Measuring, mapping, and uncertainty quantification in the space-time cube

Authors

Noel A. Cressie, University of WollongongFollow
Christopher Wikle

RIS ID

143701

Publication Details

Cressie, N. & Wikle, C. (2020). Measuring, mapping, and uncertainty quantification in the space-time cube. Revista Matematica Complutense,

Abstract

2020, Universidad Complutense de Madrid. The space-time cube is not a cube of course, but the idea of one is useful. Its base is a spatial domain, Dt, and the "cube" is traced out by a process of spatial domains, { Dt: t≥ 0 }. Now fill the cube with a spatio-temporal stochastic process { Yt(s) : s∈ Dt, t≥ 0 }. Assume that { Dt} is fixed and known (but clearly it too could be stochastic). Slicing the cube laterally for a fixed t generates a spatial stochastic process {Yt0(s):s∈Dt0}. Slicing the cube longitudinally for a fixed s generates a temporal process { Yt(s) : t≥ 0 } that, after dicing, yields a time series, { Y(s) , Y1(s) , … }. 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.