  We provide a new approach to approximate emulation of large computer
experiments. By focusing expressly on desirable properties of the predictive
equations, we derive a family of local sequential design schemes that
dynamically define the support of a Gaussian process predictor based on a local
subset of the data. We further derive expressions for fast sequential updating
of all needed quantities as the local designs are built-up iteratively. Then we
show how independent application of our local design strategy across the
elements of a vast predictive grid facilitates a trivially parallel
implementation. The end result is a global predictor able to take advantage of
modern multicore architectures, while at the same time allowing for a
nonstationary modeling feature as a bonus. We demonstrate our method on two
examples utilizing designs sized in the thousands, and tens of thousands of
data points. Comparisons are made to the method of compactly supported
covariances.
