Gaussian process regression with skewed errors

In statistical literature, the Gaussian process is used as a prior process to treat a nonlinear regression from a Bayesian viewpoint with normally distributed error terms. In this paper, we modify the Gaussian process regression (GPR) model by assuming the error terms of the GPR model follow a skew normal distribution instead of the normal distribution. We refer to this new modification as the Gaussian process regression with skewed errors (GPRSE). A key advantage of our model is that the well known GPR model is a subclass of the GPRSE model. Most importantly, we derive its predictive distribution for a new input location in a closed form. Moreover, the marginal likelihood of the GPRSE model is derived, and is used to train the model hyper-parameters. We also conduct simulation experiments to demonstrate the efficiency of our proposed approach compared to the GPR model. (C) 2019 Elsevier B.V. All rights reserved.