Invited Discussion Paper Constrained Optimization of Experimental Design

Cook, Dennis; Федоров, В. В.

doi:10.1080/02331889508802474

Cited by 91 publications

(46 citation statements)

References 23 publications

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“…Such an approach has been followed for instance by Cook and Fedorov (1995), Mentré, Mallet and Baccar (1997), Tack and Vandebroek (2004) and Fedorov and Leonov (2005). However, this can be much more difficult to implement in the case that we consider than when the total number of observations is fixed.…”

Section: Discussionmentioning

confidence: 99%

“…However, if the cost of the observations in the design region differs substantially this can be taken into account so that the budget for the study is not overspent. Elfving (1952) defines the problem, which is later addressed by many researchers including Cook and Fedorov (1995), Tack and Vandebroek (2004) and Fedorov and Leonov (2005). In all these cases a prespecified number of observations are selected using some design criterion of optimality, or a utility function, that incorporates the information about the cost of the observations.…”

Section: Introductionmentioning

confidence: 99%

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Cost-cautious designs for confirmatory bioassay

Donev

Tobias

Monadjemi

2008

Journal of Statistical Planning and Inference

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Abstract.Confirmatory bioassay experiments take place in late stages of the drug discovery process when a small number of compounds have to be compared with respect to their properties. As the cost of the observations may differ considerably, the design problem is well specified by the cost of compound used rather than by the number of observations. We show that cost-efficient designs can be constructed using useful properties of the minimum support designs. These designs are particularly suited for studies where the parameters of the model to be estimated are known with high accuracy prior to the experiment, although they prove to be robust against typical inaccuracies of these values. When the parameters of the model can only be specified with ranges of values or by a probability distribution, we use a Bayesian criterion of optimality to construct the required designs. Typically, the number of their support points depends on the prior knowledge for the model parameters. In all cases we recommend identifying a set of designs with good statistical properties but different potential costs to choose from.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Cost-cautious designs for confirmatory bioassay

Donev

Tobias

Monadjemi

2008

Journal of Statistical Planning and Inference

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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%

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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“…Kiefer and Wolfowitz [15] [16] developed the well-known Equivalence Theorem (KWT theorem), which provides a practical way to check if a design is D-optimal. This theorem shows that for continuous designs, Dand G-optimal designs are equivalent under some standard assumptions [15] [16].…”

Section: D-optimalitymentioning

confidence: 99%

Experimental Design and Its Posterior Efficiency for the Calibration of Wearable Sensors

Ye¹,

Su²

2015

JILSA

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This paper investigates experimental design (DoE) for the calibration of the triaxial accelerometers embedded in a wearable micro Inertial Measurement Unit (μ-IMU). Firstly, a new linearization strategy is proposed for the accelerometer model associated with the so-called autocalibration scheme. Then, an effective Icosahedron design is developed, which can achieve both D-optimality and G-optimality for linearized accelerometer model in ideal experimental settings. However, due to various technical limitations, it is often infeasible for the users of wearable sensors to fully implement the proposed experimental scheme. To assess the efficiency of each individual experiment, an index is given in terms of desired experimental characteristic. The proposed experimental scheme has been applied for the autocalibration of a newly developed μ-IMU.

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Invited Discussion Paper Constrained Optimization of Experimental Design

Cited by 91 publications

References 23 publications

Cost-cautious designs for confirmatory bioassay

Cost-cautious designs for confirmatory bioassay

Optimisation in space of measures and optimal design

Experimental Design and Its Posterior Efficiency for the Calibration of Wearable Sensors

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