Best Linear Unbiased Prediction And Orthogonal Designs Of Computer Experiments

With the extensive application of computer experiments in scientific experiments and industrial design,more and more statistical problems need to be solved.In the practical application,we often meet computer experiments with different precision.High computational accuracy of the computer experiment is slow,and Computer experiment with fast calculation speed has low calculation accuracy.Faced with this situation,the usual approach is to separate the accuracy of computer experiments,which is undoubtedly a waste.In addition,as the accuracy increases,the calculation speed slows down.Due to the cost and time spent,we can get the design set gradually reduced,it is often not ideal to predict the test points with fewer design sets.So we proposed in the cheap low-precision experiment by adding a small amount of expensive high-precision experiments,it is possible to correlate the data with different precision.On this basis,the computer output of any point to predict,it is possible to take into account the advantages of computer experiments,so as to improve the overall prediction accuracy.At the same time,the best linear unbiased predictor has good properties.In view of this,the BLUP of single-precision computer experiment is extended to two-precision,multi-precision and continuous precision computer experiments.The concrete work is as follows:1.We studied the best linear unbiased prediction of the computer output at any of the two-precision computer experiments.We use the Lagrange multiplier method to find the best linear unbiased prediction of the high precision computer output at any point based on low precision model and high precision model in the existing literature.When the parameters in the model are unknown,we propose a hierarchical maximum likelihood estimation to give the empirical best linear unbiased prediction.Finally,the feasibility of the method is verified by numerical simulation and example.The results show that this method has a significant effect on improving the accuracy and efficiency of the two precision computer experiment.2.We investigate the best linear unbiased prediction of computer output at any of the multi-precision computer experiments.The computer experiments of s accuracy are given,with the increase in t(t (?){1,2,…,s}),the accuracy of computer experiments increased,the speed slowed down.The best linear unbiased prediction of the computer output at any point of the s precision is obtained by using the Lagrange multiplier method.When the parameters in the model are unknown,the best linear unbiased prediction is given by the hierarchical maximum likelihood estimation.Finally,the feasibility of the method is verified by numerical simulation.The results show that this method has a significant effect on improving the accuracy and efficiency of the computer model.3.We consider the best linear unbiased prediction of the real value at any point in the continuous precision computer experiment.In the fifth chapter,we introduce the adjustment parameter t(t?0),which determines the precision of the numerical calculation and the calculation time.With the decrease of t,the calculation accuracy is improved,the calculation speed is slowed down,t becomes closer to 0,the computer output becomes closer to the real value.Find the best at any point in the real value of the linear unbiased prediction by using the Lagrange multiplier method,finally through the numerical simulation method to verify the feasibility and examples,the results show that this method has a good performance for the prediction accuracy of continuous computer experiments.Another important part of computer experiment is experimental design,we discuss a class of orthogonal space filling designs which are not restricted to Latin hypercube design,and proposes to construct the orthogonal space filling design with the coordinate descent algorithm,the numerical simulation shows that the algorithm can effectively find the orthogonal design with good space filling properties.In addition,the orthogonal maximin distance designs can be compared with the commonly used design in terms of prediction accuracy for computer outputs.