Computing the minimal efficiency of designs by a differentiable approximation of -optimality criteria.
Bušová, Lenka (2008)
Acta Mathematica Universitatis Comenianae. New Series
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Bušová, Lenka (2008)
Acta Mathematica Universitatis Comenianae. New Series
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Krzysztof Fujarewicz (2010)
International Journal of Applied Mathematics and Computer Science
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Mathematical modeling of cell signaling pathways has become a very important and challenging problem in recent years. The importance comes from possible applications of obtained models. It may help us to understand phenomena appearing in single cells and cell populations on a molecular level. Furthermore, it may help us with the discovery of new drug therapies. Mathematical models of cell signaling pathways take different forms. The most popular way of mathematical modeling is to use...
Emil Horváth (1988)
Kybernetika
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Andrej Pázman (2011)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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We discuss, partly on examples, several intuitively unexpected results in a standard linear regression model. We demonstrate that direct observations of the regression curve at a given point can not be substituted by observations at two very close neighboring points. On the opposite, we show that observations at two distant design points improve the variance of the estimator. In an experiment with correlated observations we show somewhat unexpected conditions under which a design point...
Ilya Molchanov, Sergei Zuyev (2010)
ESAIM: Probability and Statistics
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The paper develops an approach to optimal design problems based on application of abstract optimisation principles in the space of measures. Various design criteria and constraints, such as bounded density, fixed barycentre, fixed variance, etc. are treated in a unified manner providing a universal variant of the Kiefer-Wolfowitz theorem and giving a full spectrum of optimality criteria for particular cases. Incorporating the optimal design problems into conventional optimisation...
Marie Hušková, Jan Ámos Víšek, Dana Vorlíčková (1986)
Aplikace matematiky
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The paper deals with the experimental design which is optimal in the following sense: it satisfies the cost requirements simultaneously with a satisfactory precision of estimates. The underlying regression model is quadratic. The estimates of unknown parameters of the model are explicitly derived.
Krystyna Katulska, Łukasz Smaga (2016)
Kybernetika
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In this paper we consider D-optimal and highly D-efficient chemical balance weighing designs. The errors are assumed to be equally non-negatively correlated and to have equal variances. Some necessary and sufficient conditions under which a design is D*-optimal design (regular D-optimal design) are proved. It is also shown that in many cases D*-optimal design does not exist. In many of those cases the designs constructed by Masaro and Wong (2008) and some new designs are shown to be...