New modeling Procedures for Functional Data in Computer Experiments

Open Access
Author:
Zhang, Zhe
Graduate Program:
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
February 26, 2007
Committee Members:
  • Runze Li, Committee Chair
  • James Landis Rosenberger, Committee Member
  • John Fricks, Committee Member
  • Timothy William Simpson, Committee Member
Keywords:
  • functional linear model
  • functional ANOVA decomposition
  • multivariate kriging
  • computer experiment
  • semi-varying coefficient model
  • back-fitting algorithm
Abstract:
Along with the rapid development of computers, computer experiment becomes more and more important in all the scientific research area. However the computer experiment usually takes long time to run for each case and requires heavy computation hence for large, complex systems it is not feasible to get all the values over the entire experimental space. This thesis attempts to model the computer experiment with multivariate response or functional output using multivariate kriging and (partial) functional linear models. The whole purpose of the thesis is to propose some good interpolation models in computer experiments with multivariate or functional responses. In chapter 3, we proposed a multivariate kriging model and multivariate functional ANOVA decomposition for computer experiments with multivariate responses. The simulation results show that multivariate version can improve the prediction up to 30%. In chapter 4, we proposed a spatial-temporal model for the residual of functional linear model and the corresponding functional ANOVA decomposition. This model enable us to get a smooth surface which passes through each observation point. The functional ANOVA decomposition part can answers questions such as how a predictor affects the overall functional responses and how important it is. We also performed a simulation to compare the multivariate kriging and kriging with single response under this model frame. The simulation result shows that the multivariate version improves the prediction power for about 10%. In chapter 5, we proposed a spatial-temporal model for the residual of partial functional linear model. This chapter aims to reduce the complexity of the main effect model and make it more parsimonious. The spatial-temporal model also can interpolate the response at observed points. We also performed a simulation to compare the multivariate kriging and kriging with single response under this model frame. We observe the similar prediction power increasing as in chapter 4. Within each chapters, we applied the proposed models and estimation procedures to some real case examples. Although these examples deal with engine simulation, the proposed method can be applied to all computer experiments with multivariate or functional responses.