A0329
Title: The polytope of optimal approximate designs: Extending the selection of informative experiments
Authors: Radoslav Harman - Comenius University Bratislava (Slovakia) [presenting]
Lenka Filova - Comenius University in Bratislava (Slovakia)
Samuel Rosa - Comenius University in Bratislava (Slovakia)
Abstract: Consider the problem of constructing an experimental design that is optimal for a given statistical model with respect to a chosen criterion. To address this problem, the literature usually provides a single solution. Sometimes, however, there exists a rich set of optimal designs, and the knowledge of this set can lead to substantially greater freedom in selecting an appropriate experiment. It is demonstrated that the set of all optimal approximate designs generally corresponds to a polytope. Particularly important elements of the polytope are its vertices, which are called vertex optimal designs. It is proven that the vertex optimal designs possess unique properties, such as small supports, and outline strategies for how they can facilitate the construction of suitable experiments. Moreover, it is shown that for a variety of situations, it is possible to construct the vertex optimal designs with the assistance of a computer by employing error-free rational-arithmetic calculations. With this approach, the polytope of optimal designs is determined for several common multifactor regression models, thereby extending the theoretical knowledge and the choice of informative experiments for these models.
