  Deep Gaussian processes (DGPs) are increasingly popular as predictive models
in machine learning (ML) for their non-stationary flexibility and ability to
cope with abrupt regime changes in training data. Here we explore DGPs as
surrogates for computer simulation experiments whose response surfaces exhibit
similar characteristics. In particular, we transport a DGP's automatic warping
of the input space and full uncertainty quantification (UQ), via a novel
elliptical slice sampling (ESS) Bayesian posterior inferential scheme, through
to active learning (AL) strategies that distribute runs non-uniformly in the
input space -- something an ordinary (stationary) GP could not do. Building up
the design sequentially in this way allows smaller training sets, limiting both
expensive evaluation of the simulator code and mitigating cubic costs of DGP
inference. When training data sizes are kept small through careful acquisition,
and with parsimonious layout of latent layers, the framework can be both
effective and computationally tractable. Our methods are illustrated on
simulation data and two real computer experiments of varying input
dimensionality. We provide an open source implementation in the "deepgp"
package on CRAN.
