  Many scientific phenomena are studied using computer experiments consisting
of multiple runs of a computer model while varying the input settings. Gaussian
processes (GPs) are a popular tool for the analysis of computer experiments,
enabling interpolation between input settings, but direct GP inference is
computationally infeasible for large datasets. We adapt and extend a powerful
class of GP methods from spatial statistics to enable the scalable analysis and
emulation of large computer experiments. Specifically, we apply Vecchia's
ordered conditional approximation in a transformed input space, with each input
scaled according to how strongly it relates to the computer-model response. The
scaling is learned from the data, by estimating parameters in the GP covariance
function using Fisher scoring. Our methods are highly scalable, enabling
estimation, joint prediction and simulation in near-linear time in the number
of model runs. In several numerical examples, our approach substantially
outperformed existing methods.
