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A single-index model (SIM) provides for parsimonious multi-dimensionalnonlinear regression by combining parametric (linear) projection withunivariate nonparametric (non-linear) regression models. We show that aparticular Gaussian process (GP) formulation is simple to work with and idealas an emulator for some types of computer experiment as it can outperform thecanonical separable GP regression model commonly used in this setting. Ourcontribution focuses on drastically simplifying, re-interpreting, and thengeneralizing a recently proposed fully Bayesian GP-SIM combination, and thenillustrating its favorable performance on synthetic data and a real-datacomputer experiment. Two R packages, both released on CRAN, have been augmentedto facilitate inference under our proposed model(s).

Gaussian process single-index models as emulators for computer experiments