Figure 2.

Illustration of moving-window GP regression. In order to make a prediction at the grid point (x*₁, t*), data in its local neighbourhood $\mathcal{W}({\mathit{x}}_1^{\ast },t^{\ast })$ are used to first estimate the covariance parameters and then to make the prediction. When moving to the next grid point (x*₂, t*), the window moves along and the parameter estimates and the prediction are made using data within the new local neighbourhood $\mathcal{W}({\mathit{x}}_2^{\ast },t^{\ast })$. For ease of graphical presentation, the time axis is suppressed here, but the same concept applies in the full spatio-temporal space.