3/11/2023 0 Comments Rs optimal layout![]() It is known that the least squares estimator minimizes the variance of mean- unbiased estimators (under the conditions of the Gauss–Markov theorem). Minimizing the variance of estimators Įxperimental designs are evaluated using statistical criteria. Designs can be optimized when the design-space is constrained, for example, when the mathematical process-space contains factor-settings that are practically infeasible (e.g.Optimal designs can accommodate multiple types of factors, such as process, mixture, and discrete factors.Optimal designs reduce the costs of experimentation by allowing statistical models to be estimated with fewer experimental runs.Optimal designs offer three advantages over sub-optimal experimental designs: 11.2 Books for professional statisticians and researchers.11.1.2 Textbooks emphasizing block designs.11.1.1 Textbooks emphasizing regression and response-surface methodology.11.1 Textbooks for practitioners and students.6.2 Discretizing probability-measure designs.6.1 Using a computer to find a good design.6 Specifying the number of experimental runs.5.3 System identification and stochastic approximation.4.3 Model uncertainty and Bayesian approaches.4.2.1 Flexible optimality criteria and convex analysis.4.2 Choosing an optimality criterion and robustness.2 Minimizing the variance of estimators.Specifying an appropriate model and specifying a suitable criterion function both require understanding of statistical theory and practical knowledge with designing experiments. ![]() 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. In practical terms, optimal experiments can reduce the costs of experimentation. A non-optimal design requires a greater number of experimental runs to estimate the parameters with the same precision as an optimal design. In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum variance. The creation of this field of statistics has been credited to Danish statistician Kirstine Smith. In the design of experiments, optimal designs (or optimum designs ) are a class of experimental designs that are optimal with respect to some statistical criterion. 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. ![]()
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