Model-Oriented Design of Experiments

Fedorov, Valerii V.; Hackl, Peter

doi:10.1007/978-1-4612-0703-0

Cited by 336 publications

(227 citation statements)

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“…Si no hay lugar a confusión, en lo que sigue, se omite la dependencia de θ en f y en la matriz M . Para la construcción y verificación de que un diseño dado, ξ, es ϕ D -óptimo, en la literatura existe un teorema de equivalencia para el criterio D-Optimalidad [6]:…”

Section: Preliminares Y Definicionesunclassified

Metodología para incrementar el número de puntos experimentales en un diseño D-Óptimo

Galván

López-Ríos

2014

ing.cienc.

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ResumenLa finalidad de los diseños óptimos es determinar las condiciones experimentales adecuadas de tal forma que se pueda garantizar inferencias estadísticas lo más precisas posibles en términos de mínima varianza del vector de parámetros estimado. Esta teoría presupone el conocimiento de la función que relaciona las variables explicativas con la variable respuesta, en esta situación, con frecuencia, se obtienen diseños con tantos puntos de soporte como parámetros tiene el modelo propuesto en la investigación. Dado que los diseños con p−puntos de soporte asumen que la función del modelo es conocida, éstos pueden llegar a ser no tan óptimos en algunas situaciones prácticas, debido a que no permiten probar la bondad de ajuste del modelo asumido [1]. En este artículo se presenta una generalización de la metodología propuesta en [2] para aumentar el número de puntos en el criterio D-optimalidad. Se encuentra una expresión para la varianza de 1 M.Cs en Ciencias Estadística, syargumedog@unal.edu.co, Universidad Nacional de Colombia, Medellín, Colombia.

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Section: Preliminares Y Definicionesunclassified

Metodología para incrementar el número de puntos experimentales en un diseño D-Óptimo

Galván

López-Ríos

2014

ing.cienc.

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“…The design criteria are continuous functions of the Fisher information matrix F(θ 0 ), as for instance 1/ det F(θ 0 ) (D-optimal design) or λ max F −1 (θ 0 ) (E-optimal design) (compare [16,31,81]). In [7] the design criterion was introduced in order to define SE-optimal designs in the context of very general sampling strategies characterized by probability measures on the sampling interval.…”

Section: Model Validation and Parameter Estimationmentioning

confidence: 99%

Modeling the Dynamics of the Cardiovascular-respiratory System (CVRS) in Humans, a Survey

Kappel

2012

Math. Model. Nat. Phenom.

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“…As discussed in [6,11], there are situations where the design measures need to have (possibly, bounded) densities with respect to a fixed reference measure λ. In our framework this corresponds to an optimisation problem in the space M λ of measures absolutely continuous with respect λ or in the space…”

Section: Example 34 (D-optimal Designs With Bounded Densities)mentioning

confidence: 99%

“…This usually calls for major changes in proofs, since a new family of matrices has to be analysed at Step I of (1.3). Therefore, for each new type of constraint on µ both steps in (1.3) have to be reworked, for example, as in [6] and [11], where various types of constraint are analysed. Specific issues concerning optimal designs on general (not necessarily symmetric) experimental domains are considered in [19].…”

Section: Introductionmentioning

confidence: 99%

“…This allows us to treat the design problems described above as a special case of the optimisation of functionals formally defined on signed measures but the solution constrained on the cone of positive measures. This idea goes back to Fedorov and Hackl [11] who did not however explore the full scope of the related abstract constraint optimisation problems. We show that the abstract setting incorporates naturally many different optimal design problems and leads to new (apparently more efficient) steepest descent algorithms for numerical computation of optimal designs.…”

Section: Introductionmentioning

confidence: 99%

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Optimisation in space of measures and optimal design

Molchanov

Zuyev

2004

ESAIM: PS

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Abstract. 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 framework makes it possible to use the whole arsenal of descent algorithms from the general optimisation literature for finding optimal designs. The corresponding steepest descent involves adding a signed measure at every step and converges faster than the conventional sequential algorithms used to construct optimal designs. We study a new class of design problems when the observation points are distributed according to a Poisson point process arising in the situation when the total control on the placement of measurements is impossible.Mathematics Subject Classification. 62K05, 49K45, 60G55.

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Model-Oriented Design of Experiments

Cited by 336 publications

References 0 publications

Metodología para incrementar el número de puntos experimentales en un diseño D-Óptimo

Metodología para incrementar el número de puntos experimentales en un diseño D-Óptimo

Modeling the Dynamics of the Cardiovascular-respiratory System (CVRS) in Humans, a Survey

Optimisation in space of measures and optimal design

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