RobustGaSP: Robust Gaussian Stochastic Process Emulation in R

Abstract

Gaussian stochastic process (GaSP) emulation is a powerful tool for approximating computationally intensive computer models. However, estimation of parameters in the GaSP emulator is a challenging task. No closed-form estimator is available and many numerical problems arise with standard estimates, e.g., the maximum likelihood estimator. In this package, we implement a marginal posterior mode estimator, for special priors and parameterizations. This estimation method that meets the robust parameter estimation criteria was discussed in Gu et al. (2018); mathematical reasons are provided therein to explain why robust parameter estimation can greatly improve predictive performance of the emulator. In addition, inert inputs (inputs that almost have no effect on the variability of a function) can be identified from the marginal posterior mode estimation at no extra computational cost. The package also implements the parallel partial Gaussian stochastic process (PP GaSP) emulator (Gu and Berger (2016)) for the scenario where the computer model has multiple outputs on, for example, spatial-temporal coordinates. The package can be operated in a default mode, but also allows numerous user specifications, such as the capability of specifying trend functions and noise terms. Examples are studied herein to highlight the performance of the package in terms of out-of-sample prediction.