Optimal few-stage designs |
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| Institution: | 1. Dipartimento di Fisica e Chimica, Università di Palermo, Viale delle Scienze, Edificio 18, 90128 Palermo, Italy;2. Gruppo V Sezione INFN di Catania,Via Santa Sofia 64, 95123 Catania, Italy;3. Dipartimento Energia, Ingegneria dell׳Informazione e Modelli Matematici (DEIM), Università di Palermo, Viale delle Scienze, Ed. 6, 90128 Palermo, Italy;4. Laboratorio PH3DRA, Dipartimento di Fisica e Astronomia, Università di Catania Via Santa Sofia 64, 95123 Catania, Italy;5. Laboratorio di Fisica e Tecnologie Relative, UNINETLAB, Università di Palermo, Viale delle Scienze, Edificio 18, 90128 Palermo, Italy;6. Dipartimento di Biopatologia e Biotecnologie Mediche e Forensi – Sezione di Scienze Radiologiche, Università di Palermo, Via del Vespro 127, 90127 Palermo, Italy;7. Dipartimento di Ingegneria Civile e Industriale, Università di Pisa, Largo Lucio Lazzarino 2, 56126 Pisa, Italy;8. Magnetic Resonance Research Center, School of Medicine of Yale, 300 Cedar Street, PO Box 208043, New Haven, CT 06520-8043, United States;1. Department of Mathematics and CRSC, North Carolina State University, Raleigh, NC 27695, USA;2. Departments of Biomedical Engineering and Molecular Biology and Biochemistry, University of California, Irvine, CA 92697, USA;3. Department of Mathematics, University of California, Irvine, CA 92697, USA;4. Departments of Molecular Biology and Biochemistry, Chemical Engineering and Materials Science, and Biomedical Engineering, University of California, Irvine, CA 92697, USA;1. Department of Physics, K.N. Toosi University of Technology, P.O. Box 15875-4416, Tehran, Iran;2. ICT Radiotherapy Services, Livingston, NJ 07039, USA;1. Reactor Physics Department, NRC, Atomic Energy Authority, Cairo, Egypt;2. Physics Department, Faculty of Science, Zagazig University, Egypt |
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| Abstract: | Optimal designs are presented for experiments in which sampling is carried out in stages. There are two Bernoulli populations and it is assumed that the outcomes of the previous stage are available before the sampling design for the next stage is determined. At each stage, the design specifies the number of observations to be taken and the relative proportion to be sampled from each population. Of particular interest are 2- and 3-stage designs.To illustrate that the designs can be used for experiments of useful sample sizes, they are applied to estimation and optimization problems. Results indicate that, for problems of moderate size, published asymptotic analyses do not always represent the true behavior of the optimal stage sizes, and efficiency may be lost if the analytical results are used instead of the true optimal allocation.The exactly optimal few stage designs discussed here are generated computationally, and the examples presented indicate the ease with which this approach can be used to solve problems that present analytical difficulties. The algorithms described are flexible and provide for the accurate representation of important characteristics of the problem. |
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