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A note on noise-free Gaussian process prediction with separable covariance functions and grid designs

Research output: Working paper

Original languageEnglish
Number of pages5
Publication statusPublished - 2007

Abstract

Consider a random function f with a separable (or tensor product) covariance function, i.e. where x is broken into D groups (x1, x2, . . . , xD) and the covariance function has the form k(x, ˜x) = QD i=1 ki(xi, ˜xi). We also require that observations of f are made on a Ddimensional grid. We show how conditional independences for the Gaussian process prediction for f(x) (corresponding to an off-grid test input x) depend on how x matches the observation grids. This generalizes results on autokrigeability (see, e.g. Wackernagel 1998, ch. 25) to D > 2.

ID: 21841999