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Abstract:
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The "space-time cube" is not a cube, but the idea of one is useful. Its base is a spatial domain, D(0), and its shape is traced out by a process of spatial domains, {D(t): t > 0}. Now fill the cube with a spatio-temporal stochastic process {Y(s; t)}. Assume that the cube {D(t)} is fixed (but clearly it too could be stochastic). Slicing the cube laterally for a fixed t_0 generates a spatial stochastic process {Y(s; t_0)}. Slicing the cube longitudinally for a fixed s_0 generates a temporal process {Y(s_0; t)} that, after dicing, yields a time series, {Y(s_0; 0), Y(s_0; 1), . }. These are the highways that traverse the cube. In this talk, I shall investigate some of the byways and roads not taken and incorporate them into hierarchical statistical models for analyzing spatio-temporal data.
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