Subsampling Methods For Gaussian Random Process Model

Gaussian random process model is a commonly used modeling method in spa-tial statistics and computer experiments.The Gaussian random process consists of a fixed linear regression model and a random effect,and the random effect is a Gaussian random process.When the sample size is n,the parameter estimation in the Gaussian random process model and the prediction of untested points require the inverse matrix of an n×n correlation matrix,and that requires O(n~3)com-putations.With the increase of the sample size,the computational amount also increases greatly.At this time,the computational complexity can be reduced by extracting representative subsamples for modeling.In order to obtain representative subsamples,simple random sampling,ran-dom block sampling and the OA-based Latin hypercube block sampling are studied in this paper.Then these models are built based on the subsamples,and the pa-rameters are estimated by using the penalized likelihood method.The penalty function is used to compress the coefficient of the unimportant variables,so as to achieve the purpose of variable selection and parameter estimation.It is found that the above subsampling methods can effectively reduce the calculation amount of parameter estimation in the model.Through several groups of simulations,the performance of all data and the OA-based Latin hypercube block subsample are compared under different conditions.In addition,simple random sampling,random block sampling and the OA-based Latin hypercube block sampling are used respec-tively to establish the Gaussian random process models.By comparing the mean square error of prediction,it is found that the OA-based Latin hypercube block sampling method has better performance than the other two sampling methods.