Publications [#380384] of David B. Dunson

Papers Published

1. Tang, T; Mak, S; Dunson, D, Hierarchical Shrinkage Gaussian Processes: Applications to Computer Code Emulation and Dynamical System Recovery, SIAM-ASA Journal on Uncertainty Quantification, vol. 12 no. 4 (January, 2024), pp. 1085-1112 [doi]
   (last updated on 2024/11/20)

   Abstract:
   In many areas of science and engineering, computer simulations are widely used as proxies for physical experiments, which can be infeasible or unethical. Such simulations are often computationally expensive, and an emulator can be trained to efficiently predict the desired response surface. A widely used emulator is the Gaussian process (GP), which provides a flexible framework for efficient prediction and uncertainty quantification. Standard GPs, however, do not capture structured shrinkage on the underlying response surface, which is present in many applications, particularly in the physical sciences. We thus propose a new hierarchical shrinkage GP (HierGP), which incorporates such structure via cumulative shrinkage priors within a GP framework. We show that the HierGP implicitly embeds the principles of effect hierarchy, heredity, and smoothness widely used for analysis of experiments; such principles allow the HierGP to identify significant structured effects on the response surface with limited data. We propose efficient posterior sampling algorithms for model training and prediction and prove desirable consistency properties for the HierGP. Finally, we demonstrate the improved performance of HierGP over existing models in a suite of numerical experiments and an application to dynamical system recovery.