Deep Gaussian Process Emulation using Stochastic Imputation

Gaussian processes (GPs) are widely used in computer experiments to emulate computationally expensive computer models for fast uncertainty quantification tasks such as uncertainty propagation, sensitivity analysis, and calibration. The popularity of GPs is attributed to their flexibility, native uncertainty incorporation, and analytical tractability for many key properties such as the likelihood function, predictive distribution and associated derivatives. However, GP models often assume stationarity, which in practice may not be adequate to capture non-stationary behaviors. A number of papers attempt to address this challenge by constructing non-stationary GP emulators. For example, the non-stationary covariance function introduced by Paciorek & Schervish (2003) could be adopted instead of a more standard stationary kernel. Bayesian treed Gaussian processes (TGP), proposed by Gramacy & Lee (2008), emulate non-stationary computer models by splitting the input space into several partitions and using independent stationary GPs to each sub-region. Ba et al. (2012) apply the composition of two stationary GPs to model both global and local details of a non-stationary computer model.