The pairwise method for covariance parameter selection in Gaussian process regression model

With the development of computer technology, experiments of computer are being performed with a simulator, and the tuning parameters are optimized with metamodel. As a metamodel, the Gaussian process regression model (GPRM) has been used in many studies. 
GPRM consists of regression coefficient 's and covariance parameter 's. In order to make a better GPRM, many studies have been dealt with the selection of , but only Welch's algorithm (1992) for has been proposed. We propose a selection method using all possible pairwise combinations. The combinations of are classified using the Bayes information criterion(BIC) and Bonferroni correction. Welch's algorithm estimates only a few important ’s individually and estimates the remaining as a single common . In the proposed algorithm, several common ’s may appear depending on the characteristics of , and the calculation time is cheaper because only two-dimensional data are considered. The prediction performance was compared to the Welch's algorithm in the sense of root mean square error (RMSE) through three test functions.