  Random field models have been widely employed to develop a predictor of an
expensive function based on observations from an experiment. The traditional
framework for developing a predictor with random field models can fail due to
the computational burden it requires. This problem is often seen in cases where
the input of the expensive function is high dimensional. While many previous
works have focused on developing an approximative predictor to resolve these
issues, this article investigates a different solution mechanism. We
demonstrate that when a general set of designs is employed, the resulting
predictor is quick to compute and has reasonable accuracy. The fast computation
of the predictor is made possible through an algorithm proposed by this work.
This paper also demonstrates methods to quickly evaluate the likelihood of the
observations and describes some fast maximum likelihood estimates for unknown
parameters of the random field. The computational savings can be several orders
of magnitude when the input is located in a high dimensional space. Beyond the
fast computation of the predictor, existing research has demonstrated that a
subset of these designs generate predictors that are asymptotically efficient.
This work details some empirical comparisons to the more common space-filling
designs that verify the designs are competitive in terms of resulting
prediction accuracy.
