Two-phase IMSE-optimal Latin hypercube design for computer experiments

With the increasing use of simulation codes in many fields, the subject of optimal design for computer experiments has received considerable amount of attention from the researchers. This thesis develops a two-phase approach to create IMSE-optimal Latin hypercube design (LHD) for the Kriging model. It calls for supplementing an initial LHD with additional observations to produce a new optimal LHD with regard to the IMSE criterion. Three issues need to be addressed in order to implement the two-phase approach successfully. They are (1) the determination of sample size; (2) the point allocation strategy and (3) the estimations of unknown model parameters that are necessary for constructing Kriging models.;This thesis first conducts a comprehensive empirical study to address the sample size issue. A series of test functions were used to examine the relationship between the sample size and the fidelity of the fitted Kriging model for a wide variety of surfaces with as many as four input variables. This thesis develops an experiential source of recommendations for the sample size required to produce a Kriging model with the desired level of accuracy.;Then a genetic algorithm used to generate the two-phase IMSE-optimal LHDs was developed. The performances of the two-phase IMSE-optimal LHDs were evaluated and compared to the performances of some other computer experimental designs. The results indicate that the performances of the two-phase IMSE-optimal LHDs are promising when the training points are appropriately allocated between two phases.;The third part investigates the impact of the point allocation strategy. The results show that allocating a relatively large portion of the training points to the first phase to obtain decent estimates of unknown parameters is of special importance.;The last part investigates the small sample behavior of the model parameter's maximum likelihood estimators (MLE). The results indicate that small sample sizes may yield poor MLE for the unknown model parameters. The penalized NILE should be employed to estimate unknown parameters and was shown very beneficial for constructing two-phase IMSE-optimal LHDs when the number of training points allocated to the first phase is small.