  Gaussian process (GP) models are widely used to emulate propagation
uncertainty in computer experiments. GP emulation sits comfortably within an
analytically tractable Bayesian framework. Apart from propagating uncertainty
of the input variables, a GP emulator trained on finitely many runs of the
experiment also offers error bars for response surface estimates at unseen
input values. This helps select future input values where the experiment should
be run to minimize the uncertainty in the response surface estimation. However,
traditional GP emulators use stationary covariance functions, which perform
poorly and lead to sub-optimal selection of future input points when the
response surface has sharp local features, such as a jump discontinuity or an
isolated tall peak. We propose an easily implemented non-stationary GP
emulator, based on two stationary GPs, one nested into the other, and
demonstrate its superior ability in handling local features and selecting
future input points from the boundaries of such features.
