Gaussian Process Models for Computer Experiments with Qualitative and Quantitative Factors

Modeling experiments with qualitative and quantitative factors is an important issue in computer modeling. A framework for building Gaussian process models that incorporate both types of factors is proposed. The key to the development of these new models is an approach for constructing correlation functions with qualitative and quantitative factors. An iterative estimation procedure is developed for the proposed models. Modern optimization techniques are used in the estimation to ensure the validity of the constructed correlation functions. The proposed method is illustrated with an example involving a known function and a real example for modeling the thermal distribution of a data center. KEY WORDS: Cokriging; Design of experiments; Kriging; Multivariate Gaussian processes; Semi-definite programming