Chair: Yuichi Mori (Okayama University of Science, Japan)
In computer experiments, Gaussian process models are commonly used for emulation. However, when both qualitative and quantitative factors are involved in the experiments, emulation using Gaussian process models becomes challenging. In particular, when the qualitative factors contain many categories in the experiments, existing methods in the literature become cumbersome due to curse of dimensionality. Motivated by the computer experiments for the design of a cooling system, a new tree-based Gaussian process for emulating computer experiments with many-category qualitative factors is proposed. The proposed method incorporates a tree structure to split the categories in the qualitative factors, and Gaussian process models are employed for modeling the simulation outputs in the leaf nodes. The splitting rule takes into account the cross-correlations between the categories of the qualitative factors, which have been shown by a recent theoretical study to be a crucial element for improving the prediction accuracy. The application to the design of a cooling system indicates that the proposed method not only enjoys marked computational advantages and produces accurate predictions, but also provides valuable insights into the cooling system by discovering the tree structure.