The space-time cube is not a cube of course, but the idea of one is useful. Its base is a spatial domain, \(D_t\), and the “cube” is traced out by a process of spatial domains, \(\{D_t:t\ge 0\}\). Now fill the cube with a spatio-temporal stochastic process \(\{Y_t(\mathbf{s} ):\mathbf{s} \in D_t,t\ge 0\}\). Assume that \(\{D_t\}\) is fixed and known (but clearly it too could be stochastic). Slicing the cube laterally for a fixed \(t_0\) generates a spatial stochastic process \(\{Y_{t_0}(\mathbf{s} ):\mathbf{s} \in D_{t_0}\}\). Slicing the cube longitudinally for a fixed \(\mathbf{s} _0\) generates a temporal process \(\{Y_t(\mathbf{s} _0):t\ge 0\}\) that, after dicing, yields a time series, \(\{Y_0(\mathbf{s} _0),Y_1(\mathbf{s} _0),\ldots \}\). These are the main highways that traverse the cube but other, less-traveled paths, can be taken. In this paper, we discuss spatio-temporal data and processes whose domain is the space-time cube, and we incorporate them into hierarchical statistical models for spatio-temporal data.

中文翻译：

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时空立方体中的测量，映射和不确定性量化

时空立方体当然不是一个立方体，但是一个的想法很有用。它的基础是空间域\（D_t \），而“立方体”是通过空间域\（\ {D_t：t \ ge 0 \} \）找出的。现在，用时空随机过程\（\ {Y_t（\ mathbf {s}）：\ mathbf {s} \ in D_t，t \ ge 0 \} \）填充多维数据集。假定\（\ {D_t \} \）是固定的并且是已知的（但显然也可能是随机的）。横向将立方体切成固定的\（t_0 \）会生成空间随机过程\（\ {Y_ {t_0}（\ mathbf {s}）：\ mathbf {s} \ in D_ {t_0} \} \）。纵向将多维数据集切片为固定的\（\ mathbf {s} _0 \）会生成一个时间过程\（\ {Y_t（\ mathbf {s} _0）：t \ ge 0 \} \）切成小块后会产生时间序列\（\ {Y_0（\ mathbf {s} _0），Y_1（\ mathbf {s} _0），\ ldots \} \）。这些是横穿立方体的主要公路，但也可以采用其他较少人行的道路。在本文中，我们讨论时空数据和过程（其域为时空立方体），并将它们纳入时空数据的分层统计模型中。