  The Gaussian process is a standard tool for building emulators for both
deterministic and stochastic computer experiments. However, application of
Gaussian process models is greatly limited in practice, particularly for
large-scale and many-input computer experiments that have become typical. We
propose a multi-resolution functional ANOVA model as a computationally feasible
emulation alternative. More generally, this model can be used for large-scale
and many-input non-linear regression problems. An overlapping group lasso
approach is used for estimation, ensuring computational feasibility in a
large-scale and many-input setting. New results on consistency and inference
for the (potentially overlapping) group lasso in a high-dimensional setting are
developed and applied to the proposed multi-resolution functional ANOVA model.
Importantly, these results allow us to quantify the uncertainty in our
predictions. Numerical examples demonstrate that the proposed model enjoys
marked computational advantages. Data capabilities, both in terms of sample
size and dimension, meet or exceed best available emulation tools while meeting
or exceeding emulation accuracy.
