporated when the process is highly localized in space. The model is cast in a general state space framework which allows us to include additional temporal components such as trends, seasonal effects, and autoregressions, and permits fast implementation and full probabilistic inference for the parameters interpolations and forecasts. To illustrate our method, we apply it to two large datasets from the physical sciences: quarterly rainfall levels in Venezuela and water temperatures in the Atlantic Ocean.

The manuscript is available in PDF format.