On the Prediction Variance Performances of the Latin Hypercube Design in Some Response Surface Models

In space-filling designs, Latin Hypercube Design (LHD) is a common choice of experimental design strategy for computer experiments. Prediction variance describes the error involved with making a prediction using a response surface model. This study provides a theoretical bound on the prediction variance of LHD, which is useful for analyzing the efficiency of space-filling design in computer experiments. The LHDs examined in this study have one-dimensional uniformity such that, for each input variable, its range is divided into the same number of equally-spaced intervals as the number of observations. This is done for factors <img src=image/13442845_01.gif> within the second- and third-order response surface models. The G-optimality, I-optimality criteria, and Fraction of Design Space (FDS) plots were the methods employed to assess the predictive capabilities and accuracy of these LHDs. The findings revealed that LHDs performed better under third-order models when evaluated using the G-optimality criterion, while using the I-optimality criterion, LHDs performed better in second-order models. The FDS plots further indicate that as the number of factors increases, the prediction errors across the models become approximately similar. The results highlight LHDs' versatility in handling high-dimensional problems which underscores practical interest in LHDs for engineering simulations, reinforcing their role in minimizing prediction variance.