Model Averaging For Gaussian Process Regression

Model averaging is developed on the basis of model selection and has been widely used in recent years.Model averaging can reduce the risk of regression estimation,and the combination of multiple candidate models provides a kind of insurance against the variation of selected single model,thus reducing the loss of useful information.Modern industrial production has a more and more urgent demand for various complex experiments.It is necessary and feasible to use computer code to simulate physical experiments.Gaussian process regression models take into account the correlation between variables and can get more accurate prediction value.Among them,Kriging model and spatial geostatistical model have been widely used.This dissertation studies the basic theory of model-averaged of general Kriging model and spatial geostatistical model.AICc,S-AIC,S-BIC,SPMMA and MMA were selected to carry out the weighted average of the candidate models,and a model-averaged method based on Fiducial inference was proposed to consider the candidate models with different basis function sets when predicting.We probabilistically weighted each candidate model from the universal Kriging model and the spatial geostatistical model to obtain the averaged model.Numerical simulation and example analysis show that the Fiducial mothod has certain advantages in forecasting compared with other methods.Due to the identification issue in Kriging model,the orthogonal Kriging model was obtained by orthogonalizing regression terms and Gaussian process.By AICc,S-AIC,S-BIC,SPMMA,MMA and Fiducial methods,the prediction performance of the averaged model before and after orthogonal was compared via numerical simulation and example analysis.It was found that the prediction value obtained after averaging of the orthogonal Kriging model was more accurate.