A general framework for modeling Gaussian process with qualitative and quantitative factors
Published in Technometrics, 2026
Computer experiments involving both qualitative and quantitative factors require covariance structures that can handle mixed inputs. We develop a general latent-variable Gaussian process framework that applies standard kernels after mapping qualitative factors into a continuous latent space. The framework gives a unified interpretation of several existing models, introduces new covariance structures, and naturally incorporates ordinal information. We also use the Bayesian information criterion and leave-one-out cross-validation for model selection and model averaging, and evaluate the proposed methods in several examples.