Experimental design that is optimal with respect to some statistical criterion
This article is about optimal design of experiments. For optimal design in control theory, see shape optimization.
Gustav Elfving developed the optimal design of experiments, and so minimized surveyors' need for theodolite measurements (pictured), while trapped in his tent in storm-ridden Greenland.[1]
In the design of experiments, optimal experimental designs (or optimum designs[2]) are a class of experimental designs that are optimal with respect to some statistical criterion. The creation of this field of statistics has been credited to Danish statistician Kirstine Smith.[3][4]
In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum variance. A non-optimal design requires a greater number of experimental runs to estimate the parameters with the same precision as an optimal design. In practical terms, optimal experiments can reduce the costs of experimentation.
The optimality of a design depends on the statistical model and is assessed with respect to a statistical criterion, which is related to the variance-matrix of the estimator. Specifying an appropriate model and specifying a suitable criterion function both require understanding of statistical theory and practical knowledge with designing experiments.
^Nordström (1999, p. 176)
^The adjective "optimum" (and not "optimal") "is the slightly older form in English and avoids the construction 'optim(um) + al´—there is no 'optimalis' in Latin" (page x in Optimum Experimental Designs, with SAS, by Atkinson, Donev, and Tobias).
^Guttorp, P.; Lindgren, G. (2009). "Karl Pearson and the Scandinavian school of statistics". International Statistical Review. 77: 64. CiteSeerX 10.1.1.368.8328. doi:10.1111/j.1751-5823.2009.00069.x. S2CID 121294724.
^Smith, Kirstine (1918). "On the standard deviations of adjusted and interpolated values of an observed polynomial function and its constants and the guidance they give towards a proper choice of the distribution of observations". Biometrika. 12 (1/2): 1–85. doi:10.2307/2331929. JSTOR 2331929.
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