Design of experiments for regression model discrimination

During the talk, analytical and numerical methods in experimental design for regression model discrimination will be discussed. The mathematical theory of optimal experimental design allows one to minimize the number of experiments required for statistical inference by optimal choice of independent variables in the regression equation, which are interpreted as experimental conditions. Any normed discrete measure defined on the set of independent variable's values is called an experimental design (in practice one should apply rounding procedure to achieve the resulting number of repetitions for each experimental condition). The process of designing the experiment consists of finding the experimental design that minimizes some predefined convex functional which is called the optimality criterion. If there exist several competing hypotheses about the possible form of the regression model of interest, then one can perform a special kind of experiment that is called discrimination experiment, which is designed so that one could check the hypotheses optimally according to some predefined criterion. The most popular criteria for regression model discrimination from the literature are T-optimality criterion (introduced in [Atkinson, Fedorov (1975)]) and its numerous modifications. In some cases, we were able to find an analytical form for T-optimal discriminating designs and we were also able to construct the efficient numerical method that can find designs which are optimal according to some complex modifications of T-criterion.