A Comparison Between Estimating The Parameters of The Gaussian Process Regression Model Using The Maximum Likelihood and The Restricted Maximum Likelihood Methods

Gaussian process regression models are used as statistical representations of computational models, due to their flexibility in capturing the shape of smooth functions. The Gaussian process regression model has a number of parameters, the estimation of which is an essential step towards building the model. The parameters considered are the regression coefficients , the scaling parameter  and the correlation lengths . Estimating these parameters is the problem we address in this paper. The main contribution of this work is a comparison between estimating the parameters of the Gauss process regression model using the maximum likelihood method and the restricted maximum likelihood method. This comparison was made based on some validation measures. The Gauss process regression model, whose parameters were estimated using the two methods above, was applied to a real eight-dimensional example represented by the borehole function model, and all mathematical and graphical operations were carried out using the R program.