TY - UNPB

T1 - A note on noise-free Gaussian process prediction with separable covariance functions and grid designs

AU - Williams, Christopher

AU - Chai, Kian Ming A

AU - Bonilla, Edwin V

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

M3 - Working paper

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

ER -