We propose a simple and convenient method for analyzing nonstationary spatio-temporal data. To account for spatial variability, we write the mean function at each time as a locally-weighted mixture of linear regressions. To capture temporal variation, we allow the regression coefficients to change over time. A linear state-space framework is used, allowing us to explore temporal factors such as trends, seasonality, and autoregressive components. The main feature of the proposed method is computational simplicity: using the Kalman filtering and smoothing algorithms, we can obtain posterior and predictive distributions in closed form. This allows quick implementation of the model, and provides full probabilistic inference for the parameters, interpolations and forecasts. To illustrate the method, we analyze two large datasets: tropical rainfall levels and Atlantic ocean temperatures.

Keywords: Bayesian inference; Locally-weighted mixture; Space-time modeling; State-space model.

The manuscript is available in postscript format.