Scaled Vecchia Approximation for Fast Computer-Model Emulation

Many scientific phenomena are studied using computer experiments consisting of multiple runs a model while varying the input settings. Gaussian processes (GPs) popular tool for analysis experiments, enabling interpolation between settings, but direct GP inference is computationally infeasible large datasets. We adapt and extend powerful class methods from spatial statistics to enable scalable emulation experiments. Specifically, we apply Vecchia’s ordered conditional approximation in transformed space, with each scaled according how strongly it relates computer-model response. The scaling learned data by estimating parameters covariance function Fisher scoring. Our highly scalable, estimation, joint prediction, simulation near-linear time number runs. In several numerical examples, our approach substantially outperformed existing methods.