Bayesian Approach for Analyzing Computer Models using Gaussian Process Models.

Abstract

Mathematical models, usually implemented in computer programs known as computer models, are widely used in all areas of science and technology to represent complex systems in the real world. However, computer models are often so complex in such that they require a long time in computer to be implemented. To solve this problem, a methodology has been developed that is based on building a statistical representation of a computer model, known as a Gaussian process model. As any statistical model, the Gaussian process model is based on some assumptions. Several validation methods have been used for checking the assumptions of the Gaussian process model to obtain the best probabilistic model as an alternative to the computer model. These validation methods are based on a comparison between the output of the computer model and the output of the Gaussian process model for some test data. In this work, we present the Bayesian approach for constructing a Gaussian process model. We also suggeste and compare validation methods that consider the correlation between the output of the computer model and the Gaussian process model predictions with those that do not consider the correlation between these data. We apply the Gaussian process model with the suggested validation methods to real data represented by the robot arm function. We have found that the methods that consider the correlation give more accurate and reliable results. We achieved the calculations using the R program.