Model Selection for the Mean Function of Kriging Models

Kriging models are used in many scientific disciplines to investigate the behavior of physical systems. In the Kriging model (KM), the response of the computer simulation code (CSC) is considered to have a Gaussian process (GP). To discover variables influencing responses, choosing a selection of variables or creating a strongly reduced regression model is a crucial process. Selecting some variables can prevent over-fitting or under-fitting in the predictions of data in KM. There have been just a few studies on the variable selection in KM. In this work, we suggest performing variable selection to construct a good model among the KM. The results of the proposed model selection are compared in terms of prediction accuracy with other models based on different forms of the mean function. The comparison is achieved by several measures that investigate the behavior of the KMs. Based on the results, the performance of the Forward selection and Backward selection based on AIC is the best. We apply KMs to several examples of computer simulation codes.