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AbstractThe paper covers the design and analysis of experiments to discriminate between two Gaussian process models with different covariance kernels, such as those widely used in computer experiments, kriging, sensor location and machine learning. Two frameworks are considered. First, we study sequential constructions, where successive design (observation) points are selected, either as additional points to an existing design or from the beginning of observation. The selection relies on the maximisation of the difference between the symmetric Kullback Leibler divergences for the two models, which depends on the observations, or on the mean squared error of both models, which does not. Then, we consider static criteria, such as the familiar log-likelihood ratios and the Fréchet distance between the covariance functions of the two models. Other distance-based criteria, simpler to compute than previous ones, are also introduced, for which, considering the framework of approximate design, a necessary condition for the optimality of a design measure is provided. The paper includes a study of the mathematical links between different criteria and numerical illustrations are provided.

The Fifth International Workshop on Model-Oriented Data Analysis (MODA5) focused on experimental design, particularly optimum design. A strength of this series of workshops is that they bring together leading scientists from "Eastern" and "Western" Europe. The proceedings therefore provides a valuable reference to the work of groups from many countries. In addition to 11 papers on optimum designs for linear and nonlinear models, there are groups of papers on designs for quality improvement, designs in agriculture and for model building. Non-design problems include robustness in linear models and estimation problems in nonlinear models. The volume concludes with a discussion on the teaching of experimental design