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In many areas of science and engineering, computer simulations are widelyused as proxies for physical experiments, which can be infeasible or unethical.Such simulations can often be computationally expensive, and an emulator can betrained to efficiently predict the desired response surface. A widely-usedemulator is the Gaussian process (GP), which provides a flexible framework forefficient prediction and uncertainty quantification. Standard GPs, however, donot capture structured sparsity on the underlying response surface, which ispresent in many applications, particularly in the physical sciences. We thuspropose a new hierarchical shrinkage GP (HierGP), which incorporates suchstructure via cumulative shrinkage priors within a GP framework. We show thatthe HierGP implicitly embeds the well-known principles of effect sparsity,heredity and hierarchy for analysis of experiments, which allows our model toidentify structured sparse features from the response surface with limiteddata. We propose efficient posterior sampling algorithms for model training andprediction, and prove desirable consistency properties for the HierGP. Finally,we demonstrate the improved performance of HierGP over existing models, in asuite of numerical experiments and an application to dynamical system recovery.

Hierarchical shrinkage Gaussian processes: applications to computer code emulation and dynamical system recovery