Listy Biometryczne - Biometrical Letters Vol. 37(2000), No. 2, 67-95
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EQUIVALENCE THEORY FOR DESIGN AUGMENTATION AND PARSIMONIOUS MODEL CHECKING: RESPONSE SURFACES AND YIELD DENSITY MODELS A.C. Atkinson1, B. Bogacka2, S.S. Zocchi3 1Department of Statistics, The London School of Economics, London WC2A 2AE, UK, 2School of Mathematical Sciences, Queen Mary, University of London, London El 4NS, UK 3Departamento de Matematica e Estatistica, Escola Superior de Agricultura "Luiz de Queiroz", Universidade de Sao Paulo, Piracicaba, SP, Brazil |
We consider two applications of optimum design theory to three examples. In design augmentation, trials are added optimally to an existing non-optimal design. In model checking we design for departures from an assumed model, but in a way that involves few extra trials. For both problems we find D-optimum designs. Special cases of the equivalence theorem for D-optimality provide algorithms for design construction and insight into the structure of the designs. Simple examples of designs for second-order response surface models over regular and irregular regions are followed by an application of the optimum non-linear design to field experiments on plant density.
Bayesian design, D-optimality, irregular region, non-linear model, response surface
