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A Comparison Between Estimating The Parameters of The Gaussian Process Regression Model Using The Maximum Likelihood and The Restricted Maximum Likelihood Methods | ||
| Journal of Education and Science | ||
| Article 6, Volume 33, Issue 4, December 2024, Pages 51-59 PDF (727.9 K) | ||
| Document Type: Review Paper | ||
| DOI: 10.33899/edusj.2024.184630 | ||
| Authors | ||
| Amena Khalid ilyas* 1; Younus Hazim Al-Taweel2 | ||
| 1Department of Mathematics, College of Education of Pure Science, University of Mosul, Mosul, Iraq | ||
| 2Department of Mathematics, College of Education for Pure Science, University of Mosul, Iraq. | ||
| Abstract | ||
| 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. | ||
| Keywords | ||
| Computer Model; Gaussian Process; Maximum likelihood estimation (MLE); Restricted Maximum Likelihood estimation (RMLE); Borehole Function | ||
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