ii Model oriented design of experiments Preface These lecture notes are based on the theory of experimental design for courses given by Valerii Fedorov at a number of places, most recently at the University of Minnesota, the Vienna of University, and the University of Economics and Business Administration in Vienna.It was Peter Hackl's idea to publish these lecture notes and he took the lead in preparing and developing the text. The work continued longer than we expected, and we realized that a few thousand miles distance remains a serious hurdle even in the age of Internet and many electronic gadgets.While we mainly target graduate students in statistics, the book demands only a moderate background in calculus, matrix algebra and statistics. These are, to our knowledge, provided by almost any school in business and economics, natural sciences, or engineering. Therefore, we hope that the material may be easily understood by a relatively broad readership.The book does not try to teach recipes for the construction of experimental designs. It rather aims at creating some understanding -and interest -in the problems and basic ideas of the theory of experimental design. Over the years, quite a number of books have been published on that subject with a varying degree of specialization. This book is organized in four chapters that lay out in a rather compact form all ingredients of experimental designs: models, optimization criteria, algorithms, constrained optimization. The last third of the volume covers topics that are relatively new and rarely discussed in form of a book: designs for inference in nonlinear models, in models with random parameters, in stochastic processes, and in functional spaces; for model discrimination, and for incorrectly specified (contaminated) models.Data collected by performing an experiment are based on two elements: (i) a clearly defined objective and (ii) a piece of real world that generates -under control of the experimenter -the data. These elements have analogues in the statistical theory: (i) the optimality criterion to be applied has to be chosen so that it reflects appropriately the objective of the experimenter, and (ii) the model has to picturein adequate accuracy -the data generating process.When applying the theory of experimental design, it is perhaps more true than for many other areas of applied statistics that the complexity of the real world and the ongoing processes can hardly be adequately captured by the concepts and methods provided by the statistical theory. This theory contains a set of strong and iii iv beautiful results, but it permits in only rare cases closed-form solutions, and only in special situations is it possible to construct unique and clear-cut designs for an experiment. Planning an experiment means rather to work out several scenarios which together yield insights into and understanding of the data generating process, thereby strengthening the intuition of the experimenter. In that sense, a real life experiment is a compromise between results from statis...
